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Localization based on fingerprint has been viewed as a popular indoor localization technique, which uses the signal strength of different positions as the location fingerprint. The localization model can thus be constructed by analyzing the relationship between the location fingerprint and the target location. However, this method requires the manual acquisition of fingerprint signal data in an offline phase, which has become a bottleneck for practical application, especially in large-scale fields. Therefore, how to reduce the workload in fingerprint collection has become a significant issue. This paper invokes a compressive sensing-based method to reduce fingerprint construction complexity. First, the k-singular value decomposition algorithm based on an overcomplete dictionary is employed to sparse the fingerprint signal. Then, considering the uncertainty of the signal sparsity in the indoor environment, an adaptive fingerprint signal reconstruction algorithm based on error weight is proposed to construct signals with variable sparsity. We test the proposed fingerprint reconstruction on both actual RSSI and geomagnetic fingerprints. Experiments show that the fingerprint database of 132 reference positions can be reconstructed with only 50 compressed samples, which reduces the workload of offline collection by 62 % . [ABSTRACT FROM AUTHOR]

Compressive sensing (CS) of the signal ambiguity function (AF) and enforcing the sparsity constraint on the resulting signal time-frequency distribution (TFD) has been shown to be an efficient method for time-frequency signal processing. This paper proposes a method for adaptive CS-AF area selection, which extracts the magnitude-significant AF samples through a clustering approach using the density-based spatial clustering algorithm. Moreover, an appropriate criterion for the performance of the method is formalized, i.e., component concentration and preservation, as well as interference suppression, are measured utilizing the information obtained from the short-term and the narrow-band Rényi entropies, while component connectivity is evaluated using the number of regions with continuously-connected samples. The CS-AF area selection and reconstruction algorithm parameters are optimized using an automatic multi-objective meta-heuristic optimization method, minimizing the here-proposed combination of measures as objective functions. Consistent improvement in CS-AF area selection and TFD reconstruction performance has been achieved without requiring a priori knowledge of the input signal for multiple reconstruction algorithms. This was demonstrated for both noisy synthetic and real-life signals. [ABSTRACT FROM AUTHOR]

Compressive sensing is a sub-Nyquist sampling technique for efficient signal acquisition and reconstruction of sparse or compressible signals. In order to account for the sparsity of the underlying signal of interest, it is common to use sparsifying priors such as Bernoulli–Gaussian-inverse Gamma (BGiG) and Gaussian-inverse Gamma (GiG) priors on the components of the signal. With the introduction of variational Bayesian inference, the sparse Bayesian learning (SBL) methods for solving the inverse problem of compressive sensing have received significant interest as the SBL methods become more efficient in terms of execution time. In this paper, we consider the sparse signal recovery problem using compressive sensing and the variational Bayesian (VB) inference framework. More specifically, we consider two widely used Bayesian models of BGiG and GiG for modeling the underlying sparse signal for this problem. Although these two models have been widely used for sparse recovery problems under various signal structures, the question of which model can outperform the other for sparse signal recovery under no specific structure has yet to be fully addressed under the VB inference setting. Here, we study these two models specifically under VB inference in detail, provide some motivating examples regarding the issues in signal reconstruction that may occur under each model, perform comparisons and provide suggestions on how to improve the performance of each model. [ABSTRACT FROM AUTHOR]

Owing to the advantages of low cost and easy implementation, the 1-bit sampling technique attracts more and more attention recently. In many signal processing areas, such as in the direction finding problem, the complete analytical 1-bit signal is required to provide the instantaneous phase information, rather than the real-valued 1-bit signal. However, how to generate the imaginary component of the 1-bit signal continues to be an open problem in the literature. To this end, in this paper the concept of 1-bit Hilbert transform is introduced. Moreover, we propose an algorithm to construct the analytical signal for the real-valued 1-bit signal based on the 1-bit compressive sensing method. Simulations show that the proposed method can obtain the analytical 1-bit signal with a reasonable accuracy. [ABSTRACT FROM AUTHOR]

In this paper, a hybrid derivative-free conjugate gradient method that inherits the structures of two conjugate gradient methods is introduced to recover sparse signal in compressive sensing by solving the nonlinear convex constrained equations. The global convergence of the proposed method is proved, under some appropriate assumptions. Numerical experiments and comparisons suggest that the proposed algorithm is an efficient approach for sparse signal and image reconstruction in compressive sensing. [ABSTRACT FROM AUTHOR]

This paper presents a hybrid conjugate gradient (CG) approach for solving nonlinear equations and signal reconstruction. The CG parameter of the approach is a convex combination of the Dai‐Yuan (DY)‐like and Hestenes‐Stiefel (HS)‐like parameters. Independent of any line search, the search direction is descent and bounded. Under some reasonable assumptions, the global convergence of the hybrid approach is proved. Numerical experiments on some benchmark test problems show that the proposed approach is efficient compared with some existing algorithms. Finally, the proposed approach is applied in signal reconstruction. [ABSTRACT FROM AUTHOR]

Direction of arrival (DOA) estimation from sparse signal representation has gained much attention in recent years. In this, the spatial signal is reconstructed by using a Compressive sensing (CS) framework. CS is a new paradigm by which the signal acquisition and reconstruction are carried out at sub-Nyquist rates. The limitation of the Nyquist sampling theorem is overcome by sparse sampling and reconstruction. This paper uses the CS framework in DOA estimation to reduce the underlying computational cost in the reconstruction process. Many reconstruction algorithms have been described in the past years. However, the comparative study on the reconstruction performances for CS-based DOA estimation is lacking. This work primarily concentrates on different reconstruction algorithms that are utilized in CS. The performance of various reconstruction algorithms for single snapshot DOA estimation is compared in this paper. Different parameters, like finding the target failure rate, Root Mean Square Error (RMSE), execution time are considered to evaluate the performance of the techniques. [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]

The long-term operating structural health monitoring (SHM) system generates massive monitoring data, whose transmission and storage are challenging tasks. To address this issue, this study proposed an improved grey wolf optimizer-orthogonal matching pursuit (IGWO-OMP) algorithm for SHM data compression and reconstruction. The effectiveness of the proposed algorithm was validated using four SHM datasets including ultrasonic guided wave (UGW), acceleration, and audio signals. Firstly, the optimization results of IGWO were compared with those of other classical algorithms to verify its superiority in reconstruction accuracy. Secondly, the reconstruction accuracy under various compression factors was investigated and the optimal compression factor was determined. Finally, the relationship between reconstruction accuracy and signal sparsity as well as the performance of IGWO-OMP in dealing with noise-containing signals were discussed. The results demonstrate the generalizability and excellent noise robustness of IGWO-OMP in SHM data compression and reconstruction. Compared with other optimization algorithms, IGWO exhibits the best global optimal solution searching ability and obtains the reconstructed signal closest to the original one. Comprehensively considering the compressed signal length, reconstruction accuracy and computational efficiency, the optimal compression factor is suggested to be 0.2. In IGWO-OMP, the signal reconstruction accuracy is related to its sparsity, the variation of the CCD index for the reconstructed signal with relative sparsity follows an exponential growth relationship. • IGWO-OMP algorithm was proposed for signal reconstruction. • IGWO exhibits higher optimization performance than other algorithms. • The optimal compression ratio is suggested to be 0.2. [ABSTRACT FROM AUTHOR]

In this paper, we propose a method for block sparse signal recovery that minimizes the block q -ratio sparsity ‖ z ‖ 2 , 1 / ‖ z ‖ 2 , q q q − 1 with q ∈ [ 0 , ∞ ]. For the case of 1 < q ≤ ∞ , we present the theoretical analyses and the computing algorithms for both cases of the ℓ 2 -bounded and ℓ 2 , ∞ -bounded noises. The corresponding unconstrained model is also investigated. Its superior performance in block sparse signal reconstruction is demonstrated by numerical experiments. [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]

• Weighted schatten- p norm regularization has been proposed for multichannel EEG signal recovery. • Welsch estimator has been used to retrain the impulsive noise which is included in the original signal. • An effect iterative optimization method is applied to exactly solve the resulting complicated optimization problem. • RCLR can achieve the superior performance compared with existing CS techniques in the open literature. Reducing noise is an urgent problem that solved in practical application, so designing robust signal recovery approach based on compressive sensing (CS) theory is critical for the multichannel electroencephalogram (EEG) signals. However, almost all the algorithms seldom regard noise or just take Gaussian noise emerged in transmission into account. When the original signal is affected by noise before compression and transmission, all these CS approaches will be out of effect. In order to abase the impact of impulsive noise, a new robust CS approach based on cosparse and low-rank priors is proposed to recover the clean original signal near perfectly. Specially, our model employs Welsch estimator to retrain the impulsive noise, and weighted schatten- p norm to efficiently utilize low-rank prior knowledge. Moreover, we present an iterative optimization strategy to reconstruct the signals. Experimental results have demonstrated that the proposed algorithm can exactly reconstruct the multichannel EEG signals under the impact of impulsive noise. [ABSTRACT FROM AUTHOR]

In this paper, we present an approach to the reconstruction of signals exhibiting sparsity in a transformation domain, having some heavily disturbed samples. This sparsity-driven signal recovery exploits a carefully suited random sampling consensus (RANSAC) methodology for the selection of a subset of inlier samples. To this aim, two fundamental properties are used: A signal sample represents a linear combination of the sparse coefficients, whereas the disturbance degrades the original signal sparsity. The properly selected samples are further used as measurements in the sparse signal reconstruction, performed using algorithms from the compressive sensing framework. Besides the fact that the disturbance degrades signal sparsity in the transformation domain, no other disturbance-related assumptions are made—there are no special requirements regarding its statistical behavior or the range of its values. As a case study, the discrete Fourier transform is considered as a domain of signal sparsity, owing to its significance in signal processing theory and applications. Numerical results strongly support the presented theory. In addition, the exact relation for the signal-to-noise ratio of the reconstructed signal is also presented. This simple result, which conveniently characterizes the RANSAC-based reconstruction performance, is numerically confirmed by a set of statistical examples. [ABSTRACT FROM AUTHOR]

We investigate the problems of 1-D and 2-D signal recovery from subsampled Hadamard measurements using Haar wavelet as a sparsity inducing prior. These problems are of interest in, e.g., computational imaging applications relying on optical multiplexing or single-pixel imaging. However, the realization of such modalities is often hindered by the coherence between the Hadamard and Haar bases. The variable and multilevel density sampling strategies solve this issue by adjusting the subsampling process to the local and multilevel coherence, respectively, between the two bases; hence enabling successful signal recovery. In this work, we compute an explicit sample-complexity bound for Hadamard-Haar systems as well as uniform and non-uniform recovery guarantees; a seemingly missing result in the related literature. We explore the faithfulness of the numerical simulations to the theoretical results and show in a practically relevant instance, e.g., single-pixel camera, that the target signal can be recovered from a few Hadamard measurements. [ABSTRACT FROM AUTHOR]

Many physical phenomena can be modeled by compressible signals, i.e., the signals with rapidly declining sample amplitudes. Although all the samples are usually nonzero, due to practical reasons such signals are attempted to be approximated as sparse ones. Because sparsity of compressible signals cannot be unambiguously determined, a decision about a particular sparse representation is often a result of comparison between a residual error energy of a reconstruction algorithm and some quality measure. The paper explores a relation between mean square error (MSE) of the recovered signal and the residual error. A novel, practical solution that controls the sparse approximation quality using a target MSE value is the result of these considerations. The solution was tested in numerical experiments using orthogonal matching pursuit (OMP) algorithm as the signal reconstruction procedure. The obtained results show that the proposed quality metric provides fine control over the approximation process of the compressible signals in the mean sense even though it has not been directly designed for use in compressed sensing methods such as OMP. [ABSTRACT FROM AUTHOR]

The development of compressive sensing has focused on sparse signal reconstruction in recent years. Most existing greedy algorithms achieve satisfactory reconstruction performance only when the sparsity of the target signal has been known as prior information. Moreover, some greedy algorithms always involve either high‐computational expenses or low‐reconstruction accuracy caused by the process of adaptive adjustment of signal sparsity. To address these concerns, a novel variable step‐size matching pursuit based on oblique projection (VSMPOP) for compressed sensing is proposed. The proposed VSMPOP algorithm estimates the initial sparsity based on the restricted isometry property criterion. The algorithm creates a support set of the target signal after a preliminary test and oblique projection test between the sensing matrix and the residual. VSMPOP realises a similar approach to the sparsity level with a variable step size. The experimental results demonstrated that the proposed VSMPOP algorithm provides superior performance in terms of computational complexity and reconstruction efficiency compared with most of the available matching pursuit algorithms. [ABSTRACT FROM AUTHOR]

Compressive sensing retains the substantive characteristics of the original signal based on several sampling values and can realize distortionless reconstruction of signals with high probability. Hence, compressive sensing solves the contradictions among massive sampling data, signal processing speed and hardware equipment in the framework of traditional Shannon's sampling theorem. In this study, as a means of compressive sensing, a new failure recognition method of rolling bearing based on the characteristic parameters of compressed data and fuzzy-C mean (FCM) clustering is proposed. In this method, kurtosis, variance and waveform factor are used as the characteristic parameters. Using the proposed method, the sensitive characteristics were extracted by using the compressed information directly, and the eigenvectors of the sample signals were classified and identified through FCM clustering. In the experiment, the proposed method was compared with different compressed matrix methods and the traditional signal acquisition methods under the same axis diameter and different axis diameters. The results demonstrated the improved performance of the proposed method compared to the other methods. [ABSTRACT FROM AUTHOR]

Compressive sensing provides a new idea for machinery monitoring, which greatly reduces the burden on data transmission. After that, the compressed signal will be used for fault diagnosis by feature extraction and fault classification. However, traditional fault diagnosis heavily depends on the prior knowledge and requires a signal reconstruction which will cost great time consumption. For this problem, a deep belief network (DBN) is used here for fault detection directly on compressed signal. This is the first time DBN is combined with the compressive sensing. The PCA analysis shows that DBN has successfully separated different features. The DBN method which is tested on compressed gearbox signal, achieves 92.5% accuracy for 25% compressed signal. We compare the DBN on both compressed and reconstructed signal, and find that the DBN using compressed signal not only achieves better accuracies, but also costs less time when compression ratio is less than 0.35. Moreover, the results have been compared with other classification methods. [ABSTRACT FROM AUTHOR]

• The reconstruction model is established for vibration signals. • The index vector is proposed to obtain all the feature coefficients. • The improve FISTA is proposed for a better performance in reconstruction. • The simulated signals and acquired signals are used to verify the effectiveness. We consider the compressive sensing reconstruction for vibration signals, which are complex due to the harsh working environment. The recent fast iterative shrinkage-thresholding algorithm (FISTA) has paved the way for the signal reconstruction with a low complexity and high efficiency. Unfortunately, when extending to the vibration signals, the current algorithm still has some drawbacks such as the bad reconstruction effect. In this paper, we propose the improved fast iterative shrinkage-thresholding algorithm (IFISTA) to improve the reconstruction effect. Under the new scheme, the reconstruction is promoted by extracting information from the unstable signals in the process of iteration. Then the feature coefficients will be protected from shrinkage during iteration. The effectiveness of the IFISTA is verified by simulated signals and acquired signals. It is showed that the proposed scheme has superior performance in reconstruction and feature protection for vibration signals. [ABSTRACT FROM AUTHOR]

Compressive sensing can be conceptualized for a classification problem in the context of representation learning, which is frequently applied for signal reconstruction via a few measurements. A novel compressive sensing-based approach is presented to substantially reduce the number of required samples for classification. This technique considers the pixels of image as sensors and it seeks to identify the most optimum sensors as decision variables in feature space. In this study, Spatial sensor locations are acquired through learning to identify the regions within an image where the most discriminative information for classification is embedded. ℓ 1 − 2 minimization, as nonconvex but Lipschitz continuous, is solved to obtain the least non-zero elements of the full measurement vector to completely reconstruct the discriminative vector in feature space. Optimal sensors are localized from the training-set and subsequent test images are categorized based on learned sensors. The algorithm consists of three primary components: sparse minimization, feature space, and discrimination vector. ℓ 1 − 2 minimization, rank-revealing QR factorization (RRQR) and SVM are considered for enhanced sparsity exploitation, feature space extraction and discrimination vector acquiring, respectively. The proposed method is evaluated on four different experiments and is compared against a state-of-art technique. The results demonstrate the superiority of proposed method to the compared method. • Proposing a novel sparse classification algorithm. • ℓ 1 − 2 is employed as sparse minimization problem to increase sparsity. • SVM is leveraged to find most informative direction to separate classes. • RRQR decomposition has been performed to extract feature space which is more economic in terms of computation time. [ABSTRACT FROM AUTHOR]

A new form of the multivariate median is introduced. It is defined as a point in the multidimensional space whose sum of distances from a set of multidimensional hyperplanes is minimal. This median can be used to formulate and solve the problem of sparse signal reconstruction. Application of the proposed multivariate median is illustrated on examples. [ABSTRACT FROM AUTHOR]

Highlights • A back-off and rectification of greedy pursuit algorithm is proposed. • An intersection of support sets estimated by the OMP and SP algorithm is obtained first. • It selects atoms adaptively and deletes incorrect atoms effectively. • It can reconstruct a one-dimension signal or two-dimension image quickly and effectively. Abstract Image reconstruction is an important research topic in the field of multimedia processing. It aims to represent a high-resolution image with highly compressed features that can be used to reconstruct the original image as well as possible, and has been widely used for image storage and transmission. Compressed Sensing (CS) is a commonly used approach for image reconstruction; however, CS currently lacks an efficient and accurate solving algorithm. To this end, we present an iterative greedy reconstruction algorithm for Compressed Sensing called back-off and rectification of greedy pursuit (BRGP). The most significant feature of the BRGP algorithm is that it uses a back-off and rectification mechanism to select the atoms and then obtains the final support set. Specifically, an intersection of support sets estimated by the Orthogonal Matching Pursuit (OMP) and Subspace Pursuit (SP) algorithms is first set as the initial candidate support, and then a back-off and rectification mechanism is used to expand and rectify it. Experimental results show that the algorithm significantly outperforms conventional techniques for one-dimensional or two-dimensional compressible signals. [ABSTRACT FROM AUTHOR]

Sparse signals are characterized by a few nonzero coefficients in one of their transformation domains. This was the main premise in designing signal compression algorithms. Compressive sensing as a new approach employs the sparsity property as a precondition for signal recovery. Sparse signals can be fully reconstructed from a reduced set of available measurements. The description and basic definitions of sparse signals, along with the conditions for their reconstruction, are discussed in the first part of this paper. The numerous algorithms developed for the sparse signals reconstruction are divided into three classes. The first one is based on the principle of matching components. Analysis of noise and nonsparsity influence on reconstruction performance is provided. The second class of reconstruction algorithms is based on the constrained convex form of problem formulation where linear programming and regression methods can be used to find a solution. The third class of recovery algorithms is based on the Bayesian approach. Applications of the considered approaches are demonstrated through various illustrative and signal processing examples, using common transformation and observation matrices. With pseudocodes of the presented algorithms and compressive sensing principles illustrated on simple signal processing examples, this tutorial provides an inductive way through this complex field to researchers and practitioners starting from the basics of sparse signal processing up to the most recent and up-to-date methods and signal processing applications. [ABSTRACT FROM AUTHOR]

Compressive sensing relies on the sparse prior imposed on the signal of interest to solve the ill-posed recovery problem in an under-determined linear system. The objective function used to enforce the sparse prior information should be both effective and easily optimizable. Motivated by the entropy concept from information theory, in this paper we propose the generalized Shannon entropy function and Rényi entropy function of the signal as the sparsity promoting regularizers. Both entropy functions are nonconvex, non-separable. Their local minimums only occur on the boundaries of the orthants in the Euclidean space. Compared to other popular objective functions, minimizing the generalized entropy functions adaptively promotes multiple high-energy coefficients while suppressing the rest low-energy coefficients. The corresponding optimization problems can be recasted into a series of reweighted $l_1$ -norm minimization problems and then solved efficiently by adapting the FISTA. Sparse signal recovery experiments on both the simulated and real data show that the proposed entropy functions minimization approaches perform better than other popular approaches and achieve state-of-the-art performances. [ABSTRACT FROM AUTHOR]

Highlights • We focus on employing a Markov random field (MRF) in structured-compressive sensing. • We propose to adaptively estimate the MRF parameters from a few measurements. • We formulate the MRF parameter estimation as a maximum marginal likelihood (MML). • A new approximation for the MRF model is proposed to solve the MML efficiently. • The proposed method yields the state-of-the-art results on three real-world datasets. Abstract Recently, Markov random fields (MRFs) have gained much success in sparse signal recovery. One of the challenges is to adaptively estimate the MRF parameters from a few compressed measurements in compressive sensing (CS). To address this problem, a recently developed method proposes to estimate the MRF parameters based on the point estimation of sparse signals. However, the point estimation cannot depict the statistical uncertainty of the latent sparse signal, which can result in inaccurate parameters estimation; thus, limiting the ultimate performance. In this study, we propose a one-step MRF based CS that estimates the MRF parameters from the given measurements through solving a maximum marginal likelihood (MML) problem. Since the marginal likelihood is obtained from averaging over the latent sparse signal population, it offers better generalization over all the latent sparse signals than the point estimation. To solve the MML problem effectively, we approximate the MRF distribution by the product of two simpler distributions, which enables to produce closed-form solutions for all unknown variables with low computational cost. Extensive experiments on a synthetic and three real-world datasets demonstrate the effectiveness of the proposed method in recovery accuracy, noise tolerance, and runtime. [ABSTRACT FROM AUTHOR]

Highlights • Paper provides a framework for probabilistic compressive sensing. • The paper aims to address two short-comings of the traditional formulations: the ad-hoc manner for tuning sparsity levels in signal reconstructions, and the lack of uncertainty quantification. • The key idea being presented is that the problem of probabilistic output can be addressed by use of the Relevance Vector Machine (RVM). This is sparse Bayesian regression model, for which fast optimisation methods have already been developed. • It is also highlighted that for a probabilistic output to be meaningful, it is better to use data-driven, as opposed to model-based dictionaries, as this captures the covariance structure of original data sets better. • The motivation for this development lies in the compression of ultrasound signals, for engineering applications. Thus, the method is demonstrated, and illustrations are drawn from an ultrasound Non-Destructive-Test (NDT) data set. Abstract The field of Compressive Sensing (CS) has provided algorithms to reconstruct signals from a much lower number of measurements than specified by the Nyquist-Shannon theorem. There are two fundamental concepts underpinning the field of CS. The first is the use of random transformations to project high-dimensional measurements onto a much lower-dimensional domain. The second is the use of sparse regression to reconstruct the original signal. This assumes that a sparse representation exists for this signal in some known domain, manifested by a dictionary. The original formulation for CS specifies the use of an l 1 penalised regression method, the Lasso. Whilst this has worked well in literature, it suffers from two main drawbacks. First, the level of sparsity must be specified by the user, or tuned using sub-optimal approaches. Secondly, and most importantly, the Lasso is not probabilistic; it cannot quantify uncertainty in the signal reconstruction. This paper aims to address these two issues; it presents a framework for performing compressive sensing based on sparse Bayesian learning. Specifically, the proposed framework introduces the use of the Relevance Vector Machine (RVM), an established sparse kernel regression method, as the signal reconstruction step within the standard CS methodology. This framework is developed within the context of ultrasound signal processing in mind, and so examples and results of compression and reconstruction of ultrasound pulses are presented. The dictionary learning strategy is key to the successful application of any CS framework and even more so in the probabilistic setting used here. Therefore, a detailed discussion of this step is also included in the paper. The key contributions of this paper are a framework for a Bayesian approach to compressive sensing which is computationally efficient, alongside a discussion of uncertainty quantification in CS and different strategies for dictionary learning. The methods are demonstrated on an example dataset from collected from an aerospace composite panel. Being able to quantify uncertainty on signal reconstruction reveals that this grows as the level of compression increases. This is key when deciding appropriate compression levels, or whether to trust a reconstructed signal in applications of engineering and scientific interest. [ABSTRACT FROM AUTHOR]

Highlights • Developing a unifying framework for signal recovery from interferometric measurements. • Compressive recovery under constraints imposed by the interferometer structure. • Establishing performance guarantees on compressive recovery under sensing constraints. • Devising controlled sampling policies to collect more informative measurements. Abstract We develop a framework in which the problem of signal reconstruction from interferometric measurements amounts to one of basis analysis, with measurements that are linear in the basis coefficients. We leverage a generalized interferometry approach to enable the reconstruction of signals represented in different bases of arbitrary domains. Our framework is unifying in that it applies whether the sought-after information concerns the input signal or a sample object, as well as in settings where we have no control over the relative delays of the two paths of the interferometer. While the linear transformation underlying the measurement system has only a limited number of degrees of freedom set by the constrained sensing structure, we show that compressive signal recovery is achievable without introducing any additional randomization to the measurement setup. We establish performance guarantees under constrained sensing by proving that the transformation satisfies sufficient conditions for successful reconstruction. Also, we propose two control policies to guide the collection of informative measurements given prior knowledge about the constrained sensing structure. By minimizing the mutual coherence of the sampled measurements, the controlled approach is shown to yield further gains in sample size complexity. [ABSTRACT FROM AUTHOR]

Abstract In this paper, a reconfigurable, high-speed, low-power, and vendor-independent field-programmable gate array (FPGA) implementation of the orthogonal matching pursuit (OMP) algorithm is presented. Unlike existing previous work, the proposed architecture is reconfigurable, that is, the architecture can accept different signal sizes, different sparsity levels, and sampling matrix sizes. Furthermore, the Goldschmidt algorithm is used to implement the fixed point division unit that achieves state-of-the-art performance. To the best of our knowledge, the presented architecture demonstrates the fastest reconstruction times for the standard OMP algorithm on FPGA for high sparsity levels. The proposed design is able to recover a 128-length signal with K = 5 in 7.75 μs and 256-length signals with K = 8 and K = 12 in 23.27 μs and 39.56 μs respectively. The results also show that our design outperforms many other existing FPGA implementations in terms of power consumption. [ABSTRACT FROM AUTHOR]

Many problems arising from machine learning, compressive sensing, linear inverse problem, and statistical inference involve finding sparse solutions to under-determined or ill-conditioned equations. In this paper, a gradient projection method is proposed to recover sparse signal in compressive sensing by solving the nonlinear convex constrained equations. The global convergence is established with the backtracking line search. Preliminary numerical experiments coping with the sparse signal reconstruction in compressive sensing are performed, which show that the proposed method is very effective and stable. [ABSTRACT FROM AUTHOR]

To solve large-scale nonlinear equations with convex constraints efficiently and overcome the shortcomings of other algorithms, such as large storage and high complexity, we develop a descent and derivative-free algorithm based on a classical spectral gradient method, the projection technique and a new monotone line search method. The new algorithm has the following features: (1) There is lower storage and derivative-free information; (2) It is suitable to solve large-scale nonlinear equations; (3) Its direction possesses sufficient descent and trust region properties; (4) The spectral parameter is bounded. The global convergence of the new algorithm is proven under some appropriate assumptions. If the local error bound condition is satisfied, the proposed algorithm is linearly convergent. Preliminary numerical results demonstrate that the new algorithm is effective and robust. Furthermore, we also extend this algorithm to solve the sparse signal reconstruction problem and the blurred image recovery problem in compressed sensing. [ABSTRACT FROM AUTHOR]

To strike a balance between energy efficiency and data quality control, this paper proposes a sensor censoring scheme for distributed sparse signal recovery via compressive-sensing-based wireless sensor networks. In the proposed approach, each sensor node employs a sparse sensing vector with known support for data compression, meanwhile enabling making local inference about the unknown support of the sparse signal vector of interest. This naturally leads to a ternary censoring protocol, whereby each sensor: 1) directly transmits the real-valued compressed data, if the sensing vector support is detected to be overlapped with the signal support; 2) sends a one-bit hard decision if empty support overlap is inferred; and 3) keeps silent if the measurement is judged to be uninformative. Our design then aims at minimizing the error probability that empty support overlap is decided but otherwise is true, subject to the constraints on a tolerable false-alarm probability that non-empty support overlap is decided but otherwise is true, and a target censoring rate. We derive a closed-form formula of the optimal censoring rule; a low complexity implementation using bi-section search is also developed. In addition, the average communication cost is analyzed. To aid global signal reconstruction under the proposed censoring framework, we propose a modified \ell 1 -minimization based algorithm, which exploits certain sparse nature of the hard decision vector received at the fusion center. Analytic performance guarantees, characterized in terms of the restricted isometry property, are also derived. Computer simulations are used to illustrate the performance of the proposed scheme. [ABSTRACT FROM PUBLISHER]

Stochastic gradient-based adaptive algorithm has recently attracted considerable attention as one of the best candidates for solving compressive sensing (CS) problems due to its two obvious advantages: low complexity and robust performance. In this paper, in order to further improve the reconstruction accuracy for CS problems under Gaussian background noise, two novel sparse fourth-order error criterion adaptive algorithms, i.e., the ℓ0-norm normalized least mean fourth (ℓ0-NLMF) algorithm and the ℓ0-norm exponentially forgetting window NLMF (ℓ0-EFWNLMF) algorithm, are proposed. In addition, to extend the obtained results to non-Gaussian noise environment, the variants of the above two algorithms, i.e., the sign ℓ0-NLMF (ℓ0-SNLMF) algorithm and the sign ℓ0-EFWNLMF (ℓ0-EFWSNLMF) algorithm, are presented which can effectively mitigate certain impulsive noises. Numerical simulations are also given to demonstrate the evident performance improvement and extensive stability of the proposed algorithms. [ABSTRACT FROM AUTHOR]

Compressive sensing is used to reconstruct the time-harmonic electric field created by multipath fading from a limited number of measurement points over a planar region. The multipath fading signal is shown to be the superposition of multiple plane wave components and thus has a sparse representation in the spatial-frequency domain. The discrete Fourier basis used as the dictionary for orthogonal matching pursuit is oversampled to ensure sufficient resolution in the spatial-frequency domain. Experimental results at 10 GHz using an arbitrary plane wave expansion show that the signal-to-error ratio of the compressive sensing reconstruction is approximately 16 dB when randomly selecting only 7.5% of the total points. [ABSTRACT FROM PUBLISHER]

Nonstationary signals, approximately sparse in the joint time-frequency domain, are considered. Reconstruction of such signals with sparsity constraint is analyzed in this paper. The short-time Fourier transform (STFT) and time-frequency representations that can be calculated using the STFT are considered. The formula for error caused by the nonreconstructed coefficients is derived and presented in the form of a theorem. The results are examined statistically on examples. [ABSTRACT FROM AUTHOR]

Within the compressive sensing framework, reconstruction algorithms of block-sparse signal (BSS) often have special requirements on sparsity patterns. As a result, only some particular BSSs can be reconstructed. In this paper, we present a new universal greedy iteration algorithm, named block-matching pursuit (BMP), for BSS with an arbitrary sparsity pattern. The BMP can reconstruct the target signal without prior information of the signal's sparsity pattern and achieves an outstanding reconstruction probability. In each iteration, the BMP first estimates a part of support set of the signal by a correlation test. Based on the estimated support and the property of nonzero blocks, coordinates of all possible nonzero entries can be obtained to form a candidate list. Then some coordinates in the list, which are deemed sufficiently reliable by a final test, are added to the current estimated support set. When iteration ends, the true sparsity level, namely true support set, can be exactly calculated by searching a support set with the smallest cardinality; once the true set is derived, the target signal can be reconstructed. Theoretical analysis indicates that BMP can reconstruct the target signal as long as the sampling matrix meets a certain condition. Simulation results show that the reconstruction performance of BMP is better than that of other greedy algorithms. In particular, if the signal with high sparsity level contains a few blocks, BMP can still reconstruct it with a high probability. [ABSTRACT FROM AUTHOR]

Deep neural networks and model-based methods are both popular for their wide and great success in many inference problems. In this paper, resorting to deep learning, we study the efficient algorithms for two popular nonconvex regularization methods, smoothly clipped absolute deviation (SCAD) and minimax concave penalty (MCP). Approximate message passing (AMP) algorithm can be effective to optimize nonconvex regularization models. First, we unroll the AMP-based algorithm as the feed-forward neural network through leveraging the novel activation functions of neurons, dubbed as Unrolled-AMP. And then, for the case where the measurement matrix deviates from the i.i.d. Gaussian distribution, we propose two improved iterative algorithms based on the "Vector AMP (VAMP)" algorithm to solve the nonconvex regularization methods. Further, we unroll them as the feed-forward neural network, dubbed as Unrolled-VAMP. These two novel neural network architectures use a back-propagation algorithm to learn all their parameters from the training data. Finally, the convergence of Unrolled-AMP algorithm is analyzed, and the efficiency of the proposed networks is demonstrated through experiments on sparse signal reconstruction and 5G wireless communication. • We develop efficient algorithms for solving nonconvex regularization methods. • Two types iterative algorithms are unrolled as deep learning architectures. • We give convergence analysis of the proposed networks. • The proposed networks require few layers to achieve a specific level of accuracy. [ABSTRACT FROM AUTHOR]

In this paper, we study the compressive sensing effects on 2D signals exhibiting sparsity in 2D DFT domain. A simple algorithm for reconstruction of randomly undersampled data is proposed. It is based on the analytically determined threshold that precisely separates signal and non-signal components in the 2D DFT domain. The algorithm operates fast in a single iteration providing the accurate signal reconstruction. In the situations that are not comprised by the analytic derivation and constrains, the algorithm is still efficient and need just a couple of iterations. The proposed solution shows promising results in ISAR imaging (simulated data are used), where the reconstruction is achieved even in the case when less than 10 % of data are available. [ABSTRACT FROM AUTHOR]

Although wrist-type photoplethysmographic (hereafter referred to as WPPG) sensor signals can measure heart rate quite conveniently, the subjects’ hand movements can cause strong motion artifacts, and then the motion artifacts will heavily contaminate WPPG signals. Hence, it is challenging for us to accurately estimate heart rate from WPPG signals during intense physical activities. The WWPG method has attracted more attention thanks to the popularity of wrist-worn wearable devices. In this paper, a mixed approach called Mix-SVM is proposed, it can use multi-channel WPPG sensor signals and simultaneous acceleration signals to measurement heart rate. Firstly, we combine the principle component analysis and adaptive filter to remove a part of the motion artifacts. Due to the strong relativity between motion artifacts and acceleration signals, the further denoising problem is regarded as a sparse signals reconstruction problem. Then, we use a spectrum subtraction method to eliminate motion artifacts effectively. Finally, the spectral peak corresponding to heart rate is sought by an SVM-based spectral analysis method. Through the public PPG database in the 2015 IEEE Signal Processing Cup, we acquire the experimental results, i.e., the average absolute error was 1.01 beat per minute, and the Pearson correlation was 0.9972. These results also confirm that the proposed Mix-SVM approach has potential for multi-channel WPPG-based heart rate estimation in the presence of intense physical exercise. [ABSTRACT FROM AUTHOR]

Compressive sensing (CS) is able to measure sparse signals with fewer measurements than Nyquist rate. The reconstruction of sparse signals in CS is an underdetermined problem. For realistic applications, the sparsity information may not be available, the measurements are used to be disturbed by noise, and efficient hardware realization is important. Existing CS reconstruction algorithms are tradeoff between noise tolerance and low complexity. In this paper, we propose a novel reconstruction algorithm called stochastic gradient pursuit (SGP). The stochastic gradient approach is applied to replace least square process of well-known orthogonal matching pursuit (OMP) algorithm. Since stochastic gradient approach iterates toward a minimum mean square error solution, proposed algorithm shows robustness against noise. Furthermore, proposed algorithm inherits the low-complexity property of OMP and shows feasibility of hardware implementation. The SGP algorithm can achieve 36% higher success rate as well as 27% less complexity than OMP when SNR is 20 dB. Finally, we implement the algorithm with designed hardware sharing architecture in TSMC 90 nm technology. The postlayout result shows that the core size is only 1.08 mm 2 at 150 MHz operation frequency. Compared with state-of-the-art ASIC designs, the proposed engine achieves 29% higher throughput-to-area ratio. [ABSTRACT FROM AUTHOR]

A compressive sensing (CS) reconstruction method for polynomial phase signals is proposed in this paper. It relies on the Polynomial Fourier transform, which is used to establish a relationship between the observation and sparsity domain. Polynomial phase signals are not sparse in commonly used domains such as Fourier or wavelet domain. Therefore, for polynomial phase signals standard CS algorithms applied in these transformation domains cannot provide satisfactory results. In that sense, the Polynomial Fourier transform is used to ensure sparsity. The proposed approach is generalized using time–frequency representations obtained by the Local Polynomial Fourier transform (LPFT). In particular, the first-order LPFT can produce linear time–frequency representation for chirps. It provides revealing signal local behavior, which leads to sparse representation. The theory is illustrated on examples. [ABSTRACT FROM AUTHOR]

Compressive sensing (CS) theory provides a framework for signal reconstruction using a sub-Nyquist sampling rate. CS theory enables the reconstruction of a signal that is sparse or compressible from a small set of measurements. The current CS application in optical field mainly focuses on reconstructing the original image using optimization algorithms and conducts data processing in full-dimensional image, which cannot reduce the data processing rate. This study is based on the spatial sparsity of star image and proposes a new compressive measurement and reconstruction method that extracts the star feature from compressive data and directly reconstructs it to the original image for attitude determination. A pixel-based folding model that preserves the star feature and enables feature reconstruction is presented to encode the original pixel location into the superposed space. A feature reconstruction method is then proposed to extract the star centroid by compensating distortions and to decode the centroid without reconstructing the whole image, which reduces the sampling rate and data processing rate at the same time. The statistical results investigate the proportion of star distortion and false matching results, which verifies the correctness of the proposed method. The results also verify the robustness of the proposed method to a great extent and demonstrate that its performance can be improved by sufficient measurement in noise cases. Moreover, the result on real star images significantly ensures the correct star centroid estimation for attitude determination and confirms the feasibility of applying the proposed method in a star tracker. [ABSTRACT FROM AUTHOR]

Due to the capacity of compressing and recovering signal with low energy consumption, compressive sensing (CS) has drawn considerable attention in wireless telemonitoring of electrocardiogram (ECG) signals. However, most existing CS methods are designed for reconstructing single channel signal, and hence difficult to reconstruct multichannel ECG signals. In this paper, a spatio-temporal sparse model-based algorithm is proposed for the reconstruction of multichannel ECG signals by not only exploiting the temporal correlation in each individual channel signal, but also the spatial correlation among signals from different channels. In addition, a dictionary learning (DL) approach is developed to enhance the performance of the proposed reconstruction algorithm by using the sparsity of ECG signals in some transformed domain. The approach determines a dictionary by learning local dictionaries for each channel and merging them to form a global dictionary. Extensive simulations were performed to validate the proposed algorithms. Simulation results show that the proposed reconstruction algorithm has a better performance in recovering multichannel ECG signals as compared to the benchmarking methods. Moreover, the reconstruction performance of the algorithm can be further improved by using a dictionary matrix, which is obtained from the proposed DL algorithm. [ABSTRACT FROM AUTHOR]

A new signal reconstruction algorithm for compressive sensing based on the minimization of a pseudonorm which promotes block-sparse structure on the first-order difference of the signal is proposed. Involved optimization is carried out by using a sequential version of Fletcher–Reeves’ conjugate-gradient algorithm, and the line search is based on Banach's fixed-point theorem. The algorithm is suitable for the reconstruction of foot gait signals which admit block-sparse structure on the first-order difference. An additional algorithm for the estimation of stride-interval, swing-interval, and stance-interval time series from the reconstructed foot gait signals is also proposed. This algorithm is based on finding zero crossing indices of the foot gait signal and using the resulting indices for the computation of time series. Extensive simulation results demonstrate that the proposed signal reconstruction algorithm yields improved signal-to-noise ratio and requires significantly reduced computational effort relative to several competing algorithms over a wide range of compression ratio. For a compression ratio in the range from $88\%$ to $94\%$, the proposed algorithm is found to offer improved accuracy for the estimation of clinically relevant time-series parameters, namely, the mean value, variance, and spectral index of stride-interval, stance-interval, and swing-interval time series, relative to its nearest competitor algorithm. The improvement in performance for compression ratio as high as $94\%$ indicates that the proposed algorithms would be useful for designing compressive sensing-based systems for long-term telemonitoring of human gait signals. [ABSTRACT FROM AUTHOR]

We propose a novel multi-spectral imaging method based on compressive sensing (CS). In CS theory, the enhancement of signal sparsity is important for accurate signal reconstruction. The main novelty of the proposed method is the employment of a self-correlation of an image, that is a local intensity similarity and multi-spectral correlation, to enhance the sparsity of the multi-spectral image to be recovered. Local intensity similarity, which is based on the concept that spatial changes in intensity are likely to be similar within local regions, contributes to sparsity enhancement. Furthermore, we exploit multi-spectral correlation to improve the sparsity of the multi-spectral components to be recovered. In order to simultaneously exploit different types of characteristics (i.e., local intensity similarity and multi-spectral correlation) for representing a signal as sufficiently sparse, we introduce a hierarchical joint sparsity model in the CS image recovery process. Our experiments show that the use of a self-correlation significantly improves the performance of multi-spectral image reconstruction. [ABSTRACT FROM AUTHOR]

• The compression sampling and reconstruction of road roughness signal were realized. • The proposed ISA-SPA reconstruction method can adaptively match sparsity. • SA-GSM-SPA reconstruction method matched sparsity accurately and consumed less time. • The method presented in the paper was validated on hard pavement and soft pavement. • Sparsity matching equaled to extremal process of convex function approximately. To significantly reduce the storage space of collected road roughness signals and improve the collection rate, the work investigates the compressive sampling and reconstruction of road roughness signals based on compressive sensing theory. Moreover, to overcome the limitations of the classical signal reconstruction method in the case of unknown sparsity, two sparsity adaptive compressive signal reconstruction methods namely those based on the improved simulated annealing (I-SA) algorithm and the golden section method (GSM) are respectively proposed and compared. Both simulated and measured road roughness signals are used to verify the validity of the novel reconstruction methods and the feasibility of road roughness compression and collection. The research results show that the proposed ISA-SPA method (the sparsity adaptive reconstruction method based on the I-SA) completes the sparsity matching optimization with high reconstruction precision (R 2 = 0.9884), but has a high time consumption (about 16.09 s). Moreover, the proposed SA-GSM-SPA method (the sparsity adaptive reconstruction method based on the GSM) has a fast rate of calculation while inheriting the good sparsity estimation result and high reconstruction precision of the ISA-SPA method. [ABSTRACT FROM AUTHOR]

A visual vibration measurement method based on single-frame coded illumination and compressive sensing is proposed. The projector projects concentric rectangles with different sizes at different time points in a single camera exposure. According to the size of the rectangles, the image collected by the camera is separated into different sub frames. The centroids of the concentric rectangles are considered as the virtual feature points to record the vibration information of the object. The projector operates according to the random unequal interval trigger signal, and the projection is used as the sampling signal to encode the measured object. Discrete cosine transform is used as sparse basis, and sparsity adaptive matching pursuit and spectral projected gradient for L1 minimization (SPGL1) are used for signal reconstruction. Simulation analysis shows that the proposed method is feasible, and SPGL1 algorithm is more suitable for our signal reconstruction. The experiments indicate that the maximum absolute error of the proposed method for frequency measurement is 0.2985 Hz, and the maximum relative error is 1.6587 × 10 − 3. It is also applicable to multi-frequency measurement. [ABSTRACT FROM AUTHOR]