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In this article, a continuous-time complex-valued projection neural network (CCPNN) in a matrix state space is first proposed for a general complex-variable basis pursuit problem. The proposed CCPNN is proved to be stable in the sense of Lyapunov and to be globally convergent to the optimal solution under the condition that the sensing matrix is not row full rank. Furthermore, an improved discrete-time complex projection neural network (IDCPNN) is proposed by discretizing the CCPNN model. The proposed IDCPNN consists of a two-step stop strategy to reduce the calculational cost. The proposed IDCPNN is theoretically guaranteed to be global convergent to the optimal solution. Finally, the proposed IDCPNN is applied to the reconstruction of sparse signals based on compressed sensing. Computed results show that the proposed IDCPNN is superior to related complex-valued neural networks and conventional basis pursuit algorithms in terms of solution quality and computation time.

As one of the most effective technologies for network reconstruction, compressive sensing can recover signals from a small amount of observed data through sparse search or greedy algorithms in the assumption that the unknown signal is sufficiently sparse on a specific basis. However, there often occurs loss of precision even failure in the process of reconstruction without enough prior information. Therefore, the purpose of this article is to solve the problem of low reconstruction accuracy by mining implicit structural information in the network. Specifically, we propose a novel and efficient algorithm (MCM_TRA) for reconstructing the structure of the K -forked tree network. Based on evolutionary game dynamics, the modified clustering method (MCM) classifies all nodes into two sets, then a two-stage reconstruction algorithm (TRA) is illustrated to recover the node signals in different sets. The experimental results demonstrate that the MCM_TRA enhances the reconstruction accuracy prominently than previous algorithms. Moreover, extensive sensitivity analysis shows that the reconstruction effect can be promoted for a broad range of parameters, which further indicates the superiority of the proposed method.

Motivation In silico saturation mutagenesis (ISM) is a popular approach in computational genomics for calculating feature attributions on biological sequences that proceeds by systematically perturbing each position in a sequence and recording the difference in model output. However, this method can be slow because systematically perturbing each position requires performing a number of forward passes proportional to the length of the sequence being examined. Results In this work, we propose a modification of ISM that leverages the principles of compressed sensing to require only a constant number of forward passes, regardless of sequence length, when applied to models that contain operations with a limited receptive field, such as convolutions. Our method, named Yuzu, can reduce the time that ISM spends in convolution operations by several orders of magnitude and, consequently, Yuzu can speed up ISM on several commonly used architectures in genomics by over an order of magnitude. Notably, we found that Yuzu provides speedups that increase with the complexity of the convolution operation and the length of the sequence being analyzed, suggesting that Yuzu provides large benefits in realistic settings. Availability and implementation We have made this tool available at https://github.com/kundajelab/yuzu.

Millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) systems typically employ hybrid mixed signal processing to avoid expensive hardware and high training overheads. However, the lack of fully digital beamforming at mmWave bands imposes additional challenges in channel estimation. Prior art on hybrid architectures has mainly focused on greedy optimization algorithms to estimate frequency-flat narrowband mmWave channels, despite the fact that in practice, the large bandwidth associated with mmWave channels results in frequency-selective channels. In this paper, we consider a frequency-selective wideband mmWave system and propose two deep learning (DL) compressive sensing (CS) based algorithms for channel estimation. The proposed algorithms learn critical apriori information from training data to provide highly accurate channel estimates with low training overhead. In the first approach, a DL-CS based algorithm simultaneously estimates the channel supports in the frequency domain, which are then used for channel reconstruction. The second approach exploits the estimated supports to apply a low-complexity multi-resolution fine-tuning method to further enhance the estimation performance. Simulation results demonstrate that the proposed DL-based schemes significantly outperform conventional orthogonal matching pursuit (OMP) techniques in terms of the normalized mean-squared error (NMSE), computational complexity, and spectral efficiency, particularly in the low signal-to-noise ratio regime. When compared to OMP approaches that achieve an NMSE gap of {4-10} dB with respect to the Cramer Rao Lower Bound (CRLB), the proposed algorithms reduce the CRLB gap to only {1-1.5} dB, while reducing complexity by two orders of magnitude.

In this paper, we propose a compressive sampling and reconstruction system based on the shift-invariant space associated with the fractional Gabor transform. With this system, we aim to achieve the sub-Nyquist sampling and accurate reconstruction for chirp-like signals containing time-varying characteristics. Under the proposed scheme, we introduce the fractional Gabor transform to make a stable expansion for signals in the joint time-fractional-frequency domain. Then the compressive sampling and reconstruction system is constructed under the compressive sensing and shift-invariant space theory. We establish the reconstruction model and propose a block multiple response extension of sparse Bayesian learning algorithm to improve the reconstruction effect. The reconstruction error for the proposed system is analyzed. We show that, with considerations of noises and mismatches, the total error is bounded. The effectiveness of the proposed system is verified by numerical experiments. It is shown that our proposed system outperforms the other systems state-of-the-art.

It is challenging to acquire accurate channel knowledge for sufficient beamforming gain because of the large number of antennas. In this paper, a deep learning aided channel estimation algorithm is proposed for mmWave cellular systems, in which both the base station (BS) and mobile station (MS) gain directional beamforming by employing large antenna arrays. We consider the off-grid (OG) mmWave channel estimation and propose a deep network architecture for solving this problem, which is different from most existing works concerning the compressed sensing (CS)-based channel estimation. Firstly, the off-grid channel model is used to relieve the basis mismatch issue by exploiting first-order Taylor-series approximation of the array manifold taken on a fixed grid of both BS and MS. Secondly, a new formulation of this off-grid channel estimation problem is solved by using a low computational complexity alternating direction method of multipliers (ADMM)-based algorithm, dubbed ADMM-OG algorithm. Thirdly, the idea of algorithm unrolling guides us to design a deep network architecture ADMM-OGChannelNet corresponding to the ADMM-OG algorithm for the mmWave channel estimation. Based on the interpretability of this deep network architecture, the optimal parameters of this network can be learned without tuning in a hand-crafted way. The Cramer-Rao bound (CRB) of the off-grid channel model is derived for performance comparison as well. Finally, from the simulation results, we can verify that the ADMM-OGChannelNet has better estimation accuracy and relatively low computational complexity compared with the state-of-the-art algorithms.

To support massive connectivity for sporadically active devices is a challenging task, as the randomness of the channel and the large number of users lead to enormous increase of communication overhead. Different to the existing methods that differentiate users in resources including time, frequency and code, we propose a new joint activity detection and channel estimation framework for massive multiple-input multiple-output (MIMO) systems, where angular domain information of active users is exploited to enhance activity detection and channel estimation. By exploiting the sporadic activity of users and the angular spread of the wireless signals, the activity detection and channel estimation is formulated as a compressive sensing problem with multiple measurement vectors, which has a simultaneously row-sparse and clustered sparse structure. The sizes and positions of the nonzero clusters are arbitrary, which brings new challenges for algorithm derivation. To this end, we develop new algorithms based on sparse Bayesian learning, where novel hyper-priors are proposed to capture the structural signal characteristics, and appropriate approximations are employed to facilitate algorithm derivations. Numerical experiments demonstrate the improved activity detection and channel estimation performance of the proposed approach in comparison to the existing methods.

Estimating a set of orthogonal functions from a finite set of noisy data plays a crucial role in several areas such as imaging, dictionary learning and compressed sensing. The problem turns out especially hard due to its intrinsic non-convexity. In this paper, we solve it by recasting it in the framework of multi-task learning in Hilbert spaces, where orthogonality plays a role as inductive bias. Two perspectives are analyzed. The first one is mainly theoretic. It considers a formulation of the problem where non-orthogonal function estimates are seen as noisy data belonging to an infinite-dimensional space from which orthogonal functions have to be reconstructed. We then provide results concerning the existence and the convergence of the optimizers. The second one is more oriented towards applications. It consists in a learning scheme where orthogonal functions are directly inferred from a finite amount of noisy data. It relies on regularization in reproducing kernel Hilbert spaces and on the introduction of special penalty terms promoting orthogonality among tasks. The problem is then cast in a Bayesian framework, overcoming non-convexity through an efficient Markov chain Monte Carlo scheme. If orthogonality is not certain, our scheme can also understand from data if such form of task interaction really holds., Neurocomputing, 545, ISSN:0925-2312, ISSN:1872-8286

Grant-free non-orthogonal multiple access (NOMA) has recently received wide attention for reducing signaling overhead and transmission latency in massive machine-type communications (mMTC). In grant-free NOMA systems, user activity and data (UAD) has to be detected, which is challenging in practice. As an emerging technique, compressive sensing (CS) shows great promise in solving this problem by exploiting the inherent sparsity nature of user activity. This paper proposes to use the weighted l2,1 minimization (WL21M) to jointly detect UAD in realistic dynamic scenarios. At first, the average recoverability of the WL21M is analyzed. This analysis reveals the fact that the WL21M can improve the detection performance by means of an appropriate weighting and the incorporation of intrinsic temporal correlation. Motivated by the analysis, a collaborative hierarchical match pursuit (C-HiMP) algorithm is proposed for dynamic UAD detection. In the C-HiMP, a sequence of WL21M problems are solved in the subspaces spanned by all of the components in the hierarchical estimated support sets, where the weights are collaboratively updated by the solutions in previous time slots so that an attractive self-correction capacity is obtained. Simulation results demonstrate that the proposed C-HiMP can obtain significant performance improvements, in terms of detection accuracy and computational complexity, compared with several state-of-the-art CS-based detection algorithms.

Compressive Sensing (CS) is a new sampling theory used in many signal processing applications due to its simplicity and efficiency. However, signal reconstruction is considered as one of the biggest challenge faced by the CS method. A lot of researches have been proposed to address this challenge, however most of the existing techniques start with the same forward step which does not provide the best reconstruction performance. In this paper, we aim to address this challenge by proposing an Adaptive Iterative Forward-Backward Greedy Algorithm (AFB). AFB algorithm is different from all other reconstruction algorithms as it depends on solving the least squares problem in the forward phase, which increases the probability of selecting the correct columns better than other reconstruction algorithms. In addition, AFB improves the selection process by removing the incorrect columns selected in the previous step. We evaluated the AFB’s reconstruction performance using two types of data: computer-generated data and real data set (Intel Berkeley data set). The simulation results show that AFB outperforms Forward-Backward Pursuit, Subspace Pursuit, Orthogonal Matching Pursuit, and Regularized OMP in terms of reducing reconstruction error.

In this paper, we present a hybrid channel estimation algorithm for uniform planar array (UPA)-assisted millimeter-wave (mmWave) massive multiple-input-multiple-output (MIMO) internet of things (IoT) systems by exploiting the benefits from both the compressed sensing (CS) and the sparse Bayesian learning (SBL). Compared with existing studies, the distribution characteristics and correlations between propagation paths in the elevation (e)-and azimuth (a)-angle domains are considered to enhance the estimation performance. Specifically, we first re-define the e-angles and the a-angles to simplify the system model. Then, a novel autoregressive (AR)-Gaussian channel prior is proposed to capture both the sparsity and the clustering properties of mmWave massive MIMO IoT channels. After that, we provide a channel approximation method to overcome the channel uncertainty by exploiting the structure of the AR-Gaussian channel prior. The hybrid beamforming architecture with limited radio frequency (RF) chains in mmWave IoT systems is also considered. Finally, we propose a hybrid channel estimation algorithm which consists of two stages. Based on the different distribution characteristics in different angle domains, the CS-based channel estimation is performed for e-angles on stage one, while the SBL-based channel estimation is applied for a-angles on stage two. Numerical results reveal that, compared with the existing CS-and SBL-only methods, the proposed hybrid channel estimation algorithm exhibits better performance in terms of computational complexity, sparsity robustness, and estimation accuracy.

The Binary Iterative Hard Thresholding (BIHT) algorithm is a popular reconstruction method for one-bit compressed sensing due to its simplicity and fast empirical convergence. There have been several works about BIHT but a theoretical understanding of the corresponding approximation error and convergence rate still remains open. This paper shows that the normalized version of BIHT (NBHIT) achieves an approximation error rate optimal up to logarithmic factors. More precisely, using $m$ one-bit measurements of an $s$-sparse vector $x$, we prove that the approximation error of NBIHT is of order $O \left(1 \over m \right)$ up to logarithmic factors, which matches the information-theoretic lower bound $\Omega \left(1 \over m \right)$ proved by Jacques, Laska, Boufounos, and Baraniuk in 2013. To our knowledge, this is the first theoretical analysis of a BIHT-type algorithm that explains the optimal rate of error decay empirically observed in the literature. This also makes NBIHT the first provable computationally-efficient one-bit compressed sensing algorithm that breaks the inverse square root error decay rate $O \left(1 \over m^{1/2} \right)$., Comment: Submitted to a journal

In this paper, we propose a novel semi-passive elements-aided channel estimation framework for intelligent reflecting surface (IRS), where a small portion of IRS reflecting elements are able to process the received signal for facilitating the channel estimation. Specifically, the BS-IRS channel is estimated by applying the estimation of signal parameters via rotational invariance technique (ESPRIT), while the user-IRS channels are estimated by combining the use of total least square (TLS) ESPRIT and multiple signal classification (MUSIC) methods. The required training time of the proposed channel estimation scheme is irrelevant to the number of IRS reflecting elements, thus substantially reducing the training overhead. Simulation results show the great advantages of our proposed scheme over both the conventional compressed sensing (CS)-based channel estimation and cascaded channel estimation schemes.

Compressed sensing (CS) aims to reconstruct a high quality images with as little sample data as possible. Magnetic resonance imaging (MRI) plays an important role in medical imaging tools but has a slower data acquisition process. Applying CS to MRI offers significant scan time reductions. In this paper, we proposed a fast and efficient algorithm for compressed sensing magnetic resonance imaging (CS-MRI) reconstruction, denoted as adjustable shrinkage-thresholding projection algorithm (ASTP). It is designed to use adjustable shrinkage rules for lp-norm based CS-MRI model. This algorithm is established by using an iterative projection and acceleration scheme. In each iteration, the proposed adjustable shrinkage-thresholding rules are employed to ensure global convergence to accurate solution. Furthermore, the parameter p can be selected flexibly according to different practical application situations, and the orthogonal projection operation is used to reduce the dimension of the solution space to accelerate the convergence speed and improve the reconstruction quality. Numerical experiments show that proposed ASTP algorithm provides a higher accuracy, convergence speed and ability to suppress noise compared with some certain state-of-the-art algorithms.

Efficient ultrasound (US) systems that produce high-quality images can improve current clinical diagnosis capabilities by making the imaging process much more affordable and accessible to users. The most common technique for generating B-mode US images is delay-and-sum (DAS) beamforming, where an appropriate delay is introduced to signals sampled and processed at each transducer element. However, sampling rates that are much higher than the Nyquist rate of the signal are required for high-resolution DAS beamforming, leading to large amounts of data, making remote processing of channel data impractical. Moreover, the production of US images that exhibit high resolution and good image contrast requires a large set of transducer elements, which further increases the data size. Previous works suggest methods for reduction in sampling rate and in array size. In this work, we introduce compressed Fourier domain convolutional beamforming, combining Fourier domain beamforming (FDBF), sparse convolutional beamforming, and compressed sensing methods. This allows reducing both the number of array elements and the sampling rate in each element while achieving high-resolution images. Using in vivo data, we demonstrate that the proposed method can generate B-mode images using 142 times less data than DAS. Our results pave the way toward efficient US and demonstrate that high-resolution US images can be produced using sub-Nyquist sampling in time and space.

Massive access is a critical design challenge of Internet of Things (IoT) networks. In this paper, we consider the grant-free uplink transmission of an IoT network with a multiple-antenna base station (BS) and a large number of single-antenna IoT devices. Taking into account the sporadic nature of IoT devices, we formulate the joint activity detection and channel estimation (JADCE) problem as a group-sparse matrix estimation problem. This problem can be solved by applying the existing compressed sensing techniques, which however either suffer from high computational complexities or lack of algorithm robustness. To this end, we propose a novel algorithm unrolling framework based on the deep neural network to simultaneously achieve low computational complexity and high robustness for solving the JADCE problem. Specifically, we map the original iterative shrinkage thresholding algorithm (ISTA) into an unrolled recurrent neural network (RNN), thereby improving the convergence rate and computational efficiency through end-to-end training. Moreover, the proposed algorithm unrolling approach inherits the structure and domain knowledge of the ISTA, thereby maintaining the algorithm robustness, which can handle non-Gaussian preamble sequence matrix in massive access. With rigorous theoretical analysis, we further simplify the unrolled network structure by reducing the redundant training parameters. Furthermore, we prove that the simplified unrolled deep neural network structures enjoy a linear convergence rate. Extensive simulations based on various preamble signatures show that the proposed unrolled networks outperform the existing methods in terms of the convergence rate, robustness and estimation accuracy.

The sparsity of multipaths in wideband channel has motivated the use of compressed sensing for channel estimation. In this letter, we propose an entirely different approach to sparse channel estimation. We exploit the fact that $L$ taps of channel impulse response in time domain constitute a non-orthogonal superposition of $L$ geometric sequences in frequency domain. This converts the channel estimation problem into the extraction of the parameters of geometric sequences. Notably, the proposed scheme achieves the error-free estimation of the whole bandwidth with a few pilot symbols if the excess delay is bounded to a certain value.

Time Series SAR interferometry (InSAR) (TS-InSAR) has been widely applied to monitor the crustal deformation with centimeter- to millimeter-level accuracy. Phase unwrapping (PU) errors have proven to be one of the main sources of bias that hinder achieving such high accuracy. In this article, a new time series PU approach is developed to improve the unwrapping accuracy. The rationale behind the proposed method is to first improve the sparse unwrapping by mitigating the phase gradients in a 2-D network and then correcting the unwrapping errors in time, based on the triplet phase closure. Rather than the commonly used Delaunay network, we employ the all-pairs-shortest-path (APSP) algorithm from graph theory to maximize the temporal coherence of all edges and to approach the phase continuity assumption in the 2-D spatial domain. Next, we formulate the PU error correction in the 1-D temporal domain as compressed sensing (CS) problem, according to the sparsity of the remaining phase ambiguity cycles. We finally estimate phase ambiguity cycles by means of integer linear programming (ILP). The comprehensive comparisons using synthetic and real Sentinel-1 data covering Lost Hills, California, confirm the validity of the proposed 2-D + 1-D unwrapping approach and its superior performance compared to previous methods.

When conducting computed tomography (CT) image reconstruction, the existing algorithms do not analyze the physical and mathematical bases of CT image reconstruction, which leads to the lack of detailed information of reconstructed images and the problem of poor reconstruction effect. In this research, compressed sensing theory is applied in the process of fast-iterative CT reconstruction. The physical and mathematical basis for CT reconstruction is analyzed. A fast-iterative reconstruction algorithm for sparse angle CT images is proposed. Combined with algebraic iterative algorithm and gradient total variation minimization algorithm, CT reconstruction problem is transformed into gradient optimal solution problem, to complete the fast-iterative reconstruction of sparse angle CT images. Experimental results show that the proposed algorithm has high signal-to-noise ratio for CT image reconstruction, small reconstruction error, and good reconstruction effect for sparse angle CT images.

The distributed source parameter estimator (DSPE) is one of the well-known angular parameter estimation techniques for coherently distributed sources. However, the computational cost of DSPE is not attractive due to the two-dimensional spectrum peak search. To overcome this problem, this letter proposes a novel DSPE algorithm based on compressive sensing theory, named as LP-DSPE algorithm. In the proposed method, at first, the nominal direction of arrival (DOA) estimation can be transformed into a linear programming problem through sparse recovery theory, whose feasible solution set is further expanded to improve the estimation accuracy. Then the angular spread can be obtained via a one-dimensional peak search utilizing the estimated nominal DOA. Compared with the previous works, the proposed algorithm can offer more accurate parameter estimation performance with lower computational complexity, even if in large angular spread scenarios. Theoretical analysis and simulation results demonstrate the performance of the proposed approach.

Total variation (TV) and non-local self-similarity (NSS) are powerful tools for successfully enhancing compressive sensing performance. However, standard TV approaches often over-smooth detailed edges in the image, due to the uniform regularization of gradient magnitude. In this paper, a novel compressed sensing method for the reconstruction of medical images is proposed, the image edges are well preserved with the proposed reweighted TV. The redundancy of the NSS patch also is leveraged through the sparse regression model. The proposed model was solved with an efficient strategy of the Alternating Direction Method of Multipliers (ADMM) algorithm. Experimental results on thesimulated phantom, brain Magnetic resonance imaging (MRI) show that the proposed method outperforms the state-of-the-art compressed sensing approaches.

Compressed sensing is now regarded as an effective method for dimension reduction during signal acquisition. One significant, yet under-addressed issue regarding the transmission of compressively sensed images is how to compress and code measurements, the output of a compressed sensing sensor. As the spatially adjacent correlation in the measurement domain is weak, conventional encoding algorithms cannot be applied directly for measurements. In this paper, we propose the adjacent pixels based measurement coding system (APMC) to generate compressed image bit-steams. Firstly, a deterministic measurement matrix based on the correlation of adjacent pixels (APMM) is applied to embed the pixel-domain boundary information of each block to the measurement domain. By adopting APMM, the pixel-domain information can be efficiently used for measurement-domain intra prediction. Moreover, to avoid the interference of pixels that are far apart and achieve a high prediction accuracy, we employ boundary measurements of neighboring blocks as references for prediction. Finally, we propose a rate control algorithm to process the residuals between measurements and predictions, to generate a coded bit sequence for transmitting. Experimental results demonstrated superiority in rate-distortion performance and bandwidth costs in transmitting as compared to previous schemes. Compared to the state-of-the-art, this work achieves a 24% decrease in bitrate and a 1.68 dB increase in Peak Signal-to-Noise Ratio (PSNR) on average.

Compressed sensing (CS) demonstrates significant potential to improve image quality in 3-D millimeter-wave imaging compared with conventional matched filtering (MF). However, existing sparsity-driven 3-D imaging algorithms always suffer from large-scale storage, excessive computational cost, and nontrivial tuning of parameters due to the huge-dimensional matrix-vector multiplication in complicated iterative optimization steps. In this article, we present a novel range migration (RM) kernel-based iterative-shrinkage thresholding network, dubbed as RMIST-Net, by combining the traditional model-based CS method and data-driven deep learning method for near-field 3-D millimeter-wave (mmW) sparse imaging. First, the measurement matrices in ISTA optimization steps are replaced by RM kernels, by which matrix-vector multiplication is converted to the Hadamard product. Then, the modified ISTA optimization is unrolled into a deep hierarchical architecture, in which all parameters are learned automatically instead of manually tuned. Subsequently, 1000 pairs of oracle images with randomly distributed targets and their corresponding echoes are simulated to train the network. A well-trained RMIST-Net produces high-quality 3-D images from range-focused echoes. Finally, we experimentally prove that RMIST-Net is capable process 512 x 512 large-scale imaging tasks within 1 s. Besides, we compare RMIST-Net with other state-of-the-art methods in near-field 3-D imaging applications. Both simulations and real-measured experiments demonstrate that RMIST-Net produces impressive reconstruction performance while maintaining high computational speed compared with conventional and sparse imaging algorithms.

A novel method based on covariance vector sparse Bayesian learning (CV-SBL) is proposed in this letter to reconstruct the vertical structure of forests using a small number of synthetic aperture radar (SAR) images. This method regards the inversion of forests reflectivity profiles in the wavelet domain as a sparse signal reconstruction (SSR). Based on the covariance matrix matching criterion, the backscatter power of forests signal and noise will be jointly solved adaptively. Through a few iterations, the exact positions of the closely spaced phase centers can be obtained to simplify the characterization of the vertical structure of the forests. Unlike the traditional compressive sensing (CS) method based on l₁ norm convex optimization, the novel method can obtain a real sparse solution without setting hyper-parameters and has a more reliable and accurate reconstruction performance. Besides, the computational efficiency of the new method is much higher than that of the l₁ minimization CS method, and it is more suitable for large-scale forests mapping applications. The proposed method is validated using P-band TropiSAR 2009 data set over a test site in Paracou, French Guiana. Furthermore, the reconstruction performance of the proposed method is compared with the spectral analysis methods (Beamforming and Capon) and the l₁ minimization super-resolution CS.

Hyperspectral compressed sensing (HCS) for the miniaturized satellite is challenging mainly due to the required lightweight onboard hardware and the necessary low sampling rate. Optical devises involved in conventional HCS include spectral splitter (SS), digital micromirror device (DMD) array, and cylindrical lens (CL), while DMD array (used for implementing random projections) is known to be bulky. We are, hence, thinking of the possibility of just using SS and CL, mathematically meaning that only the deterministic addition operator is available in the coding stage. Another recent advance in the multifunctional metamaterial also motivates us to solve such mathematical challenges. Specifically, SS and CL can be designed on a single nanoscale metasurface (flat), more in line with the miniaturized satellite application. We show that this all-addition coding scheme is achievable though it induces a far more challenging decoding stage, for which a convex decoding criterion is proposed based on self-similarity, a well-known property in imaging inverse problems. Self-similarity regularizer has recently been explicitly defined as a convex function and is demonstrated to be effective in decoding even with a low sampling rate. In addition, as the fundamental role of the John ellipsoid (JE) has been revealed in recent hyperspectral analysis literature, we build a JE-based convex analysis framework to ensure exact recovery even with low data purity. Experimental evidence shows the superiority of the proposed method.

There has been an increasing interest in addressing the issue of high-resolution inverse synthetic aperture radar (ISAR) imaging from sparse sampling data. Traditional compressed sensing (CS) and matrix completion (MC) methods are based on sparse and low-rank constraints, respectively, which do not make full use of the structure of ISAR data. In this article, a sparse ISAR imaging algorithm using a structured low-rank approach is proposed for enhanced imaging performance. Based on the observation that the structured Hankel matrix has better low-rank property, the proposed algorithm can outperform the group of conventional MC methods in terms of accuracy to data quality and quantity. Rather than using the traditional singular value decomposition (SVD) solution of nuclear norm minimization, the proposed algorithm restates the nuclear norm via an equivalent reformulation that the structured Hankel matrix can be decomposed into two disjointed parts to avoid the dimensional expansion of the Hankel matrix. Meanwhile, the alternative direction method of multipliers (ADMMs) is applied to effectively reduce the computational complexity. Finally, the effectiveness of the proposed algorithm is further validated using the experiments on simulated and measured data.

Integrating compressed sensing (CS) with millimeter-wave (mmW) holography has shown great potential to achieve lightweight onboard hardware, low sampling ratio, and high-speed sensing. However, conventional CS-driven algorithms are always limited by nontrivial adjusting of parameters and excessive computational cost caused by plenty of iterations. To address this problem, we propose a lightweight model-based deep learning framework (LFIST-Net) for mmW 3-D holography, by combining the interpretability of fast iterative shrinkage-thresholding algorithm (FISTA) and tuning-free merit of data-driven deep neural network. First, the single-frequency (SF) holographic imaging technique is integrated into FISTA, which serves as the sensing kernels, to avoid large-scale matrix multiplications. Subsequently, the kernel-based FISTA (KFISTA) is mapped into layer-fixed and parameter-learnable LFIST-Net, whose weights are relaxed to be layer-varied. The updating of key parameters in LFIST-Net, including step sizes, thresholds, and momentum coefficients, are regularized by soft-plus function to ensure the non-negativity and monotonicity. As for 3-D holography implementation, the ``1-D + 2-D'' scheme is adopted, where the matched filtering (MF) and well-trained LFIST-Net are used for range focusing and reconstructions of azimuth slices. Without losing efficiency, the range-focused subechoes are processed parallelly in 3-D cube form. Experiments, including both simulated and measured tests based on a commercial mmW radar, prove that LFIST-Net is capable of reconstructing the imaging scene precisely. In particular, in near-field mmW 3-D holography tests, both numerical and visual results demonstrate LFIST-Net yields compelling reconstruction performance while maintaining high computational speed compared with MF-based, conventional CS-driven, and network-based methods.

Due to the nonsparse representation, the use of compressed sensing (CS) for physiological signals, such as a multichannel electroencephalogram (EEG), has been a challenge. We present a generalized Bayesian CS framework that is capable of handling representations that arise in the spatiotemporal setting. The proposed model utilizes the standard linear Gaussian observation model associated with the hierarchical modeling of data using the matrix-variate Gaussian scale mixture (GSM). It deploys various random and deterministic parameters to incorporate the knowledge of spatial and temporal correlation present in data. By varying distributions over random parameters, a family of generalized hyperbolic matrix variate distributions is derived. For estimation, we rely on variational Bayes (VB) for random parameters and expectation-maximization (EM) for deterministic parameters. Furthermore, the model is compared with recent developments in matrix-variate distribution-based modeling of data, and we briefly discuss its extension to finite mixtures of skewed distributions. Finally, the framework is applied to the steady-state visual evoked potential (SSVEP)-based EEG benchmark data set, and a comparative study is conducted to show its effectiveness for the frequency detection task. One of the crucial features of the proposed model is that it simultaneously processes multichannel signals with low computational cost and time, making it suitable for real-time systems, especially in a resource-constrained environment.

In microwave remote sensing applications, some areas need to be observed frequently. Compared with the historical observations, the current observation has a little new content. This means that the increment is sparse, making it possible for imaging with under sampled echoes. For the increment imaging, we first establish the linear observation model and the increment model, making it a two-variable optimization problem. Then, the block coordinate descent strategy is used to implement the increment imaging. To estimate the unknown phase matrix, we make the uniform quantification assumption, and an extended Lagrangian multiplier method is applied. For the sparse increment, Bayesian compressed sensing (BCS) is used. Two different resolution scenes are used to verify the feasibility of this algorithm. The performance under different signal-to-noise ratios (SNRs) and undersampling ratios has been discussed as well.

The seismic data regularization problem is vital to seismic data processing. We propose a joint sparsity-promotion method based on the compressive sensing theory named the curvelet-data-driven-tight-frame-based sparsity-promoting (CDSP) method. The CDSP method regularizes the seismic data directly on the nonequispaced grid along the spatial dimension. The joint sparsity is exploited in the curvelet and data-driven tight frame transform simultaneously on the projected regular spatial grid. The projection from the nonequispaced grid to the equispaced grid is achieved by the nonequispaced discretized Fourier transform. Comparing with the curvelet-sparsity-promotion-based (CSP) regularization method, CDSP combines the advantage of the predefined curvelet transform and adaptive-learned sparse transform into one single optimization model. An alternative directional method of multipliers (ADMM) is applied to solve the optimization problem. One synthetic and two field examples show that the CDSP method performs better on the preservation of the continuity of events and produces less artifacts than the CSP method.

Spectrum mapping has emerged as an important problem in wireless communications, which generates a spectrum map for the spectrum resource analysis and management. Given the constrained transceiver volume and the limited energy consumption, how to effectively reconstruct the spectrum situation by the limited sampling data is a pressing challenge for spectrum mapping. In this paper, by exploiting the sparse nature of spectrum situation, we firstly attempt to solve the three-dimensional (3D) compressed spectrum mapping problem in the way of compressed sensing. Then, we develop a quadrature and right-triangular (QR) pivoting based measurement matrix optimization algorithm. By iteratively selecting new dominant sampling locations, it promotes the recovery accuracy compared to random measurement. After that, we propose a 3D spatial subspace based orthogonal matching pursuit (OMP) algorithm to recover spectrum situation for 3D compressed spectrum mapping. Finally, simulations are presented to show the comparisons in terms of localization, source signal strength recovery, recovery success rate and situation recovery. Results show our proposed 3D spectrum mapping scheme not only effectively reduces the sampling number, but also achieves a high level of spectrum mapping accuracy.

3-D computerized ionospheric tomography (CIT) is an ill-posed problem due to the insufficient amount of observations, it remains challenging for practical applications. In this article, we proposed an ionospheric tomography method that combined data-driven methods with compressed sensing (CS) to deal with the ill-posed problem. First, slant total electron content (STEC) data were extracted by undifferenced and uncombined precise point positioning (UCPPP) with known fixed station coordinates. Second, data-driven methods were adopted to construct the projection matrix from the ionospheric model. Third, compressed sensing was used to derive the sparse solution based on L₁ norm. The ionospheric tomography can be achieved well by using observations during the shorter time interval and in a sparse receiver distribution based on the property of compressed sensing. Results of experiment based on real Global Positioning System (GPS) observation data verified the effectiveness of the proposed methods. By comparing with the colocated ionosonde, it is found that the CS methods are more consistent with the actual ionospheric fluctuation than the modified constrained algebraic reconstruction technique (CART). In terms of the differential STEC (dSTEC) analysis, the error of the tomography model by Compressed Sensing-Principal Component Analysis (CS-PCA) is less than 0.2 TEC unit (TECU), and the time resolution is 5 min. The UCPPP with constraint by CS-PCA shows the best performance of 12.2%, 40.9% and 0.31% improvement in positioning accuracy, convergence time, and fixed rate over the UCPPP with constraint by modified CART. The proposed data-driven methods may be important for high-resolution 4-D ionospheric tomography in the future.

Multitarget detection is very challenging, especially when targets are densely distributed. In conventional constant false alarm rate (CFAR) detection algorithms, the detection threshold is determined based on a pre-estimated background level (BL). However, interfering targets inevitably lead to inaccurate BL estimation, resulting in degraded detection performance. In our previous work, a new solution was developed and verified to be effective; in that solution, compressed sensing (CS)-based detector performs target detection without relying on BL estimation, and a subsequent CFAR regulation processor achieves the desired false alarm rate based on the statistical information of the reduced samples obtained by removing the detected targets and adjacent guard cells from the original samples. However, for scenes with a high target density, the CS-based detector suffers from performance degradation while acquiring the correlation between linear measurements of the signal and the sensing matrix due to the high local signal sparsity. To address this shortcoming, this article proposes a deep neural network (DNN)-based detector that further improves the detection performance by converting the target detection into a problem of peak sequence classification of frequency intensity (FI) measurements from radar. A DNN detector trained on augmented simulated data shows excellent generalization ability for deployment in real scenes. In addition, to achieve better computational efficiency, a Taylor-series-based approximate maximum likelihood estimator with an explicit expression is applied in the CFAR regulation process for the first time. Both simulation and field tests are performed to verify the superiority of the proposed algorithm over conventional algorithms.

This letter proposes a novel sparse recovery method of multiple-input and multiple-output (MIMO) radar compressed sensing (CS) imaging algorithms. This method leverages the prior structure of the measurement matrix to judge targets' locations and to estimate the sparsity level in the grid roughly and finally inhabits the emergence of false targets in the imaging figure. Explicitly, the algorithm we propose is inspired by the orthogonal matching pursuit (OMP) algorithm. First, the measurement matrix can be divided into some submatrices by column. Then, we estimate which submatrices do not contain signal components by the algorithms we propose in this literature to achieve the reconstruction of the measurement matrix. Finally, we use the sparse Bayesian learning algorithm and the sparsity adaptive matching pursuit algorithm to recover the target location and scattering intensity. Experiments validate that the reconstruction error of the algorithm we propose is much lower than other sparse recovery algorithms, and targets in the imaging are more obvious than other algorithms.

Radar imaging with 1-bit data is attractive thanks to its low storage and transmission burden. Existing 1-bit radar imaging methods cannot satisfactorily suppress the artifacts in the imaging result induced by 1-bit quantization error and noise. In this article, we propose a new 1-bit compressive sensing (CS) based algorithm, i.e., the adversarial-sample-based binary iterative hard thresholding (AS-BIHT) algorithm, to improve the 1-bit radar imaging performance. First, we formulate a parametric model for 1-bit radar imaging with a new adjustable quantization level parameter. The parametric 1-bit radar imaging model updates the imaging scene and the quantization level parameter in an iterative fashion based on adversarial samples. Then, we design a mechanism to generate adversarial samples by attacking the 1-bit radar imaging model to resist the quantization consistency condition, such that forcing quantization consistent reconstruction on adversarial samples mitigates the quantization error and noise. The quantization level parameter is then tuned based on the adversarial samples. In this way, the ability of the model to adapt to echo data contaminated by noise and quantization error is enhanced, and the artifacts are well suppressed. Simulation and experimental results on real radar data demonstrate the effectiveness of the proposed AS-BIHT algorithm in 1-bit radar imaging.

Inverse synthetic aperture radar (ISAR) imaging and autofocusing are challenging under sparse aperture (SA) conditions. Traditional imaging or autofocusing methods fail to obtain satisfying results due to the nonuniform and incomplete data caused by SA. To address this problem, a novel compressive sensing (CS)-based imaging and autofocusing framework is proposed to obtain high cross-range resolution for SA ISAR. To achieve well-focused imaging results of better performance and higher efficiency simultaneously, we merge the phase error estimation into the CS framework, then iteratively solve the compound CS problem in matrix form with approximate message-passing (AMP), dubbed as AF-AMP. Moreover, a deep learning approach is also proposed by mapping AF-AMP into a deep network, dubbed as AF-AMPNet, with extensive modifications to further improve the efficiency. The adaptively and layer-wisely optimal parameters learned by the training process are also promising to enhance the performance and robustness against noise. Besides, the loss function for training is subjoined with regularized l₁ and l₂ constraints to ensure the sparsity and quality of imaging results. Furthermore, the proposed AF-AMP and corresponding network-based AF-AMPNet are verified by simulated and measured experiments, both of which show superior performance, robustness, and higher efficiency than other state-of-the-art methods. AF-AMPNet can achieve the best performance in much less computational time.

The most common technique for generating B-mode ultrasound (US) images is delay-and-sum (DAS) beamforming, where the signals received at the transducer array are sampled before an appropriate delay is applied. This necessitates sampling rates exceeding the Nyquist rate and the use of a large number of antenna elements to ensure sufficient image quality. Recently, we proposed methods to reduce the sampling rate and the array size relying on image recovery using iterative algorithms based on compressed sensing (CS) and the finite rate of innovation (FRI) frameworks. Iterative algorithms typically require a large number of iterations, making them difficult to use in real time. In this article, we propose a reconstruction method from sub-Nyquist samples in the time and spatial domain, which is based on unfolding the iterative shrinkage thresholding algorithm (ISTA), resulting in an efficient and interpretable deep network. The inputs to our network are the subsampled beamformed signals after summation and delay in the frequency domain, requiring only a subset of the US signal to be stored for recovery. Our method allows reducing the number of array elements, sampling rate, and computational time while ensuring high-quality imaging performance. Using in vivo data, we demonstrate that the proposed method yields high-quality images while reducing the data volume traditionally used up to 36 times. In terms of image resolution and contrast, our technique outperforms previously suggested methods as well as DAS and minimum-variance (MV) beamforming, paving the way to real-time applicable recovery methods.

State-of-the-art model-driven Direction-Of-Arrival (DOA) estimation methods for multipath signals face great challenges in practical application because of the dependence on the precise multipath model. In this paper, we introduce a framework, based on deep learning, for synchronizing perturbation auto-elimination with effective DOA estimation in multipath environment. Firstly, a signal selection mechanism is introduced to roughly locate specific signals to spatial subregion via frequency domain filters and compressive sensing-based method. Then, we set the mean of the correlation matrix’s row vectors as the input feature to construct the spatial spectrum by the corresponding single network within the parallel deep capsule networks. The proposed method enhances the generalization capability to untrained scenarios and the adaptability to non-ideal conditions, e.g., lower SNRs, smaller snapshots, unknown reflection coefficients and perturbational steering vectors, which make up for the defects of the previous model-driven methods. Simulations are carried out to demonstrate the superiority of the proposed method.

In this letter, a novel pattern synthesis algorithm that jointly optimizes the number, positions, and excitation of elements in a sparse linear array (SLA) is designed based on continuous compressed sensing (CCS). The pattern synthesis problem is first formulated as a sparse recovery problem, which can be solved using semidefinite programming (SDP) involving atomic norm minimization (ANM). The parameters of the designed SLA, including the corresponding element positions and excitations, are determined via Vandermonde decomposition and least squares in the continuous domain. As ANM works directly in the continuous domain, the proposed algorithm is able to synthesize the desired patterns with a small mismatch and a small number of elements. A number of representative numerical experiments show the effectiveness of our algorithm.

The compressed sensing (CS)-based synthetic aperture radar (SAR) imaging methods have emerged as the standard approach to obtain super-resolution (SR) SAR images and achieve extraordinary performances. However, they face three challenges. First, this kind of method is mainly based on the point scattering model and not suitable for characterizing the line-segment-scattering and surface-scattering features of distributed targets. Second, the hyperparameters in these methods are hard to tune to optimal values. Third, due to a large amount of calculation, these methods are difficult to apply in practice. In this article, to solve these problems, we introduce the line-segment-scatterers (LSSs) and rectangular-plate-scatterers (RPSs) in SAR echo model to develop the SAR hybrid echo model and propose two SAR parametric SR image reconstruction methods based on solving a CS problem, where three penalties are utilized to exploit the sparsity of the point scatterers, LSSs, and RPSs, respectively. At the core of the first method is a direct solver called multicomponent alternating direction method of multipliers (MC-ADMM) solver that solves the CS problem quickly and iteratively based on closed derivative expressions. In contrast, the second method maps the MC-ADMM solver into a deep unfolded neural network, i.e., the parametric SR imaging network (PSRI-Net), which is faster, and the parameters can be automatically set to the optimum. Since all the parameters of the MC-ADMM solver are learned discriminatively through end-to-end training in PSRI-Net. Extensive simulation and practical experiments are carried out to demonstrate the effectiveness of the proposed methods.

In the unmanned aerial vehicle-based wireless sensor network, the compressive sensing approach can simultaneously locate multiple ground radio frequency sources, while the existing algorithms’ localization accuracies would deteriorate confronting the heavy noise. Hence, we exploit the potential priori knowledge and propose a robust localization algorithm named priori knowledge-aided Bayesian compressive sensing. Firstly, the problem of multi-emitter localization is transformed to that of sparse recovery, whose sparse dictionary is constructed based on the lognormal signal propagation model. Besides, we replace the Gaussian prior in the conventional hierarchical model with the Laplace prior to enhance the localization accuracy. Finally, the sparse recovery problem is solved under the sparse Bayesian learning framework, where the priori knowledge is incorporated to increase localization accuracy further. The improved performance of the proposed algorithm is testified by the simulations where both the state-of-the-art methods and Cramer-Rao lower bound are compared.

Binary sensing matrices can offer rapid multiplier-less data acquisition, owing to their binarization structure and competitive sampling efficiency, which promise to promote compressive sensing from theory to application. However, the size of existing binary constructions is often limited, and the generating strategies require extensive computational complexity. In this work, we propose a trivial strategy to deterministically construct non-Cartesian spiral binary sensing matrices (SbMs) with arbitrary size for compressive sensing. The mutual coherence of SbMs is proven to satisfy the Welch bound, i.e., optimal theoretical guarantee. Moreover, the simulation results show that the proposed SbMs can not only outperform their counterparts in sampling performance but also facilitate reconstruction speed.

The application of multimedia sensors is widespread, and people need to transmit images more securely and efficiently. In this paper, an image transmission scheme based on two chaotic maps is proposed. The proposed scheme consists of two parts, secure image transmission between sensor nodes and sink nodes (SIT-SS) and secure image transmission between sensor nodes and receivers (SIT-SR). For resource-constrained environments, SIT-SS utilizes Tent-Logistic Map (TLM) to generate chaotic sequences and adopts TLM-Driven permutation and transformation to confuse image pixels. Then the cipher image is obtained through TLM-Driven two-dimensional compressed sensing. Compared with existing schemes, the secret key design of SIT-SS is more reasonable and requires fewer hardware resources. When sampling ratio is greater than 0.6, its image reconstruction quality has obvious advantages. For environments with huge security threats, SIT-SR adopts dynamic permutation and confusion based on discrete logarithms to confuse the image and exploits dynamic diffusion based on discrete logarithms to generate final cipher image. Similarly, compared with some existing schemes, the design of SIT-SR is more practical, and the statistical characteristics of the cipher image are better. Finally, extensive simulation tests confirm the superiority of the proposed scheme.

Non-uniform sampling (NUS) is a popular way of reducing the amount of time taken by multidimensional NMR experiments. Among the various non-uniform sampling schemes that exist, the Poisson-gap (PG) schedules are particularly popular, especially when combined with compressed-sensing (CS) reconstruction of missing data points. However, the use of PG is based mainly on practical experience and has not, as yet, been explained in terms of CS theory. Moreover, an apparent contradiction exists between the reported effectiveness of PG and CS theory, which states that a “flat” pseudo-random generator is the best way to generate sampling schedules in order to reconstruct sparse spectra. In this paper we explain how, and in what situations, PG reveals its superior features in NMR spectroscopy. We support our theoretical considerations with simulations and analyses of experimental data from the Biological Magnetic Resonance Bank (BMRB). Our analyses reveal a previously unnoticed feature of many NMR spectra that explains the success of ”blue-noise” schedules, such as PG. We call this feature “clustered sparsity”. This refers to the fact that the peaks in NMR spectra are not just sparse but often form clusters in the indirect dimension, and PG is particularly suited to deal with such situations. Additionally, we discuss why denser sampling in the initial and final parts of the clustered signal may be useful. Supplementary Information The online version contains supplementary material available at 10.1007/s10858-021-00385-7.

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.

Compressive sensing (CS) is a promising technique recognized for its merits in recovering sparse signals with enhanced resolution entailing specific constraints. In recasting the CS model within a Bayesian framework, its formulation can be interpreted and solved under various prior assumptions that may correspond to, e.g., the $\mathcal {L}_{1}$ or reweighted $\mathcal {L}_{1}$ constraint. Bayesian CS (or Bayesian sparse learning, BSL) achieves improved resolution and robustness compared with the deterministic CS. Therefore, BSL has been invoked to solve the single and multisnapshot beamforming models for direction-of-arrival (DOA) estimation. However, the recovery performance deteriorates for complicated signals because of nonsparsity. In this article, a multiconstraint BSL approach is proposed to solve the multisnapshot beamforming model (termed M-MCRBSL), which reconstructs the amplitude and DOA of the source simultaneously. With a proper assembly of constraints, the source can be represented sparsely and the transformation coefficients can be recovered accurately in multiple sparse domains. As demonstrated in the simulations, M-MCRBSL outperforms other state-of-the-art multisnapshot beamforming methods gauged by both the normalized mean square error (NMSE) and the structural similarity (SSIM) index. In particular, a deficiency sensitivity experiment is devised to elaborate the feasibility of the invoked invertibility approximation. As attested with an underwater acoustics experiment, M-MCRBSL with joint identity and Haar wavelet constraints achieves improved performance in terms of enhanced resolution and suppressed interference sources.