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With the widespread application of digital images, image processing technology plays an important role in fields such as computer vision and image analysis. Based on the orthogonal matching pursuit algorithm, an image processing method is proposed. In the process, sparse representation and reconstruction algorithm are used for image compressed sensing to complete image sampling operation. Afterwards, the theory of overcomplete sparse representation is introduced to optimize sparse representation, and an overcomplete dictionary is used to remove Gaussian noise, achieving the goal of image processing. The experimental results indicate that the research method do not show significant deficiencies in signal reconstruction when testing reconstructed signals under sparsity of 8; When testing the calculation time, the calculation time of the research method is about 0.212 s when the sparsity is 5 in the Lenna; In the error test, the mean square difference of the research method in the Lenna is stable at about 14.6; When conducting application analysis, the variance eigenvalues of the research method remained below 9.4. This indicates that the research method has good performance and can effectively process images, providing new technical support for image processing. [ABSTRACT FROM AUTHOR]

In this article, two Hager–Zhang (HZ) type projection algorithms are presented for large-dimension nonlinear monotone problems and sparse signal recovery in compressed sensing. This goal is attained by conducting singular value analysis of a nonsingular HZ-type search direction matrix as well as applying the idea by Piazza and Politi [J Comput Appl Math. 2002;143(1):141–144] and minimizing the Frobenius norm of an orthornormal matrix. The paper attempts to fill the gap in the work of Hager and Zhang [Pac J Optim. 2006;2(1):35–58], Waziri et al. [Appl Math Comput. 2019;361:645–660], Sabi'u et al. [Appl Numer Math. 2020;153:217–233] and Babaie-Kafaki [4OR-Q J Oper Res. 2014;12:285-292], where the sufficient descent or global convergence condition is not satisfied when the HZ parameter is in the interval $ (0,\frac {1}{4}) $ (0 , 1 4). The proposed schemes are also suitable for solving non-smooth nonlinear problems. Also, by employing some mild conditions, global convergence of the schemes are established, while numerical comparison with four effective HZ-type methods show that the new methods are efficient. Furthermore, to illustrate their practical application, both methods are applied to solve the $ \ell _1 $ ℓ 1 -norm regularization problems to recover a sparse signal in compressive sensing. The experiments conducted in that regard show that the methods are promising and perform better than two other methods in the literature. [ABSTRACT FROM AUTHOR]

Traditional bridge health monitoring methods that necessitate sensor installation are not only costly but also time-consuming. In contrast, utilizing smartphone data collected from vehicles as they traverse bridges offers an efficient and cost-effective alternative. This paper introduces a cutting-edge damage detection framework for indirect monitoring of bridge structures, leveraging a substantial volume of acceleration data collected from smartphones in vehicles passing over the bridge. Our innovative approach addresses the challenge of collecting and transmitting high-frequency data while preserving smartphone battery life and data plans through the integration of compressed sensing (CS) into the crowdsensing-based monitoring framework. CS employs random sampling and signal recovery from a significantly reduced number of samples compared to the requirements of the Nyquist–Shannon sampling theorem. In the proposed framework, acceleration signals from vehicles are initially acquired using smartphone sensors, undergo compression, and are then transmitted for signal reconstruction. Subsequently, feature extraction and dimensionality reduction are performed using Mel-frequency cepstral coefficients and principal component analysis. Damage indexes are computed based on the dissimilarity between probability distribution functions utilizing the Wasserstein distance metric. The efficacy of the proposed methodology in bridge monitoring has been substantiated through the utilization of numerical models and a lab-scale bridge. Furthermore, the feasibility of implementing the framework in a real-world application has been investigated, leveraging the smartphone data from 102 vehicle trips on the Golden Gate Bridge. The results demonstrate that damage detection using the reconstructed signals obtained through compressed sensing achieves comparable performance to that obtained with the original data sampled at the Nyquist measurement sampling rate. However, it is observed that to retain severity information within the signals for accurate damage severity identification, the compression level should be limited to 20%. These findings affirm that compressed sensing significantly reduces the data collection requirements for crowdsensing-based monitoring applications, without compromising the accuracy of damage detection while preserving essential damage-sensitive information within the dataset. [ABSTRACT FROM AUTHOR]

Structural modal estimation has consistently remained one of the most crucial areas of research in mechanical vibration analysis and signal processing. It is imperative to accurately monitor the vibration signals of rotor blades and their corresponding structural modal parameters. Blade tip timing (BTT) is a promising approach used to measure vibration and monitor the health of blades. However, most existing BTT methods focus on frequency accuracy, neglecting damping, a key physical quantity that represents the strength of the structure. This research focuses on damping modal estimation of blade vibration and proposes a sparse reconstruction algorithm based on a two-dimensional Laplace wavelet family, which addresses the inherent under-sampled problem of BTT technology while enabling estimations of both the structural modal frequency and modal damping of the blades. Firstly, the proposed algorithm is achieved by designing a Laplace wavelet dictionary based on prior information and using a convex optimization objective function with a regularization term. Secondly, Laplace wavelet dictionary matches the signal better than the traditional Fourier dictionary based on the similarity between the damped vibration signal and the Laplace wavelet, then a sparser representation vector can be obtained. Moreover, the research object is not limited to a single blade, but can be easily expanded to multiple stages and multiple rotating blades monitored simultaneously. Finally, the simulation and physical test results indicate that the proposed method exhibits high reconstruction accuracy, reliability, and anti-noise abilities. [ABSTRACT FROM AUTHOR]

When traditional EEG signals are collected based on the Nyquist theorem, long-time recordings of EEG signals will produce a large amount of data. At the same time, limited bandwidth, end-to-end delay, and memory space will bring great pressure on the effective transmission of data. The birth of compressed sensing alleviates this transmission pressure. However, using an iterative compressed sensing reconstruction algorithm for EEG signal reconstruction faces complex calculation problems and slow data processing speed, limiting the application of compressed sensing in EEG signal rapid monitoring systems. As such, this paper presents a non-iterative and fast algorithm for reconstructing EEG signals using compressed sensing and deep learning techniques. This algorithm uses the improved residual network model, extracts the feature information of the EEG signal by one-dimensional dilated convolution, directly learns the nonlinear mapping relationship between the measured value and the original signal, and can quickly and accurately reconstruct the EEG signal. The method proposed in this paper has been verified by simulation on the open BCI contest dataset. Overall, it is proved that the proposed method has higher reconstruction accuracy and faster reconstruction speed than the traditional CS reconstruction algorithm and the existing deep learning reconstruction algorithm. In addition, it can realize the rapid reconstruction of EEG signals. [ABSTRACT FROM AUTHOR]

Differences between conventional sonar and Multiple-Input Multiple-Output (MIMO) sonar systems arise in achieving high angular and range resolution. MIMO sonar uses Matched Filtering (MF) with well-correlated transmitted signals to enhance spatial resolution by obtaining virtual arrays. However, imperfect correlation characteristics yield high sidelobe values, which hinder accurate target localization in underwater imagery. To address this, a Compressed Sensing (CS) method is proposed by reconstructing echo signals to suppress correlation noise between orthogonal waveforms. A shifted dictionary matrix and a deterministic Discrete Fourier Transform (DFT) measurement matrix are used to multiply received echo signals to yield compressed measurements. A sparse recovery algorithm is applied to optimize signal reconstruction before joint transmit–receive beamforming forms a 2D sonar image in the angle-range domain. Numerical simulations and lake experimental results confirm the effectiveness of the proposed method, by obtaining a lower sidelobe sonar image under sub-Nyquist sampling rates as compared with other approaches. [ABSTRACT FROM AUTHOR]

The improved Sparse Signal Reconstruction (SR) algorithm for Trusted Artificial Intelligence (AI) and Distributed Compressed Sensing (DCS) technology was thoroughly investigated. The study verified its effectiveness and advantages in trusted AI and DCS systems, which have significant implications for enhancing the credibility, security, and performance of signal processing and AI algorithms. The reconstruction performance was evaluated using Orthogonal Matching Pursuit (OMP), Basis Pursuit (BP), and Least Absolute Shrinkage and Selection Operator (LASSO). The analysis primarily focused on runtime, refactoring errors, and the number of successful reconstruction attempts. When K = 4, K = 6, K = 8, and K = 10, OMP outperformed BP and LASSO in terms of successful reconstructions, demonstrating better performance and higher reconstruction precision. [ABSTRACT FROM AUTHOR]

In this paper, a new Dai–Liao (DL)-type projection algorithm is presented for large-dimension nonlinear monotone problems with signal reconstruction and image recovery applications. The inspiration behind the work comes from two of the open problems propounded by Andrei (Bull Malays Math Sci Soc 34(2):319–330, 2011) involving the optimal value for the DL nonnegative parameter and the best conjugacy condition as well as the fine attributes expressed by four-term methods for unconstrained optimization. Based on the eigenvalue study of a symmetric DL-type iteration matrix, another optimal choice of the DL parameter is obtained, which is incorporated in a five-term direction scheme. Combining this with the projection method, a new DL algorithm which converges globally is developed. To implement the algorithm, a derivative-free line search mechanism is employed. Also, by conducting some numerical experiments with the new scheme and some recent DL-type methods, the efficiency of the former in solving nonlinear monotone problems as well as the ℓ 1 - n o r m regularized problems in compressed sensing is demonstrated. [ABSTRACT FROM AUTHOR]

As a sub-Nyquist sampling structure based on compressed sensing (CS), modulated wideband converter (MWC) was proposed to overcome the sampling rate limitation of analog-to-digital converters (ADCs) for wide spectral multiband signals. Different from ideal conditions when analyzing its theory, in practice, the MWC system is implemented with non-ideal devices. Due to this deviation between the ideal model and practical hardware, any imperfection of the analog device will lead to an imperfect signal reconstruction. Although the non-ideal factors can be compensated and calibrated, the conventional compensation and calibration methods easily introduce additional phase errors. This paper aims to evaluate the impact of those phase errors on signal reconstruction performance. We point out that phase errors deteriorate the normalized mean squared errors (NMSE) and even lead to incorrect support set recovery in serious cases. We thus propose a method using the SINC signal and DC signal to measure the MWC channel response which avoids the phase errors introduced in the compensation process. To verify this method, an MWC system and a measuring platform are implemented on hardware. The measurement results show that the recovery NMSE of − 13.09dB is achieved after being measured and compensated with an input SNR of 25.47dB. [ABSTRACT FROM AUTHOR]

Ultrasound plane-wave imaging has the advantage of high frame rate in addition to high data volume. High data sampling rates and large amounts of data storage can become bottlenecks in ultrasound system design. Although compressed sensing technology can help reduce the burden of sampling and transmission, it achieves relatively low image quality because of its reliance solely on signal sparsity. Therefore, we proposed reconstructing the ultrasound signal by applying additional prior knowledge, such as plane-wave imaging and its echo characteristics. Inspired by multi-hypothesis prediction methods in video compression coding, the plane-wave multi-hypothesis prediction compressed sensing reconstruction method was proposed to improve the accuracy of reconstructions. We applied multi-hypothesis prediction and residual reconstruction on the plane wave to enhance the quality of reconstruction and correct predicted values. Also, to acquire high-quality hypotheses, two hypothesis acquisition schemes were evaluated, constructing search windows on both preceding and subsequent frames as well as the reference frame. Compared with traditional reconstruction methods that rely on sparsity, multi-hypothesis prediction compressed sensing methods can reduce signal reconstruction errors and significantly eliminate image artifacts. Furthermore, by using improved hypotheses, signal reconstruction and image quality can be enhanced, resulting in higher contrast. Comparative simulation experimental results based on the publicly available Plane-Wave Imaging Challenge in Medical Ultrasound (PICMUS) and acoustic radiation force imaging data sets demonstrate that the proposed method outperforms other methods in both reconstruction errors and image quality. This helps to reduce the complexity of sampling and transmission of the ultrasound system. [ABSTRACT FROM AUTHOR]

Greedy pursuit algorithms are widely used in sparse signal processing for their computational efficiency. However, research on the reconstruction error properties is far from comprehensive. This paper derives the statistical properties of reconstruction error in greedy pursuit algorithms, including probability density function (PDF), expectation, and covariance. The reconstruction error follows a mixture distribution, which is composed of multiple multivariate random variables and weighted by the probability of support sets. The multivariate random variable obeys a truncated distribution that results from restricting the noise domain. The validity of the derivations is verified by using the orthogonal matching pursuit (OMP) algorithm as an example. [ABSTRACT FROM AUTHOR]

With the rapid development of multimedia technology, it is very important to improve the accuracy of sparse signal reconstruction for image or speech based on compressed sensing technology. In this work, a matching pursuit algorithm for sparse signal reconstruction based on Jaccard coefficient and backtracking strategy is proposed to improve the accurate reconstruction probability. Jaccard coefficient matching criterion and inner product matching criterion are combined to preserve more features of the original vector. A mean-based thresholding strategy is used to selects atoms adaptively, and the backtracking method is introduced to filter out the wrong atoms. Experimental results show that the reconstruction performance of the proposed algorithm is much better than other greedy algorithms when the sparsity K is large (K>35). For speech signals, the proposed algorithm has better reconstruction performance than other algorithms for both male and female voice signals. Under different compression ratios, the AFSNR and the PESQ scores of the reconstructed speech by the proposed algorithm are increased by at least 1.5348 dB and 0.5629, respectively, especially showing superior performance under larger compression ratio. The proposed algorithm has bright application prospect in intelligent speech interaction with accurate reconstruction of speech signal under large compression ratios. [ABSTRACT FROM AUTHOR]

We provide a theoretical study of the iterative hard thresholding with partially known support set (IHT-PKS) algorithm when used to solve the compressed sensing recovery problem. Recent work has shown that IHT-PKS performs better than the traditional IHT in reconstructing sparse or compressible signals. However, less work has been done on analyzing the performance guarantees of IHT-PKS. In this paper, we improve the current RIP-based bound of IHT-PKS algorithm from δ 3 s − 2 k < 1 32 ≈ 0.1768 to δ 3 s − 2 k < 5 − 1 4 , where δ3s−2k is the restricted isometric constant of the measurement matrix. We also present the conditions for stable reconstruction using the IHTμ-PKS algorithm which is a general form of IHT-PKS. We further apply the algorithm on Least Squares Support Vector Machines (LS-SVM), which is one of the most popular tools for regression and classification learning but confronts the loss of sparsity problem. After the sparse representation of LS-SVM is presented by compressed sensing, we exploit the support of bias term in the LS-SVM model with the IHTμ-PKS algorithm. Experimental results on classification problems show that IHTμ-PKS outperforms other approaches to computing the sparse LS-SVM classifier. [ABSTRACT FROM AUTHOR]

Non‐sidelooking airborne radar encounters significant non‐stationary and heterogeneous clutter environments, resulting in a severe shortage of samples. Sparse recovery‐based space‐time adaptive processing (SR‐STAP) methods can achieve good clutter suppression performance with limited samples. Nonetheless, grid‐based SR‐STAP algorithms encounter off‐grid effects in non‐sidelooking arrays, which can severely degrade the clutter suppression performance. In this study, the authors propose a novel gridless SR‐STAP method in the continuous spatial‐temporal domain to address the issue of off‐grid effects. Inspired by the fact that sparse Bayesian learning (SBL) framework implicitly performs a structured covariance matrix estimation, the authors reparameterise its cost function to directly estimate the block‐Toeplitz structured matrix from the measurements in a gridless manner. Since the proposed cost function is non‐convex, we utilise a majorisation‐minimisation‐based iterative procedure to estimate the clutter covariance matrix. Finally, using the standard concept of semidefinite programming, the authors derive a convex gridless implementation of the SBL cost function for uniformly sampled radar systems. Extensive simulation experiments demonstrate the exceptional clutter suppression and target detection performance of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Partial discharge (PD) signals have a large amount of data and a low energy proportion of pulse signals, resulting in difficult data transmission and poor reconstruction efficiency. To this end, a PD signal compression reconstruction method based on transfer sparse representation and dual residual ratio threshold (TSR‐DRRT) is proposed. TSR‐DRRT is centred on the sparse representation (SR) and accurate reconstruction of noisy signals. The intrinsic pulse of PD signals is extracted by signal decomposition, and jointly trained with different types of signals to establish the transfer SR dictionary. The compressed signal accurately retains the essential characteristics of the pulse information by improving the match between the dictionary atoms and the polymorphic PD pulses. To match the transfer SR dictionary, the inner and outer DRRT iteration termination conditions are set adaptively during the reconstruction process based on the correlation difference between the dictionary and signal frames. Independent control of PD pulse recognition and reconstruction accuracy is achieved, and its performance under noisy signals is improved. The results show that the method can achieve high ratio compression and efficient reconstruction of noisy signals. Different types of PD signals can also have high matching accuracy. This method can meet the demand for PD signals compression and transmission to the terminal for accurate reconstruction. [ABSTRACT FROM AUTHOR]

The "compressed sensing" theory is the foundation for the compressed sampling system's design. In addition to the sparse representation and observation matrix, more studies in compressed sensing theory focus on signal reconstruction and recovery. Only a small number of research studies estimate the original signal parameter information using the compressed sample data. In this research, we propose a linear frequency modulation (LFM) signal parameter estimation approach based on the Gabor transform for the enhanced Modulated Wideband Converter (MWC) system, which can directly estimate the parameters of an LFM signal utilizing compressed sampling data. Based on the MWC system prototype, a better MWC system based on Gabor transform is created by fusing the Gabor transform with compressed sensing theory, and the system's structure, function, parameter settings, and viability are all examined. Finally, we show through a simulation experiment that the proposed method is capable of accurately estimating the parameter information of a huge broadband LFM signal by merely restoring Gabor coefficients. [ABSTRACT FROM AUTHOR]

Objective. Although deep learning-based current methods have achieved impressive results in electrocardiograph (ECG) arrhythmia classification issues, they rely on using the original data to identify arrhythmia categories. However, a large amount of data generated by long-term ECG monitoring pose a significant challenge to the limited-bandwidth and real-time systems, which limits the application of deep learning in ECG monitoring. Approach. This paper, therefore, proposed a novel multi-task network that combined compressed sensing and convolutional neural networks, namely CSML-Net. According to the proposed model, the ECG signals were compressed by utilizing a learning measurement matrix and then recovered and classified simultaneously via shared layers and two task branches. Among them, the multi-scale feature module was designed to improve model performance. Main results. Experimental results on the MIT-BIH arrhythmia dataset demonstrate that our proposed method is superior to all the approaches that have been compared in terms of reconstruction quality and classification performance. Significance. Consequently, the proposed model achieving the reconstruction and classification in the compressed domain can be an improvement and become a promising approach for ECG arrhythmia reconstruction and classification. [ABSTRACT FROM AUTHOR]

We investigate the problems of reconstruction signals' distinct subcomponents, that are approximately sparse in terms of morphologically different dictionaries, from a few noisy linear measurements. We show that under common assumptions on a restricted isometric property adapted to the composed dictionary and a mutual coherence condition between the two different dictionaries, the two distinct subcomponents can be stably and approximately recovered via the unconstrained l 1 -split analysis, with an error bound that is in general unimprovable for the Gaussian noises. [ABSTRACT FROM AUTHOR]

The traditional greedy algorithm requires the signal sparsity as a known condition, and in most application scenarios, the signal sparsity is unknown, resulting in poor signal reconstruction accuracy. In order to solve such problems, this paper proposes an adaptive dual threshold matching pursuit algorithm based on a variable-step backtracking strategy (SBATMP). Firstly, the suboptimal set of atoms is selected through two adaptive thresholds. Then, through the variable-step backtracking strategy, the atoms are selected twice to obtain the optimal atomic set. The algorithm can improve the complete reconstruction rate of the signal under the condition of unknown sparsity, and the variable-step backtracking strategy can effectively reduce the complexity of the algorithm. Through the reconstruction simulation experiment, the one-dimensional signal reconstruction accuracy can reach 100 % under the condition that the ratio of the sparsity to the measured value is less than 0.25. The reconstruction speed can be improved by 0.021 - 0.186 s. For the two-dimensional image signal, the PSNR of the reconstructed image by the SBATMP algorithm is increased by 1.193–5.781dB, and the SSIM is increased by 0.0116 - 0.0645 under the compression ratio of 0.7. [ABSTRACT FROM AUTHOR]

Underdetermined blind source separation has received increasing attention in recent years as an effective method for speech-signal processing. Hence, a self-organizing mapping-density peak clustering and compressed sensing approach, which is a two-step approach, is proposed herein to improve the accuracy of underdetermined blind source separation. The approach features the following two aspects: (1) A mixing matrix estimation method based on self-organizing mapping and density peak clustering, which can intuitively determine the number of source signals, remove outliers, and determine the column vector of the mixing matrix based on local density; (2) a compressed sensing-based source signal reconstruction method, which can exploit the sparsity of signals in the frequency domain and use a hierarchical coupling method to reconstruct the source signal accurately and efficiently under the premise that the prior knowledge of the signal is unknown. The proposed method does not require the number of source signals and exhibits excellent performance under different noise conditions. Theoretical analysis and experimental results demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Chronic obstructive pulmonary disease (COPD) concerns the serious decline of human lung functions. These have emerged as one of the most concerning health conditions over the last two decades, after cancer around the world. The early diagnosis of COPD, particularly of lung function degradation, together with monitoring the condition by physicians, and predicting the likelihood of exacerbation events in individual patients, remains an important challenge to overcome. The requirements for achieving scalable deployments of data-driven methods using artificial intelligence for meeting such a challenge in modern COPD healthcare have become of paramount and critical importance. In this study, we have established the experimental foundations for acquiring and indeed generating biomedical observation data, for good performance signal analysis and machine learning that will lead us to the intelligent diagnosis and monitoring of COPD conditions for individual patients. Further, we investigated on the multi-resolution analysis and compression of lung audio signals, while we performed their machine classification under two distinct experiments. These respectively refer to conditions involving (1) "Healthy" or "COPD" and (2) "Healthy", "COPD", or "Pneumonia" classes. Signal reconstruction with the extracted features for machine learning and testing was also performed for securing the integrity of the original audio recordings. These showed high levels of accuracy together with the performances of the selected machine learning-based classifiers using diverse metrics. Our study shows promising levels of accuracy in classifying Healthy and COPD and also Healthy, COPD, and Pneumonia conditions. Further work in this study will be imminently extended to new experiments using multi-modal sensing hardware and data fusion techniques for the development of the next generation diagnosis systems for COPD healthcare of the future. [ABSTRACT FROM AUTHOR]

Taking on the problems of unstable reconstruction performance and high reconstruction method computational cost induced by the unpredictability of the measurement matrix during power quality signal reconstruction, this research provides a power quality reconstruction model based on a self-encoding network and compressed sensing for the first time. The model includes a noise-adding module, an encoder module and a decoder module. The noise-adding module adds a specific amount of white noise in relation to the original signal to simulate the disturbance signal collected in the real scene. The encoder module uses a nonlinear measurement method to observe the power quality signal, and the decoder module completes the signal through a compressed sampling matching tracking algorithm. Refactoring. The outcomes of the experiment reveal that the compressed reconstruction model proposed in this paper significantly improves the efficiency and stability of power quality signal reconstruction. [ABSTRACT FROM AUTHOR]

Orthogonal/vector approximate message-passing (AMP) is a powerful message-passing (MP) algorithm for signal reconstruction in compressed sensing. This paper proves the convergence of Bayes-optimal orthogonal/vector AMP in the large system limit. The proof strategy is based on a novel long-memory (LM) MP approach: A first step is a construction of LM-MP that is guaranteed to converge systematically. A second step is a large-system analysis of LM-MP via an existing framework of state evolution. A third step is to prove the convergence of state evolution recursions for Bayes-optimal LM-MP via a new statistical interpretation of existing LM damping. The last is an exact reduction of the state evolution recursions for Bayes-optimal LM-MP to those for Bayes-optimal orthogonal/vector AMP. The convergence of the state evolution recursions for Bayes-optimal LM-MP implies that for Bayes-optimal orthogonal/vector AMP. Numerical simulations are presented to show the verification of state evolution results for damped orthogonal/vector AMP and a negative aspect of LM-MP in finite-sized systems. [ABSTRACT FROM AUTHOR]

Conventional sparse phase retrieval schemes can recover sparse signals from the magnitude of linear measurements only up to a global phase ambiguity. This work proposes a novel approach that instead utilizes the magnitude of affine measurements to achieve ambiguity-free signal reconstruction. The proposed method relies on two-stage approach that consists of support identification followed by the exact recovery of nonzero signal entries. In the noise-free case, perfect support identification using a simple counting rule is guaranteed subject to a mild condition on the signal sparsity, and subsequent exact recovery of the nonzero signal entries can be obtained in closed-form. The proposed approach is then extended to two noisy scenarios, namely, sparse noise (or outliers) and non-sparse bounded noise. For both cases, perfect support identification is still ensured under mild conditions on the noise model, namely, the support size for sparse outliers and the power of the bounded noise. Under perfect support identification, exact signal recovery can be achieved using a simple majority rule for the sparse noise scenario, and reconstruction up to a bounded error can be achieved using linear least-squares (LS) estimation for the non-sparse bounded noise scenario. The obtained analytic performance guarantee for the latter case also sheds light on the construction of the sensing matrix and bias vector. In fact, we show that a near optimal performance can be achieved with high probability by the random generation of the nonzero entries of the sparse sensing matrix and bias vector according to the uniform distribution over a circle. Computer simulations using both synthetic and real-world data sets are provided to demonstrate the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

Based on compressed sensing technology, a DOA estimation algorithm for reconstructing the original signal is proposed. First, the over‐complete dictionary of signal vectors is established based on the sparsity of signals in spatial domain. The DOA estimation problem is transformed into sparse signals reconstruction problem, and signals in spatial domain are reconstructed using iterative soft thresholding (IST) algorithm. At the same time, combined with the second‐order statistical characteristic of non‐circular signal, the array is virtual extended, and the spectrum estimation is performed by MUSIC algorithm. In addition, in order to further distinguish coherent signals, spatial smoothing technology is added to the algorithm. The simulation results show that the proposed algorithm can effectively resolve incoherent signals and coherent signals under small snapshots and low SNR. [ABSTRACT FROM AUTHOR]

A random matrix needs large storage space and is difficult to be implemented in hardware, and a deterministic matrix has large reconstruction error. Aiming at these shortcomings, the objective of this paper is to find an effective method to balance these performances. Combining the advantages of the incidence matrix of combinatorial designs and a random matrix, this paper constructs a structured random matrix by the embedding operation of two seed matrices in which one is the incidence matrix of combinatorial designs, and the other is obtained by Gram–Schmidt orthonormalization of the random matrix. Meanwhile, we provide a new model that applies the structured random matrices to semi-tensor product compressed sensing. Finally, compared with the reconstruction effect of several famous matrices, our matrices are more suitable for the reconstruction of one-dimensional signals and two-dimensional images by experimental methods. [ABSTRACT FROM AUTHOR]

Objective. Overcomplete dictionaries are widely used in compressed sensing (CS) to improve the quality of signal reconstruction. However, dictionary learning under the â„" 0 -norm or â„" 1 -norm constraint inevitably produces dictionary atoms that are negatively correlated with the original signal; meanwhile, when we use a sparse linear combination of dictionary atoms to represent a signal, it is suboptimal for the dictionary atoms to “cancel each other out” by addition and subtraction to approximate the sample. In this paper, we propose a non-negative constrained dictionary learning (NCDL) algorithm to improve the reconstruction performance of CS with electrocardiogram (ECG) signals. Approach. Non-NCDL was divided into an encoding stage and a dictionary learning stage. In the encoding stage, non-negative constraints were imposed on the encoding coefficients and obtained the sparse solution using the alternating direction method of multipliers. At the same time, a penalty term was integrated into the objective function in order to remove small coding coefficients and achieve the effect of sparse coding. In the dictionary learning stage, the block coordinate descent algorithm was utilized to update the dictionary with a view to obtaining an overcomplete dictionary. Results. The performance of the proposed NCDL algorithm was evaluated using the standard MIT-BIH database. Quantitative performance metrics, such as percent root mean square difference (PRD1) and root mean square error, were compared with existing CS approaches to quantify the efficacy of the proposed scheme. For a PRD1 value of 9%, the compression ratio (CR) of the NCDL approach was around 2.78. When CR ranged from 1.05 to 2.78, the proposed NCDL approach outperformed the method of optimal direction, k-means singular value decomposition, and online dictionary learning approaches in ECG signal reconstruction based on CS. Significance. This promising preliminary result demonstrates the capability and feasibility of the proposed bioimpedance method and may open up a new direction for this application. The non-NCDL method proposed in this paper can be used to obtain a sparse basis and improve the performance of CS reconstruction. [ABSTRACT FROM AUTHOR]

The present work proposes to locate harmonic frequencies that distort the fundamental voltage and current waves in electrical systems using the compressed sensing (CS) technique. With the compressed sensing algorithm, data compression is revolutionized, a few samples are taken randomly, a measurement matrix is formed, and according to a linear transformation, the signal is taken from the time domain to the frequency domain in a compressed form. Then, the inverse linear transformation is used to reconstruct the signal with a few sensed samples of an electrical signal. Therefore, to demonstrate the benefits of CS in the detection of harmonics in the electrical network of this work, power quality analyzer equipment (commercial) is used. It measures the current of a nonlinear load and issues its results of harmonic current distortion (THD-I) on its screen and the number of harmonics detected in the network; this equipment acquires the data based on the Shannon–Nyquist theorem taken as a standard of measurement. At the same time, an electronic prototype senses the current signal of the nonlinear load. The prototype takes data from the current signal of the nonlinear load randomly and incoherently, so it takes fewer samples than the power quality analyzer equipment used as a measurement standard. The data taken by the prototype are entered into the Matlab software via USB, and the CS algorithm run and delivers, as a result, the harmonic distortions of the current signal THD-I and the number of harmonics. The results obtained with the compressed sensing algorithm versus the standard measurement equipment are analyzed, the error is calculated, and the number of samples taken by the standard equipment and the prototype, the machine time, and the maximum sampling frequency are analyzed. [ABSTRACT FROM AUTHOR]

In this paper, we present two variations of an algorithm for signal reconstruction from one-bit or two-bit noisy observations of the discrete Fourier transform (DFT). The one-bit observations of the DFT correspond to the sign of its real part, whereas, the two-bit observations of the DFT correspond to the signs of both its real and imaginary parts. We focus on images for analysis and simulations, thus using the sign of the 2D-DFT. This choice of the class of signals is inspired by previous works on this problem. For our algorithm, we show that the expected mean squared error (MSE) in signal reconstruction is asymptotically proportional to the inverse of the sampling rate. The samples are affected by additive zero-mean noise of a known distribution. We solve this signal estimation problem by designing an algorithm that uses contraction mapping, based on the Banach fixed point theorem. Numerical tests with four benchmark images are provided to show the effectiveness of our algorithm. Various metrics for image reconstruction quality assessment such as PSNR, SSIM, ESSIM, and MS-SSIM are employed. On all four benchmark images, our algorithm outperforms the state-of-the-art in all of these metrics by a significant margin. [ABSTRACT FROM AUTHOR]

Summary: The designed algorithms for wireless sensor networks (WSNs) should not impose a high computational load on sensor nodes because they are battery‐powered devices. To distribute the computations between sensors, distributed algorithms are required. On the other hand, since the sensors observe related phenomena, the acquired signals, besides the intra‐signal correlation, also have some inter‐signal correlation. When the designed algorithms are cooperative, these joint structures are used. In this study, we propose a distributed and cooperative algorithm based on the focal underdetermined system solver (FOCUSS) for compressive sensing signal reconstruction in WSNs. Unlike the other FOCUSS‐based sparse recovery algorithms, the proposed algorithm is quite distributed and implemented by one‐hop communication between the neighboring node without collaborating any fusion center (FC). In the suggested system model, the reconstructed signals from the underdetermined systems of equations are different for each sensor node. The obtained results verified that the proposed approach performs better than the existing works regarding signal reconstruction and convergence rate. [ABSTRACT FROM AUTHOR]

Fast iterative soft threshold algorithm (FISTA) is one of the algorithms for the reconstruction part of compressed sensing (CS). However, FISTA cannot meet the increasing demands for accuracy and efficiency in the signal reconstruction. Thus, an improved algorithm (FIPITA, fast iterative parametric improved threshold algorithm) based on mended threshold function, restart adjustment mechanism and parameter adjustment is proposed. The three parameters used to generate the gradient in the FISTA are carefully selected by assessing the impact of them on the performance of the algorithm. The developed threshold function is used to replace the soft threshold function to reduce the reconstruction error and a restart mechanism is added at the end of each iteration to speed up the algorithm. The simulation experiment is carried out on one-dimensional signal and the FISTA, RadaFISTA and RestartFISTA are used as the comparison objects, with the result that in one case, for example, the residual rate of FIPITA is about 6.35% lower than those three and the number of iterations required to achieve the minimum error is also about 102 less than that of FISTA. [ABSTRACT FROM AUTHOR]

Many real-world phenomena in engineering, economics, statistical inference, compressed sensing and machine learning involve finding sparse solutions to under-determined or ill-conditioned equations. Our interest in this paper is to introduce a derivative-free method for recovering sparse signal and blurred image arising in compressed sensing by solving a nonlinear equation involving a monotone operator. The global convergence of the proposed method is established under the assumptions of monotonicity and Lipschitz continuity of the underlying operator. Numerical experiments are performed to illustrate the efficiency of the proposed method in the reconstruction of sparse signals and blurred images. [ABSTRACT FROM AUTHOR]

Aiming at the problems of low data reconstruction accuracy in wireless sensor networks and users unable to receive accurate original signals, improvements are made on the basis of the stagewise orthogonal matching pursuit algorithm, combined with sparseness adaptation and the pre-selection strategy, which proposes a sparsity adaptive pre-selected stagewise orthogonal matching pursuit algorithm. In the framework of the stagewise orthogonal matching pursuit algorithm, the algorithm in this article uses a combination of a fixed-value strategy and a threshold strategy to screen the candidate atom sets in two rounds to improve the accuracy of atom selection, and then according to the sparsity adaptive principle, the sparse approximation and accurate signal reconstruction are realized by the variable step size method. The simulation results show that the algorithm proposed in this article is compared with the orthogonal matching pursuit algorithm, regularized orthogonal matching pursuit algorithm, and stagewise orthogonal matching pursuit algorithm. When the sparsity is 35 < K < 45, regardless of the size of the perception matrix and the length of the signal, M = 128, N = 256 or M = 128, N = 512 are improved, and the reconstruction time is when the sparsity is 10, the fastest time between 25 and 25, that is, less than 4.5 s. It can be seen that the sparsity adaptive pre-selected stagewise orthogonal matching pursuit algorithm has better adaptive characteristics to the sparsity of the signal, which is beneficial for users to receive more accurate original signals. [ABSTRACT FROM AUTHOR]

Wireless communication in vehicular networks is highly vulnerable to electromagnetic interference, which seriously undermines the communication effectiveness. Thus, interference estimation and elimination are essential in vehicular communications. To solve the multitasking problem of interference estimation and cancelation within the transformation domain of vehicular communications where they are divided into the consistency and inconsistency based on the different conditions of spectrum sensing, the present study proposes an iterative Bayesian sparse learning approach for simultaneous interference recovery and elimination which applies multiple Bayesian learning for measured signals, and the structured sparse learning method for simultaneous interference mitigation with signal recovery. Furthermore, the updating optimization based on Bayesian estimation framework is performed to facilitate the learning process and improve the performance of interference estimation and signal reconstruction. Simulation results show that the proposed algorithms achieved more rapid convergence and more accurate recovery (31.84% and 27.88% higher in spectrum sensing with consistency and inconsistency, respectively) than conventional algorithms. During all iterations, the proposed algorithms, because of updating optimization, were more robust than conventional ones, but the computational complexity remained largely the same. To explore the correlation between the parameters and the interference recovery performance, we performed experiments, which revealed linear, logarithmic, and exponential regression correlations for particular forms of interference. We also compared the demodulation performance of the proposed algorithm with existing methods, and it turned out the proposed algorithm also obtained higher gains on average in the bit error rate. [ABSTRACT FROM AUTHOR]

Compared with traditional onsite wind turbine condition monitoring systems (CMSs), the remote CMSs can use better computational resources to process data with more advanced algorithms and, thus, can provide more advanced condition monitoring capabilities, but may suffer from a data loss problem, especially when wireless data transmission is used. To solve this problem, this article proposes a compressive sensing-based missing-data-tolerant fault detection method for remote condition monitoring of wind turbines. First, the condition monitoring signals collected from wind turbines are conditioned to increase their sparsity. Then, a compressive-sensing-based sampling algorithm is designed to sample the conditioned signals. The resulting data samples, called measurements of the conditioned signals are transmitted wirelessly during which some data samples are possibly lost. At the data receiving end, the conditioned signals are reconstructed from the received data samples, which might be incomplete, via a compressive-sensing-based signal reconstruction algorithm. Finally, spectrum analysis is performed on the reconstructed signals for wind turbine fault detection via fault characteristic frequency identification. The proposed method is validated for bearing fault detection of a Skystream 3.7 wind turbine and an Air Breeze wind turbine by using the data of a generator current signal collected from each wind turbine remotely while considering different data loss rates. [ABSTRACT FROM AUTHOR]

Nonlinear complementarity problems (NCP) have been extensively studied in optimization due to its widespread applications. In this paper, we utilize the neural dynamic approach to solve the NCP. By integrating the famous FB function an NR function, we construct a new type of complementarity functions with one parameter p , which is aesthetically pleasing and easy to apply. Combined with the Lagrange multiplier method, a new type of merit function is also developed. Based on the complementarity function and merit function, we transform the NCP into an unconstrained minimization problem. Then, by KKT condition and gradient descent method, we propose a Lagrange neural network method. Under mild conditions, every equilibrium point of the proposed neural network model is a solution of the NCP. More importantly, by throwing a delay factor, we also develop a novel delayed neural network model. Both of these networks are shown to be global convergent, Lyapunov stable and exponential stable. Finally, we give some numerical experiments of the two neural network approaches and also give some applications to the compressed sensing signal reconstruction. Simulation results indicate that the parameter p in the complementarity function plays an important role on the convergence rate of the two neural networks. The delayed neural network outperforms the non-delayed neural network in some specific situations. It also demonstrates that the two networks can efficiently reconstruct the original signals. • A new type of complementary functions is constructed. • A new neural network method is proposed. • We propose a delayed neural network and give its complete convergence analysis. • The two neural networks are applied to solve the CS efficiently. [ABSTRACT FROM AUTHOR]

X-ray Absorption Fine Structure (XAFS) spectroscopy is an analytical technique of chemical insight. Improvements to this technique are continuously carried out for reduction of the acquisition time and increasing the resolution, especially for studying operando processes. The accurate reconstruction of XAFS signals requires that the collected data are noise-free to extract elemental structure information in post-processing. A novel approach to rapid sampling (encoded measurement) is validated conceptually. The technique relies on sparse signal recovery, i.e. using compressed sensing to reconstruct under-sampled signals. The proof of concept is demonstrated by using a python code to reconstruct under-sampled XAFS spectra. A case study of transition metal samples and their oxides is considered for this purpose. The results demonstrate a robust recovery of chemical information from a 30% sampled signal for the near-edge region analysis and from a 45% sampled signal for extended-edge region analysis. The application of this procedure is important for demonstrating the feasibility of tabletop operation using laboratory X-ray sources which are not continuously tunable. [Display omitted] • Compressed sensing permits XAFS signal reconstruction from factor of 3 less data; • Data are encoded upon collection, which opens way to cryptoanalytics. • Data are decoded with the suitable conversion matrix, and the code has been optimized. • Smarter data procedures permits light data loads and faster operation also on tabletop setups. [ABSTRACT FROM AUTHOR]

Practical sensing systems have a limited dynamic range, which gives rise to saturation noise in signal acquisition if the signal attains values outside this range at certain locations. Despite rapid advances in compressed sensing theory and systems over the years, the effect of saturation on compressed sensing measurements, especially in the presence of additive Gaussian noise, has often been overlooked in many existing approaches. Some methods for compressive recovery under saturation noise simply discard saturated measurements, while others impose some ad hoc hard constraints to ensure consistency with the known saturation threshold. In this paper, we propose a novel maximum likelihood based estimator for compressive reconstruction in the presence of both Gaussian and saturation noise. Our proposed method ensures probabilistic consistency between the estimated signal and the saturated measurements and helps account for both the saturation effect and the potentially unbounded Gaussian noise in the measurements. We also derive upper bounds on the reconstruction error for our estimator, and argue that they follow intuitive trends. We analyze an important curvature term in these bounds, and show that it is superior to methods such as saturation rejection, indicating better stability and robustness. Furthermore, we present extensive simulation results to demonstrate the effectiveness of our method over several other existing methods in reconstructing synthetic signals and images from compressive measurements with saturation and Gaussian noise. We also show simulation results in audio signal de-clipping. • We present a novel likelihood based estimator for compressive reconstruction from measurements that are saturated and are also corrupted with Gaussian noise. • We prove important properties of this estimator and derive performance bounds for the associated reconstruction error, which we show are provably superior to those associated with an estimator which would just discard saturated measurements. • We present numerical results for reconstruction of synthetic signals and images from compressive measurements using our estimator, and demonstrate superior numerical performance in comparison to several existing estimators. We also demonstrate an application of our estimator in audio de-clipping. [ABSTRACT FROM AUTHOR]

This paper introduces a novel framework and corresponding methods for sampling and reconstruction of sparse signals in shift-invariant (SI) spaces. We reinterpret the random demodulator, a system that acquires sparse bandlimited signals, as a system for the acquisition of linear combinations of the samples in the SI setting with the box function as the sampling kernel. The sparsity assumption is exploited by the compressive sensing (CS) paradigm for a recovery of the SI samples from a reduced set of measurements. The SI samples are subsequently filtered by a discrete-time correction filter to reconstruct expansion coefficients of the observed signal. Furthermore, we offer a generalization of the proposed framework to other compactly supported sampling kernels that span a wider class of SI spaces. The generalized method embeds the correction filter in the CS optimization problem which directly reconstructs expansion coefficients of the signal. Both approaches recast an inherently continuous-domain inverse problem in a set of finite-dimensional CS problems in an exact way. Finally, we conduct numerical experiments on signals in polynomial B-spline spaces whose expansion coefficients are assumed to be sparse in a certain transform domain. The coefficients can be regarded as parametric models of an underlying continuous-time signal, obtained from a reduced set of measurements. Such continuous signal representations are particularly suitable for signal processing without converting them into samples. [ABSTRACT FROM AUTHOR]

In this article, the signal detection problem in indoor visible light communication (VLC) system aided by generalized space shift keying (GSSK) is modeled as a sparse signal reconstruction problem, which has lower computational complexity by exploiting the sparse reconstruction algorithms in compressed sensing (CS). In order to satisfy the measurement matrix property to perform sparse signal reconstruction, a preprocessing approach of measurement matrix is proposed based on singular value decomposition (SVD), which theoretically guarantees the feasibility of utilizing CS based sparse signal detection method in indoor GSSK-VLC system. Then, by adopting classical orthogonal matching pursuit (OMP) algorithm and compressed sampling matching pursuit (CoSaMP) algorithm, the GSSK signals are efficiently detected in the considered indoor GSSK-VLC system. Furthermore, a more efficient detection algorithm combined with OMP and maximum likelihood (ML) is also presented especially for SSK scenario. Finally, the effectiveness of the proposed sparsity aided detection algorithms in indoor GSSK-VLC system are verified by computer simulations. The results show that the proposed algorithms can achieve better bit error rate (BER) and lower computation complexity than ML based detection method. Specifically, a signal-to-noise ratio (SNR) gain as high as 12 dB is observed in the SSK scenario and about 5 dB in case of a GSSK scenario upon employing our proposed detection methods. [ABSTRACT FROM AUTHOR]

Sound field reconstruction technology is used to provide accurate primary reference signals for active noise control systems by reconstructing the interior sound field. Traditionally, time-domain noise signal-based reconstruction modeling has certain deficiencies, such as large data volume, noise reconstruction model complexity and considerable time consumption. Hence, a novel Signal compression optimisation-based BP network for passenger head position signal reconstruction (CBHSR) algorithm is proposed. Based on compressed sensing, the proposed algorithm converts raw multi-source signals into the compressed domain to implement compressed sampling. The signal reconstruction model is created by regarding the optimal fitness value as the initial weight and the threshold of the signal reconstruction BP network, and training with the compressed multi-source data. The recovery compression signal method realizes the time-domain signal reconstruction of the passenger head position. The effectiveness of the proposed CBHSR algorithm is validated using noise signal sources collected from a vehicle. Compared with the reconstruction model of the BP algorithm, the proposed algorithm is superior in reconstruction accuracy and time consumption. [ABSTRACT FROM AUTHOR]

Under the framework of compressed sensing theory, the greedy algorithm achieves good reconstruction performance with known signal sparsity. However, unknown sparsity of sparse signals in practical applications brings obstacles for signal reconstruction. Specifically, the conventional sparsity adaptive adjustment algorithm takes long time to finish the reconstruction, and the accuracy of reconstruction is not good enough. To solve this problem, this paper proposes a new matching pursuit reconstruction algorithm based on bidirectional sparsity adaptive adjustment and weak selection of atoms (BSA-WSAMP). In this algorithm, the optimization strategy for atom weak selection is employed to update the support set, and the idea of "zoom" bidirectional variable step-size is applied to achieve the sparsity adaptive adjustment. Based on this, the number of iterations can be reduced effectively, and the accurate reconstruction of the sparse signal is obtained. Simulation results indicate that the proposed BSA-WSAMP algorithm achieves better adaptive characteristic of the sparsity, higher reconstruction quality, lower reconstruction complexity, and less reconstruction time than some existing reconstruction algorithms. [ABSTRACT FROM AUTHOR]

Compressed sensing is widely used to compress electrocardiogram (ECG) signals, but the major challenges of the compressed sensing algorithms are their highly complex signal reconstruction processes. In this paper, a reconfigurable high-speed and low-power field-programmable gate array (FPGA) implementation of the least support denoising-orthogonal matching pursuit (LSD-OMP) algorithm for the real-time reconstruction of the ECG signals is presented. The contribution of this study is two-fold: Firstly, LSD-OMP can pick more than one element at each iteration and reconstruct the sparse signal using less number of iterations as compared to the standard OMP algorithms. Latency of the proposed design is therefore reduced by exploiting the multiple index selection feature of LSD-OMP. Secondly, the proposed architecture is the first reconfigurable LSD-OMP reconstruction architecture which can take different signal sizes and different sparsity levels. The proposed design also includes an efficient inverse wavelet transform (IWT) module to convert the reconstructed signal back into the time-domain. Together with the overhead of the IWT module, the proposed design demonstrates faster execution times while consuming lower power than the existing FPGA implementations; therefore, it can be utilized in wireless body area networks as a back-end unit to reconstruct the compressed ECG signals. [ABSTRACT FROM AUTHOR]

In multiple-input multiple-output–orthogonal frequency-division multiplexing underwater acoustic communication systems, the correlation of the sampling matrix is the key of the channel estimation algorithm based on compressed sensing. To reduce the cross-correlation of the sampling matrix and improve the channel estimation performance, a pilot design algorithm for co-sparse channel estimation based on compressed sensing is proposed in this article. Based on the time-domain correlation of the channel, the channel estimation is modeled as a common sparse signal reconstruction problem. When replacing each pilot indices position, the algorithm selects multiple pilot indices with the least cross-correlation from the alternative positions to replace the current pilot indices position, and it uses the inner and outer two-layer loops to realize the bit-by-bit optimal replacement of the pilot. The simulation results show that the channel estimation mean squared error of pilot design algorithm for co-sparse channel estimation based on compressed sensing can be reduced by approximately 18 dB compared with the least square algorithm. Compared with the genetic algorithm and search space size methods, the structural sequence search proposed by pilot design algorithm for co-sparse channel estimation based on compressed sensing is used to design the pilot to complete the channel estimation. Thus, the mean squared error of the channel estimation can be reduced by 2 dB. At the same bit error rate of 0.03, the signal-to-noise ratio can be decreased by approximately 7 dB. [ABSTRACT FROM AUTHOR]

We investigate the statistical and algorithmic properties of random neural-network generative priors in a simple inference problem: spiked-matrix estimation. We establish a rigorous expression for the performance of the Bayes-optimal estimator in the high-dimensional regime, and identify the statistical threshold for weak-recovery of the spike. Next, we derive a message-passing algorithm taking into account the latent structure of the spike, and show that its performance is asymptotically optimal for natural choices of the generative network architecture. The absence of an algorithmic gap in this case is in stark contrast to known results for sparse spikes, another popular prior for modelling low-dimensional signals, and for which no algorithm is known to achieve the optimal statistical threshold. Finally, we show that linearising our message passing algorithm yields a simple spectral method also achieving the optimal threshold for reconstruction. We conclude with an experiment on a real data set showing that our bespoke spectral method outperforms vanilla PCA. [ABSTRACT FROM AUTHOR]

When bearing vibration of instruments is monitored, a large number of data are produced. This requires a massive capacity of storage and high bandwidth of data transmission whereby costs and complex installation are concerned. In this study, we aim to propose an effective framework to address such the amount of bearing signals to which only meaningful information is extracted. Based on the compressed sensing (CS) theory. We proposed a reconstruction algorithm based on the multiple side information signal (RAMSI) with a purpose to effectively obtain important information from recorded bearing signals. In the process of sparse optimization, the RAMSI algorithm was implemented to solve the n - 11 minimization problem with the weighting adaptive multiple side information signals. Wavelet basis and Hartley matrix were applied for the reconstruction process, for which the effective sparse optimization processing of bearing signals was able to adaptively computed. The performance of our RAMSI-based CS theory was compared with the basis pursuit (BP) which is based on the alternating direction method of multiplier (ADMM) and orthogonal matching pursuit (OMP). The error indices of the reconstruction algorithms were evaluated. This proves that the performance of the sparse optimization algorithm from our proposed framework is superior to the BP based on the ADMM and OMP algorithm. After recovering vibration signals, some strong noise caused by the incipient fault characteristic of the bearing. The complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) method was performed to extract the bearing fault component from such noise. In terms of performance, the CEEMDAN method was compared to the standard ensemble empirical mode decomposition (EEMD) method. The results show that the CEEMDAN method yields a better decomposition performance and is able to extract meaningful information of bearing fault characteristic. [ABSTRACT FROM AUTHOR]

Group/Pooled testing is a technique which involves testing n samples for a rare disease in an indirect manner: instead of individually testing each of the p samples, it involves creating n < p pools and testing each pool, where a pool consists of a mixture of small, equal portions of a subset of the p samples. Group testing is known to save a large amount of testing time and resources in a variety of application settings. There also exist good theoretical guarantees for the recovery of the status of the p samples from results on n pools, if certain conditions are satisfied. The popularity of group testing for RT-PCR testing is also well-known. The noise in quantitative RT-PCR is known to follow a multiplicative and data-dependent model, which emerges from properties inherent to RT-PCR. In recent literature, the corresponding linear systems for inference of the health status of p samples from results on n pools, have been solved using the well-known Lasso estimator and its variants (Ghosh et al., 2021), which have been widely used in the compressed sensing literature. However, the Lasso has typically been used in additive Gaussian noise settings. There is no existing literature which establishes performance bounds for Lasso for the multiplicative noise model associated with RT-PCR. After noting that a general technique proposed in Hunt et al. (2018) works well for establishing performance bounds for Lasso in Poisson inverse problems, we adapt it to handle sparse signal reconstruction from compressive measurements with multiplicative noise, as would appear in pooled RT-PCR testing. In particular, we present high probability performance bounds and data-dependent weights for the Lasso and a weighted version of the Lasso under multiplicative lognormal Noise. We also show numerical results on simulated pooled RT-PCR data to empirically validate our developed bounds. • We analyze the LASSO estimator for signal recovery in compressive RT-PCR. • We assume multiplicative lognormal noise in measurements. • This is the first theoretical analysis of the LASSO for pooled RT-PCR. • This is the first analysis of compressed sensing with multiplicative lognormal noise. • Our numerical results show that our theoretical bounds are empirically tight. [ABSTRACT FROM AUTHOR]

• It is possible to design deterministic universal multicoset sampling strategies implemented with both asynchronous TI-ADC structures and synchronous multirate TI-ADC schemes for the reconstruction of sparse multiband signals. • For a signal block length L, if the indices of the selected samples are in arithmetic progression of difference D coprime with the block length L, then the sampling pattern is universal. • Most 2M-1 bands of the multiband signal can be reconstructed for M ADCs working at different sampling rates and a block length that is the lcm of the M subsampling factors. Signal acquisition is a basic function in signal processing systems. In the context of digital communications, the analog-to-digital (ADC) converters have to be carefully designed as part of the radio frequency front end, to reduce power consumption while avoiding aliasing. When operating with sparse multiband signals, compressive sampling becomes an attractive alternative to enable low sampling rates at the front end. Starting from previous results on multicoset sampling and compressed sensing, we analyze sampling strategies for sparse multiband signals based on the operation of a set of ADC converters working in parallel. Different architectures are considered, with equal and different sampling rates in the ADCs, and their associated deterministic measurement matrices and sampling patterns are studied. The matrices involved in the corresponding reconstruction equations for the different architectures are also analyzed in terms of their mutual coherence. As a result, we are able to design different universal multicoset sampling patterns. We obtain the parameters for the different sampling architectures that guarantee reconstruction of the multiband sparse signal, even at high compression rates. Simulation results show the effectiveness of the theoretical designs for sparse reconstruction of this type of signals. [ABSTRACT FROM AUTHOR]