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This article investigates into signal regularity in ac series arc fault (SAF) detection. The regularity can solve the vital problem that SAF current characteristics change or disappear in unknown multiload circuits. A coupling method is adopted to capture high-frequency differential signals. The coupling signals show that the waveform in single-load circuits closely resembles the waveform in multiload ones. However, the coupling method confuses normal signals with arcing ones in dimmer loads. To address the issue, this article presents a time-series reconstruction method based on spectral features. First, the spectral features are analyzed between fault-like signals and fault signals. According to the spectral features and the desirable margin, the time series is self-adaptively decomposed and reconstructed. Then, the pulse-recognition algorithm is used to extract arcing features of the reconstructed signals. Finally, the detection method determined by single-load circuits is used to identify SAFs in unknown multiload ones. The results show the presented approach has good generalization performance and identification precision under arbitrary circuits. [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]

As the complexity of the multicore system grows, the large workload diversity results in serious thermal problems. In a practical way, the number of placed thermal sensors is usually limited due to the manufacturing cost. In recent years, the compressive sensing (CS) theory is proven as an efficient way to reconstruct the original signal by using fewer sampling data. However, due to the high computational complexity during the signal reconstruction, the CS theory is not appropriate to apply to the real-time temperature monitoring in the current multicore system. In this article, we propose a grid-based sensor placement approach to placement the number-limited thermal sensors on the target multicore system. On the other hand, we adopt the matrix inversion bypass (MIB) property to reduce the computational complexity of two widely used signal reconstruction approaches in CS theory [i.e., the orthogonal matching pursuit (OMP) and stagewise OMP (StOMP)]. Due to the characteristic of random sampling in CS theory, the complexity of thermal sensor placement for multicore systems can be reduced significantly. In addition, the proposed MIB-based temperature reconstruction method helps to satisfy the requirement of real-time temperature estimation. The experimental results show that the proposed approach can reduce 57%–93% average full-system temperature reconstruction error compared with the previous non-CS-based approaches. Besides, we can also reduce 22%–41% computing latency compared with the current CS-based reconstruction algorithm. Due to the MIB-based operation, we can bypass the matrix inversion operation for temperature reconstruction. Therefore, the hardware overhead of the temperature reconstruction unit can be reduced significantly. Compared with the conventional approaches, we can reduce 24%–87% area overhead and improve 50%–220% hardware efficiency. [ABSTRACT FROM AUTHOR]

Traditional time–frequency analysis (TFA) methods can effectively obtain instantaneous frequency (IF) features of nonstationary signals by constructing the signal model in the time domain. However, they fail to deal with the transient signal because the IF of the transient signal is discontinuous in the time domain and is a multivalued function with respect to time. Thus, in this article, we introduce a new TFA method, termed generalized transient-extracting transform (GTET), to obtain sharper time–frequency representation (TFR) of the transient signal by constructing frequency-domain model. First, we propose a new computational framework for group delay (GD). By deriving the general explicit formula for the Nth-order GD, the programming implementation of any order GD can be achieved. Next, the concentrated TFR of GTET can be generated by extracting the energy from the generalized GD estimation. Finally, the signal reconstruction of GTET is derived from a new perspective. It overcomes the difficulty that the reconstruction method of transient-extracting transform cannot be generalized to high-order algorithms. The analysis result of the simulated signal with high-order GD shows that GTET has better performance than other TFA methods. Experimental results demonstrate that GTET can be used to analyze practical transient signals. [ABSTRACT FROM AUTHOR]

In large-scale applications, parts of harmonic data are inevitably lost during transmission. This study presents an approach for the recovery of missing harmonic data based on the spectral graph theory. The proposed methodology involves graph theory for constructing a Laplacian matrix and a graph signal reconstruction function, the merging K-means algorithm for building a priori information model, and the accelerated segmentation Bregman iterative algorithm for solving the reconstruction function. Compared with existing methods on data recovery in power systems, the method maintains a good recovery accuracy when the data correlation of measurement units is low and the prior information is little. The proposed method has good anti-noise performances and low computational complexity. The feasibility and accuracy of the proposed method are verified through simulation and field recorded data. [ABSTRACT FROM AUTHOR]

This article presents the implementation and experimental testing of the wavelet-modulation technique for three-phase ($3\phi$) 5-level (5L) power electronic converters (PECs). This version of the wavelet modulation technique is structured as a multiresolution analysis that can support a redundant nonuniform recurrent sampling-reconstruction of three reference-modulating signals. The reconstruction of reference-modulating signals is achieved by sets of resolution-segmented scale-base linearly combined synthesis wavelet basis functions, which are used as switching signals to activate the switching elements of a $3\phi$ , 5L, VS dc–ac PEC. The presented wavelet-modulation technique is implemented in real time using a digital signal-processing board. Switching pulses generated by the extended wavelet-modulation technique are used to operate $3\phi$ , 5L, VS, diode-clamped and flying-capacitor dc–ac PECs. Experimental performance of the tested 5L dc–ac PECs is evaluated, when operated by the presented wavelet modulation, level-shifted pulsewidth modulation (PWM), phase-shifted PWM, and space vector modulation techniques. Experimental tests are conducted for linear, dynamic, and nonlinear loads fed by the tested 5L PECs. Test results show that magnitudes of output voltage fundamental components can be significantly increased, and harmonic distortions can be effectively reduced using the wavelet-modulation technique. These features are further demonstrated by performance comparisons with other techniques under similar operating conditions. [ABSTRACT FROM AUTHOR]

The echo separation issue for multiple-input–multiple-output (MIMO) synthetic aperture radar (SAR) is usually regarded as a more technical challenge. Spotlighted as a promising solution to echo separation, the well-known short-term shift-orthogonal (STSO) beamforming scheme has become increasingly popular. However, for airborne MIMO SAR systems, the digital beamforming (DBF) involved in the STSO scheme usually encounters more issues, e.g., the direction-of-arrival (DOA) mismatch induced by topography variation. Up until now, relatively less research on robust DBF processing has been conducted for airborne MIMO SAR systems. In this respect, an adaptive DBF technique, based on interference plus noise covariance matrix (IPNCM) reconstruction and desired signal steering vector estimation, has been proposed in this article. IPNCM reconstruction and steering vector estimation can not only cope with the DOA mismatch problem but also remove the desired signal component in the training data cells to increase the beamformer convergence rates. Consequently, the proposed approach really improves the array output signal-to-interference-plus-noise ratio (SINR). Moreover, numerous discussions and simulations are carried out to prove the effectiveness of the proposed DBF technique under various disturbance environments. Compared with the current DBF techniques, the proposed method provides a bright application prospect for the STSO scheme. [ABSTRACT FROM AUTHOR]

Image compression is one of the most fundamental techniques and commonly used applications in the image and video processing field. Earlier methods built a well-designed pipeline, and efforts were made to improve all modules of the pipeline by handcrafted tuning. Later, tremendous contributions were made, especially when data-driven methods revitalized the domain with their excellent modeling capacities and flexibility in incorporating newly designed modules and constraints. Despite great progress, a systematic benchmark and comprehensive analysis of end-to-end learned image compression methods are lacking. In this paper, we first conduct a comprehensive literature survey of learned image compression methods. The literature is organized based on several aspects to jointly optimize the rate-distortion performance with a neural network, i.e., network architecture, entropy model and rate control. We describe milestones in cutting-edge learned image-compression methods, review a broad range of existing works, and provide insights into their historical development routes. With this survey, the main challenges of image compression methods are revealed, along with opportunities to address the related issues with recent advanced learning methods. This analysis provides an opportunity to take a further step towards higher-efficiency image compression. By introducing a coarse-to-fine hyperprior model for entropy estimation and signal reconstruction, we achieve improved rate-distortion performance, especially on high-resolution images. Extensive benchmark experiments demonstrate the superiority of our model in rate-distortion performance and time complexity on multi-core CPUs and GPUs. [ABSTRACT FROM AUTHOR]

Performance of direction of arrival (DOA) estimation is one of the most important issues in array signal processing. Subspace-based algorithms provide a good compromise between the estimation accuracy and computational complexity. However, these methods are exposed to performance breakdown at low SNR scenarios. A major reason for such performance breakdown is the subspace swap phenomenon (intersubspace leakage). In this article, we elaborate on a novel modified signal subspace model through exploiting a supervised index for the estimation of DOA. With the developed model we refine the signal subspace so as to enhance the performance of the DOA estimation. In the proposed scheme, we define a fuzzy similarity matrix for the eigenvalues of the array output correlation matrix to capture the distribution of the eigenvalues. Then, we build up a transformation matrix between the fuzzy similarity matrix and the eigenspace of the correlation matrix, and construct a nonlinear transformation function to adjust the fuzzy similarity matrix. Subsequently, we define a supervised evaluation index named signal subspace reconstruction error for DOA estimation and construct a cost function of the signal subspace to develop a supervised model for the signal subspace. The signal subspace can be modified through adjusting the parameter in the nonlinear transformation function and optimizing the abovementioned cost function. Finally, the performance of DOA estimation can be enhanced with the modified signal subspace. The main characteristic of the proposed model is circularly applied feedback of the estimated DOA for refining the estimated subspace. It is a closed loop and supervised method not reported before. This article opens a specific way for improving the performance of the DOA estimation in array signal processing by a supervised index. However, the proposed method is still unsatisfying in some scopes of signal-to-noise ratio. We believe that exploiting a validity index for DOA estimation in array signal processing is still a general and interesting problem. [ABSTRACT FROM AUTHOR]

Monitoring the operating conditions of residential appliances by collecting the total power consumption data of households has a great significance for smart power utilization. In this study, a graph least squares reconstruction approach is proposed. First, the graph signal is constructed using the collected active power consumption data, providing unique appliance signature information. The signal smoothness of the graph and an iterative least squares reconstruction algorithm are utilized for classification. The proposed graph reconstruction method relies on only low-sampling data from installed smart meters. It aims to address some existing problems of event-based NILM methods like measurement noise, indistinguishable load signatures, and inaccurate power reconstruction. Also, extensive training and associated calculations are not required. Simulation results on the REDD benchmark dataset demonstrate that the proposed method outperforms some of the current state-of-the-art techniques. [ABSTRACT FROM AUTHOR]

Computational microwave imaging (CMI) based on the frequency diversity metasurface apertures (FDMAs) is an emerging technology and has attracted wide attention. FDMA-based CMI (FDMA-CMI) can be considered as microwave compressive sensing imaging with the frequency diversity pattern of the FDMA being the sensing matrix and solved by sparse signal reconstruction algorithms. However, the imaging quality is affected by the sensing matrix error and off-grid error seriously. In this article, we propose a novel algorithm for FDMA-CMI, referred to as off-grid sparse Bayesian learning (SBL) method based on sinc interpolation (OGSISBL), by taking both the off-grid error and sensing matrix error into account. First, we establish the measurement model with both the off-grid error and sensing matrix error. Specifically, the off-grid error is represented as a set of parameters to be estimated in the measurement model, and the sensing matrix error is represented as the amplitude–phase drift of the transceiver channels of the imaging system due to the principle of the FDMA. Then, under the framework of the SBL, a robust imaging algorithm OGSISBL is developed via the variational Bayesian expectation maximization (VBEM), which can not only recover the amplitude and position of the return of the scattered, but also simultaneously calibrate the amplitude–phase drift of the transceiver channels and the off-grid error. The performance of the proposed algorithm is evaluated by both the simulation data and the measured data collected by the self-designed experimental FDMA-CMI system, and the results validate the effectiveness and robustness of the proposed method. [ABSTRACT FROM AUTHOR]

Traditional signal postprocessing methods suffer from the repeated assignment problem (RAP), which can result in inaccurate instantaneous frequency (IF) estimation and signal recovery. In this article, to solve this problem, a novel time-frequency (TF) analysis (TFA) method called the synchro-reassigning transform (SRT) is proposed. This method aims to obtain the ideal TF representation (TFR) by utilizing derivatives of the constructed amplitude function and a three-step selection rule to adaptively extract the TF coefficients on the IF trajectories in the TF plane, and reassigning these TF coefficients into a new TFR. In this way, SRT can eliminate the RAP, thus obtaining an approximately ideal TFR that helps to realize more accurate IF estimation and signal reconstruction. Furthermore, SRT shows satisfactory performance on signals with high nonlinear IFs or relatively close IFs, even under strong noise conditions. Two simulated signal and three real-life signals were used to demonstrate the performance of SRT. [ABSTRACT FROM AUTHOR]

Phase retrieval (PR) is about reconstructing a signal from the magnitude of a number of its complex-valued linear measurements. Recent rapid progress has been made on the development of neural network (NN) based methods for PR. Most of these methods employ pre-trained NNs for modeling target signals, and they require collecting large-scale datasets with ground-truth signals for pre-training, which can be very challenging in many scenarios. There are a few unsupervised learning methods employing untrained NN priors for PR which avoid using external datasets; however, their performance is unsatisfactory compared to pre-trained-NN-based methods. This paper proposes an unsupervised learning method for PR which does not rely on pre-trained NNs while providing state-of-the-art performance. The proposed method trains a randomly-initialized generative NN for signal reconstruction directly on the magnitude measurements of a target signal, which approximates the minimum mean squared error estimator via dropout-based model averaging. Such a model-averaging-based approach provides a better internal prior for the target signal than existing untrained-NN-based methods. The experiments on image reconstruction demonstrate both the advantage of our method over existing unsupervised methods and its competitive performance to pre-trained-NN-based methods. [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]

Conventionalliterature on array signal processing (ASP) is based on the “capture first, process later” philosophy and to this end, signal processing algorithms are typically decoupled from the hardware. This poses fundamental limitations because if the sensors result in information loss, the algorithms may no longer be able to achieve their guaranteed performance. In this paper, our goal is to overcome the barrier of information loss via sensor saturation and clipping. This is a significant problem in application areas including physiological monitoring and extra-terrestrial exploration where the amplitudes may be unknown or larger than the dynamic range of the sensor. To overcome this fundamental bottleneck, we propose “computational arrays” which are based on a co-design approach so that a collaboration between the sensor array hardware and algorithms can be harnessed. Our work is inspired by the recently introduced unlimited sensing framework. In this context, our computational arrays encode the high-dynamic-range information by folding the signal amplitudes, thus introducing a new form of information loss in terms of the modulo measurements. On the decoding front, we develop mathematically guaranteed recovery algorithms for spatio-temporal array signal processing tasks that include DoA estimation, beamforming and signal reconstruction. Numerical examples corroborate the applicability of our approach and pave a path for the development of novel computational arrays for ASP. [ABSTRACT FROM AUTHOR]

Global navigation systems (GNSS) receivers are designed to be highly accurate. Next generation receivers may also need to provide high flexibility to exploit the probabilities of new specifications and algorithms. Quadrature bandpass sampling (QBPS) RF front-ends offer a possible architecture to meet this requirement. For QBPS, delay offset errors between analog-to-digital converters will introduce phase distortions. Quantification of the effects of these distortions on signal reconstruction was performed and characterized using image rejection ratio (IRR). This article investigates the best delay offset when using QBPS in multiband systems. It first analyzes the combined effect of delay offset error and in-band frequency offset for a single frequency component, then a combined IRR is defined for multiband receivers. Also, a delay offset setting scheme is proposed to maximize the combined IRR. The results show that, for a specific GNSS all-system receiver, the optimal delay offset is 158.7ps in noise-free conditions. Further, the optimal delay offset can be shifted in the presence of sampling jitter. [ABSTRACT FROM AUTHOR]

Objective: To investigatecardiac activation maps estimated using electrocardiographic imaging and to find methods reducing line-of-block (LoB) artifacts, while preserving real LoBs. Methods: Body surface potentials were computed for 137 simulated ventricular excitations. Subsequently, the inverse problem was solved to obtain extracellular potentials (EP) and transmembrane voltages (TMV). From these, activation times (AT) were estimated using four methods and compared to the ground truth. This process was evaluated with two cardiac mesh resolutions. Factors contributing to LoB artifacts were identified by analyzing the impact of spatial and temporal smoothing on the morphology of source signals. Results: AT estimation using a spatiotemporal derivative performed better than using a temporal derivative. Compared to deflection-based AT estimation, correlation-based methods were less prone to LoB artifacts but performed worse in identifying real LoBs. Temporal smoothing could eliminate artifacts for TMVs but not for EPs, which could be linked to their temporal morphology. TMVs led to more accurate ATs on the septum than EPs. Mesh resolution had anegligible effect on inverse reconstructions, but small distances were important for cross-correlation-based estimation of AT delays. Conclusion: LoB artifacts are mainly caused by the inherent spatial smoothing effect of the inverse reconstruction. Among the configurations evaluated, only deflection-based AT estimation in combination with TMVs and strong temporal smoothing can prevent LoB artifacts, while preserving real LoBs. Significance: Regions of slow conduction are of considerable clinical interest and LoB artifacts observed in non-invasive ATs can lead to misinterpretations. We addressed this problem by identifying factors causing such artifacts. [ABSTRACT FROM AUTHOR]

Sparse Bayesian learning (SBL) is a popular and robust algorithm for sparse signal reconstruction (SSR). Unfortunately, the SBL algorithm suffers from heavy computational complexity when it is implemented directly since the inversion and multiplying operations of the estimation of the covariance matrix are involved in each iteration, which is proportional to the cube of the observed data length and thus prevents it solving large-scale problems. In many applications, such as radar imaging and array signal processing, the signal to be recovered is sparse in the Fourier dictionary. In this article, we propose an efficient implementation method for the Fourier dictionary-based SBL (FD-SBL). In the case that the Fourier dictionary is adopted, the estimation of the covariance matrix is a Toeplitz matrix for 1-D data or a Toeplitz-block-Toeplitz (TBT) matrix for 2-D data during the FD-SBL iterations. By utilizing this property, we employ the Gohberg–Semencul (G-S)-type factorization to accelerate the implementation of FD-SBL. To be noted, there is no approximation in our proposed method, and the computational cost is reduced by several orders of magnitude compared with the direct implementation of SBL. Finally, the experimental results verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Spectrograms are fundamental tools in time-frequency analysis, being the squared magnitude of the so-called short time Fourier transform (STFT). Signal analysis via spectrograms has traditionally explored their peaks, i.e. their maxima. This is complemented by a recent interest in their zeros or minima, following seminal work by Flandrin and others, which exploits connections with Gaussian analytic functions (GAFs). However, the zero sets (or extrema) of GAFs have a complicated stochastic structure, complicating any direct theoretical analysis. Standard techniques largely rely on statistical observables from the analysis of spatial data, whose distributional properties for spectrograms are mostly understood only at an empirical level. In this work, we investigate spectrogram analysis via an examination of the stochastic geometric properties of their level sets. We obtain rigorous theorems demonstrating the efficacy of a spectrogram level sets based approach to the detection and estimation of signals, framed in a concrete inferential set-up. Exploiting these ideas as theoretical underpinnings, we propose a level sets based algorithm for signal analysis that is intrinsic to given spectrogram data, and substantiate its effectiveness via extensive empirical studies. Our results also have theoretical implications for spectrogram zero based approaches to signal analysis. To our knowledge, these results are arguably among the first to provide a rigorous statistical understanding of signal detection and reconstruction in this set up, complemented with provable guarantees on detection thresholds and rates of convergence. [ABSTRACT FROM AUTHOR]

In this paper, a novel energy flow analysis (EFA) is proposed based on the signal reconstruction and decomposition to investigate the electromechanical oscillations. In contrast to the conventional EFA, the connection between the proposed EFA and modal analysis (MA) can be quantitatively revealed for arbitrary models of synchronous generators in multi-machine power systems. Firstly, the time-domain implementation (TDI) of the proposed EFA is designed. Specifically, the measurements at the terminal of a local generator are reconstructed through an exponential operator and then decomposed with respect to an angular frequency. Then, the mode-screened damping torque coefficient is defined to extract the damping feature with respect to an electromechanical oscillation mode. After that, the frequency-domain implementation (FDI) is derived. Specifically, the Parseval's Theorem is applied to transform the proposed EFA from the time domain to frequency domain. On this basis, the consistency between the proposed EFA and MA is strictly proved, which is applicable for arbitrary models of synchronous generators in multi-machine power systems. Additionally, the application procedure of the proposed EFA in investigating electromechanical oscillations is given. Finally, the proposed EFA are substantially demonstrated in multiple case studies. [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]

Objective: Nocturnal recordings of heart rate and respiratory rate usually require several separate sensors or electrodes attached to different body parts – a disadvantage for at-home screening tests and for large cohort studies. In this paper, we demonstrate that a state-of-the-art accelerometer placed at subjects’ wrists can be used to derive reliable signal reconstructions of heartbeat (pulse wave intervals) and respiration during sleep. Methods: Based on 226 full-night recordings, we evaluate the performance of our signal reconstruction methodology with respect to polysomnography. We use a phase synchronization analysis metrics that considers individual heartbeats or breaths. Results: The quantitative comparison reveals that pulse-wave signal reconstructions are generally better than respiratory signal reconstructions. The best quality is achieved during deep sleep, followed by light sleep N2 and REM sleep. In addition, a suggested internal evaluation of multiple derived reconstructions can be used to identify time periods with highly reliable signals, particularly for pulse waves. Furthermore, we find that pulse-wave reconstructions are hardly affected by apnea and hypopnea events. Conclusion: During sleep, pulse wave and respiration signals can simultaneously be reconstructed from the same accelerometer recording at the wrist without the need for additional sensors. Reliability can be increased by internal evaluation if the reconstructed signals are not needed for the whole sleep duration. Significance: The presented methodology can help to determine sleep characteristics and improve diagnostics and treatment of sleep disorders in the subjects’ normal sleep environment. [ABSTRACT FROM AUTHOR]

Based on the ensemble empirical mode decomposition (EEMD) method, a DAF method for signal construction is proposed that repeatedly decomposes (D) the signal, amplifies (A) the local signal characteristics, and then filters (F) the signal. This method is used to decompose and reconstruct the electric field waveform (called a sferic) of an energetic in-cloud pulse (EIP) with a 247-kA peak current detected by a fast antenna (FA). Based on synchronous sub-microsecond very high-frequency (VHF, 14–88 MHz) radio interferometer (INTF) observations and observed downward fast positive and upward fast negative breakdowns, which occurred simultaneously with the EIP, the EIP sferic is decomposed by the DAF method in 11 steps into two independent sferics: a smoother filtered EIP sferic and an embedded narrow bipolar-like event (NBE). It is verified that strong VHF radiation is generated by the NBE-like event, rather than being associated with the smooth EIP sferic. The analysis, decomposition, and reconstruction of the correlated signals by the EEMD-based DAF method proposed in this article support the idea that the large-amplitude EIP sferic was generated by relativistic discharge responsible for an accompanying terrestrial gamma-ray flash (TGF) rather than by streamer or leader activity. [ABSTRACT FROM AUTHOR]

Multichannel SAR system operating in the sliding spotlight mode has the capacity of imaging with very high resolution as requested by future spaceborne synthetic aperture radar (SAR) mission; hence, it has been attracted more and more attention in the SAR community. In a multichannel sliding spotlight SAR system with $N$ channels, the overall Doppler bandwidth of the data acquired by each channel is greater than $N \cdot \text {PRF}$ ; thus, the preprocessing algorithms (channel mismatch calibration and signal reconstruction) are no more available. To address this issue, a full-aperture imaging method for azimuth multichannel sliding spotlight mode is proposed in this article. First, the raw data of each channel need to be preprocessed based on a deramping operation, which can obtain an unambiguous Doppler spectrum. Afterward, the algorithm proposed for single-channel sliding spotlight mode can be performed. Finally, to avoid possible back-folded SAR images, postprocessing after focusing is demanded in some cases. The imaging results of the data acquired by GaoFen-3 (GF-3) are given for the first time in this article, which proves the effectiveness of the proposed imaging method and demonstrates the capacity of high-resolution wide-swath imaging of the multichannel sliding spotlight mode. [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]

To achieve high resolution, orthogonal frequency division multiplex (OFDM) radars deploy two-dimensional multiple signal classification (2D-MUSIC) in the joint range-velocity estimator. However, it is obvious that both of the signal reconstruction and 2D smoothing affect the noise statistical distribution and virtual array aperture in the joint range-velocity estimator with 2D-MUSIC. Therefore, the conventional accuracy analysis methods for the MUSIC are no longer suitable. In this paper, we propose an estimation accuracy analysis for the joint range-velocity estimator with 2D-MUSIC. Firstly, we present that the noise statistical distribution of the signals being reconstructed and 2D smoothed has a 2-fold Hankel structure. Then, the closed-forms of the range and velocity estimation accuracies are derived, respectively, which both show that the estimation accuracies highly depend on the 2D smoothing and could be improved by properly choosing the 2D smoothing window. Further, we formulate the smoothing optimization and propose the quasi-optimal size of the 2D smoothing window. Finally, both theoretical analyses and simulations validate that the proposed smoothing optimization could significantly improve the estimation accuracies with a lower computational burden than the conventional smoothing. [ABSTRACT FROM AUTHOR]

We address the problem of the reconstruction of time-frequency characteristics of sparse multi-band signals by using the discrete multi-coset sampling (DMCS) model. In this article, the signal is characterized by complicated time-variable components. According to the feature of the short-time Fourier transform (STFT) analysis method, we obtain the rewritten matrix form of the discrete STFT. Then, an analysis method of the multi-coset sliding window (MCSW) is proposed, and the discrete multi-coset sampling sequence is locally windowed. The sparse signal reconstruction algorithm is used to obtain the optimal time-frequency reconstruction value of the original signal. Numerical simulations show the feasibility of this method. We simulate the effects of measurement noise, sampling rate, and time-frequency analysis parameters on the reconstruction accuracy. Our method can carry out time-frequency reconstruction for undersampled signals obtained from multi-coset sampling to ensure the time-varying feature of the original signals, which can well highlight the characteristics of signals. The method is of great significance to the research and development of the sub-Nyquist sampling technique. [ABSTRACT FROM AUTHOR]

Error vector magnitude (EVM) or alternately offset EVM (OEVM) is one of the most important performance to verify for RF circuits, such as ZigBee transmitters in order to ensure that the quality of the generated modulated signal complies with the requirements of the wireless communication standard. The conventional solution to measure this performance relies on the use of an automatic test equipment (ATE) equipped with expensive RF channels. This article presents a low-cost solution that permits to realize EVM measurement using only a standard digital ATE. The approach is based on 1-bit undersampled acquisition of the RF modulated signal by a digital tester channel associated with a specifically tailored processing algorithm. This algorithm involves many different steps that are detailed in this article, including phase and amplitude fluctuation extraction, RF signal reconstruction, symbol clock recovery, symbol bits detection, and synthesis of reference data for EVM calculation. The proposed digital test solution is first evaluated through lab hardware experiments and then validated with EVM measurements on an industrial ATE. [ABSTRACT FROM AUTHOR]

Deep unfolding methods design deep neural networks as learned variations of optimization algorithms through the unrolling of their iterations. These networks have been shown to achieve faster convergence and higher accuracy than the original optimization methods. In this line of research, this paper presents novel interpretable deep recurrent neural networks (RNNs), designed by the unfolding of iterative algorithms that solve the task of sequential signal reconstruction (in particular, video reconstruction). The proposed networks are designed by accounting that video frames’ patches have a sparse representation and the temporal difference between consecutive representations is also sparse. Specifically, we design an interpretable deep RNN (coined reweighted-RNN) by unrolling the iterations of a proximal method that solves a reweighted version of the $\ell _{1}$ - $\ell _{1}$ minimization problem. Due to the underlying minimization model, our reweighted-RNN has a different thresholding function (alias, different activation function) for each hidden unit in each layer. In this way, it has higher network expressivity than existing deep unfolding RNN models. We also present the derivative $\ell _{1}$ - $\ell _{1}$ -RNN model, which is obtained by unfolding a proximal method for the $\ell _{1}$ - $\ell _{1}$ minimization problem. We apply the proposed interpretable RNNs to the task of video frame reconstruction from low-dimensional measurements, that is, sequential video frame reconstruction. The experimental results on various datasets demonstrate that the proposed deep RNNs outperform various RNN models. [ABSTRACT FROM AUTHOR]

As a typical nonstationary signal, rolling bearing fault signals exhibit dynamic characteristics and low signal-to-noise ratio, which lead to fuzzy spectrograms from traditional time–frequency analysis (TFA) methods. It is a challenging task to accurately represent its instantaneous frequency (IF) trajectory. To solve this problem, this article proposes a TFA method which is called match-extracting chirplet transform for analyzing multicomponent dynamic signals. It generates a time–frequency (TF) representation of high energy concentration by constructing a basis function that matches the chirp rate with the original signal at any TF point. A matching extraction operator is built to extract the best matching ridges on the IF trajectory to further improve the quality of the spectrum. The proposed method can effectively characterize the dynamic characteristics of multicomponent signals and reduce the energy divergence. Meanwhile the algorithm retains signal reconstruction and can be used to recover significant components by adaptively searching modal ridges. Numerical verification shows that this method has a better performance in TF location and noise robustness. Finally, the validity of this method in mechanical fault diagnosis is verified by applying it to actual bearing signals. [ABSTRACT FROM AUTHOR]

Nuclear magnetic resonance (NMR) spectroscopy, whose time domain data is modeled as the sum of damped exponential signals, has become an indispensable tool in various scenarios, such as biomedicine, biology, and chemistry. NMR spectroscopy signals, however, are usually corrupted by Gaussian noise in practice, raising difficulties in sequential analysis and quantification. The low-rank Hankel property of exponential signals plays an important role in the denoising issue, but selecting an appropriate parameter still remains a problem. In this work, we explore the effect of the regularization parameter of a convex optimization denoising method based on low-rank Hankel matrices for exponential signals corrupted by Gaussian noise. An accurate estimate on the spectral norm of weighted Hankel matrices is provided as a guidance to set the regularization parameter. The bound can be efficiently calculated since it only depends on the standard deviation of the noise and a constant. Aided by the bound, one can easily obtain an auto-setting regularization parameter to produce promising denoised results. Our results on synthetic and realistic NMR spectroscopy data demonstrate a superior denoising performance of the proposed approach over typical Cadzow and the state-of-the-art QR decomposition methods, especially in the low signal-to-noise ratio regime. [ABSTRACT FROM AUTHOR]

Time–frequency (TF) analysis (TFA) provides an effective tool to characterize nonstationary signals with time-varying features. However, the TFA of gas turbine’s vibration signals is a challenging topic due to high complexity and strong nonstationarity. There is an obstacle to generate more accurate and sharper TF results for such multicomponent signals. This article proposes a novel TFA technique, named local maximum synchrosqueezing chirplet transform (LMSSCT), to deal with this problem. This method can not only well match window function and modulated frequency but produce an unbiased instantaneous frequency (IF) estimator to correct the deviation caused by strong frequency modulation (FM) in TF results. We give the theoretical analysis that this method is an improvement of classical local maximum synchrosqueezing transform (LMSST), and we also prove that it allows for perfect signal reconstruction. The numerical validation shows that the proposed method can be employed to effectively address the multicomponent signals with complex FM laws, even those with heavy noise. The experimental analysis on the test-bench signal and the vibration signal of a dual-rotor gas turbine validates that this method can capture more detailed features that are helpful to identify the origins of abnormal vibration of gas turbine. [ABSTRACT FROM AUTHOR]

Synchrosqueezing transform (SST) is a currently proposed novel postprocessing time–frequency (TF) analysis tool. It has been widely shown that SST is able to improve TF representation. However, so far, how to improve the TF resolution while ensuring the accuracy of signal reconstruction is still an open question, particularly for the vibration signal with time-varying instantaneous frequency (IF) characteristics, due to the fact that the vibration signals of mechanical equipment usually contain many types of noise generated by harsh operating conditions, and the SST will mix these noise into the real signal. Our first contribution is using the Gaussian modulated linear chirp (GMLC) signal model to represent the general nonstationary signals. The GMLC signal model can more accurately represent the time-varying nonstationary signal, compared with the SST signal model composed of linear phase function and constant amplitude. Our second contribution in this work is proposing a method to improve the TF resolution and reconstruction accuracy for nonstationary signals with time-varying IF, which we coined the second-order synchroextracting transform (SET2). In SET2, we apply the GMLC to deduce the nonstationary signal model and then only use the energy at the IF to characterize the TF distribution, which improves the TF while reducing the impact of noise on the real signal. [ABSTRACT FROM AUTHOR]

Phaseless measurement is widely used in various fields, and phase retrieval is a key step in signal reconstruction of phaseless measurement. The occurrence of outliers will cause the optimal solution of the traditional phase retrieval objective function to deviate from the original signal, thereby reducing the reconstruction accuracy. This article modifies the objective function by introducing a weight vector so that its optimal solution will still approximate the original signal when outliers appear and proposes a specific implementation strategy for this idea under the background of Fourier phase retrieval. For the weight vector, we design a two-channel measurement structure using a discrete Fourier transform frequency-domain cyclic shift theorem and mask technique to obtain a weight vector. For the improved objective function, we use the majorization–minimization framework to derive an iterative algorithm to get an optimal solution. Extensive simulation and hardware experiments show that the proposed method can effectively suppress the adverse effects of outliers. [ABSTRACT FROM AUTHOR]

Lift-offs of the sensor could significantly affect the measurement signal and reconstruction of material properties when using the electromagnetic (inductive) eddy current (EC) sensor. Previously, various methods (including novel sensor designs, and features like zero-crossing frequency, lift-off point of intercept) have been used for eliminating the measurement error caused by the lift-off distance effect of the sensor. However, these approaches can only be applied for a small range of lift-off variations. In this article, a linear relationship has been found between the sensor lift-off and ratio of dual-frequency EC signals, particularly under the high working dual frequencies. Based on this linear relationship, the lift-off variation can be reconstructed first with a small error of 2.5% when its actual value is up to 10 mm (10.1% for 20 mm). The reconstructed lift-off is used to further get the property of the material under a low single frequency. Experiments on different ferrous metals have been carried out for the testing of the reconstruction scheme. Since the inductance is more sensitive to the material property (and less sensitive to the lift-off) under low frequencies, the reconstruction error of the material property is much smaller than that of the lift-off, with 1.4% under 12 mm (and 4.5% under 20 mm). [ABSTRACT FROM AUTHOR]

Image reconstruction from discrete samples is fundamental in remote sensing. The reconstruction problem is more complicated when the sample locations are irregularly spaced and employ different aperture functions. Further, not all 2-D sampling configurations permit full image reconstruction of band-limited signals. In this article, 2-D signal reconstruction from irregular samples with variable apertures is considered using theory and examples. Exact reconstruction requires that the signal be band-limited and the sampling matrix be invertable. The results are sensitive to the sample locations and noise in the measurements. Illustrative examples are provided using simulation and actual data from the L-band Soil Moisture Active Passive (SMAP) radiometer. The general approach can be employed with other sensors. [ABSTRACT FROM AUTHOR]

A signal processing technique is presented for determining the composition of multiphase oil–water–gas flow in a pipe using noninvasive ultrasonic speed of sound measurements from a transmitter–receiver pair bonded to diametrically opposite sides of a pipe. A linear chirp excitation is used to send broadband ultrasonic energy that propagates in two paths from transmitter to receiver such as: 1) a wave through the pipe wall and then the multiphase mixture and 2) ultrasonic guided waves along the pipe wall in the circumferential direction. As the ultrasonic attenuation of the multiphase mixture increases, the amplitude of the signal through the fluid mixture decreases relative to that of circumferential guided waves, making it difficult to determine the time of arrival of the fluid-path signal and, hence, the speed of sound in the mixture. The proposed signal processing technique overcomes this challenge by using: 1) a guided wave subtraction approach to suppress the strength of guided wave signals relative to the fluid-path signal and 2) a Gaussian reconstruction approach for synthetic enhancement of the fluid-path signal by output signal reconstruction at frequencies corresponding to peak transmission of ultrasonic energy. The efficacy of the technique is demonstrated using experiments carried out in a field-scale flow loop with varying compositions of oil–water–gas mixtures. It is shown that the proposed approach can enhance the signal detectability by approximately 20 dB in comparison with the traditional approach that does not utilize guided wave subtraction and also improves the gas tolerance of composition measurements up to 20% in gas volume fraction. [ABSTRACT FROM AUTHOR]

Accurate rotor position is necessary for high-performance control of a permanent-magnet synchronous motor. Compared with the methods using position sensors to detect rotor position, the sensorless methods can simplify the motor structure and enhance the reliability. To improve the estimation accuracy of sensorless methods, the position error correction method based on the low-order harmonic suppression is proposed in this article. The low-order harmonics generated by the position error are analyzed in detail, which will cause extra motor losses. The position error signal can be reconstructed by low-order harmonics that are extracted by rotating the frame transformation and low-pass filter. And the estimated position can be corrected using the reconstructed signal. The proposed method can not only improve the position estimation accuracy, but also suppress the low-order harmonics, which can reduce motor losses and enhance the motor performance. Based on space vector pulsewidth modulation, the proposed method is independent of motor parameters. It can be applied to the sensorless methods that can obtain voltages. The position error correction method has well dynamic performance and great robustness. The effectiveness is verified by the experiments on the turbo molecular pump. [ABSTRACT FROM AUTHOR]

A theoretical framework for photoacoustic (PA) signal simulation using a discrete particle approach is discussed, and the tomographic image reconstruction using such signals is reported. Various numerical phantoms in two dimensions were constructed by inserting monodisperse/polydisperse solid circles/disks of uniform strength occupying regular or random locations within the imaging region. In particular, a blood vessel network phantom was simulated by positioning solid circles mimicking red blood cells randomly within the vessel using a Monte Carlo method. The PA signal from a single disk was obtained by numerically evaluating the analytical formula, and then, such signals from many disks were summed up linearly to generate the resultant signals at detector locations. Classical backprojection and time-reversal algorithms were employed to form reconstructed images. Two model-based approaches, namely impulse response-based (IRB) and interpolation-based (IPB) methods, were also deployed for image reconstruction. Some standard parameters were calculated to assess the performance of these reconstruction algorithms. The simulation results demonstrate that the Monte Carlo method can be applied in practice for the fast simulation of tissue realization keeping microscopic details intact, and accordingly, PA signals can be calculated for photoacoustic tomography (PAT) imaging. Furthermore, the IRB technique produces images with superior quality and outperforms other algorithms. [ABSTRACT FROM AUTHOR]

A low-power differential input to single-ended output digital-to-analog converter (DAC) is presented, which is capable of providing radio frequency (RF)-signals with a data rate of up to $\mathrm {8~G}$ bit/s. A constant direct current (dc) current source is realized as a self-bootstrapping device in the presented 0.25- $\mu \text{m}$ in-house gallium nitride (GaN) technology. First, measurements with a low-power [1-V peak–peak voltage ($V_{pp}$)] differential input signal show the feasibility of switching constant currents with a clock frequency of up to 2 GHz. Furthermore, a 2-b DAC that uses a differential sampling to generate RF-signals is introduced. Measurement results prove the feasibility of synthesizing custom-modulated voltage waveforms with data rates of up to 8 Gbit/s in the sub-6-GHz frequency range. [ABSTRACT FROM AUTHOR]

The impulse features in a condition monitoring (CM) signal usually imply the occurrence of a defect in a rotating machine. To accurately capture the impulse components in a CM signal, a concentrated time-frequency analysis (TFA) method based on time-reassigned synchrosqueezing transform (TSST) is proposed. First, the limitation of the TSST method in dealing with strong frequency-varying signals is explored. Second, an iteration procedure is introduced to address the blurry time frequency representation problem of TSST. The convergence of the iteration algorithm is also analyzed. Finally, an algorithm is proposed to extract the impulse features for signal reconstructions, which are also useful for an accurate diagnosis of the fault type. A simulated noise-contaminated signal and three sets of experimental data are employed in this article to evaluate the performance of the proposed method. Results obtained from this article confirm that the proposed method has a better performance in dealing with impulsive-like signals than other TFA methods. [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]

A new inverse synthetic aperture radar (ISAR) imaging framework is proposed to obtain high cross-range resolution under sparse aperture conditions, which is a challenge when the signal-to-noise ratio is low. Motivated by the sparsity and low rank of target’s 2-D distribution, the imaging problem is converted to the simultaneously sparse and low-rank signal matrix reconstruction problem under multiple measurement vector (MMV) model, and a novel reconstruction method based on joint constraints of sparsity and low rank is proposed. Due to the over-relax problem, the traditional convex optimization method cannot achieve a better performance using joint structures than exploiting just one of the constraints. As such, a nonconvex penalty function is introduced. To avoid the local minima, the convexity of the cost function should be ensured when constructing the nonconvex penalty function. The adaptive filtering framework, which is a powerful way to recovery the sparse low-rank matrix accurately from its noisy observation, is adopted as a reconstruction algorithm. Furthermore, the optimal step size formula and the idea of smoothed zero norm are used to enhance the convergence and the ability to suppress noise. The newly proposed method is verified by the simulation experiment, which has a better performance in image quality, robustness to noise, and imaging speed. [ABSTRACT FROM AUTHOR]

We propose an entirely redesigned framework of bandlimited signal reconstruction for the time encoding machine (TEM) introduced by Lazar and Tóth. As the encoding part of TEM consists in obtaining integral values of a bandlimited input over known time intervals, it theoretically amounts to applying a known linear operator on the input. We then approach the general question of signal reconstruction by pseudo-inversion of this operator. We perform this task numerically and iteratively using projections onto convex sets (POCS). The algorithm can be implemented exactly in discrete time with multiplications that are all reduced to scaling by signed powers of two, thanks to the use of relaxation coefficients. Meanwhile, the algorithm achieves a rate of convergence similar to that of Lazar and Tóth. For real-time processing, we propose an approximate time-varying FIR implementation, which avoids the splitting of the input into blocks. We finally propose some preliminary semi-convergence analysis of the algorithm under data noise. [ABSTRACT FROM AUTHOR]