Sparse Recovery Methods Research Articles

A nonconvex sparse recovery method for DOA estimation based on the trimmed lasso

Sparse direction-of-arrival (DOA) estimation methods can be formulated as a group-sparse optimization problem. Meanwhile, sparse recovery methods based on nonconvex penalty terms have been a hot topic in recent years due to their several appealing properties. Herein, this paper studies a new nonconvex regularized approach called the trimmed lasso for DOA estimation. We define the penalty term of the trimmed lasso in the multiple measurement vector model by ℓ2,1-norm. First, we use the smooth approximation function to change the nonconvex objective function to the convex weighted problem. Next, we derive sparse recovery guarantees based on the extended Restricted Isometry Property and regularization parameter for the trimmed lasso in the multiple measurement vector problem. Our proposed method can control the desired level of sparsity of estimators exactly and give a more precise solution to the DOA estimation problem. Numerical simulations show that our proposed method overperforms traditional approaches, which is more close to the Cramer-Rao bound.

Airborne Radar Space–Time Adaptive Processing Algorithm Based on Dictionary and Clutter Power Spectrum Correction

Sparse recovery space–time adaptive processing (SR-STAP) technology improves the moving target detection performance of airborne radar. However, the sparse recovery method with a fixed dictionary usually leads to an off-grid effect. This paper proposes a STAP algorithm for airborne radar based on dictionary and clutter power spectrum joint correction (DCPSJC-STAP). The algorithm first performs nonlinear regression in a non-stationary clutter environment with unknown yaw angles, and it corrects the corresponding dictionary for each snapshot by updating the clutter ridge parameters. Then, the corrected dictionary is combined with the sparse Bayesian learning algorithm to iteratively update the required hyperparameters, which are used to correct the clutter power spectrum and estimate the clutter covariance matrix. The proposed algorithm can effectively overcome the off-grid effect and improve the moving target detection performance of airborne radar in actual complex clutter environments. Simulation experiments verified the effectiveness of this algorithm in improving clutter estimation accuracy and moving target detection performance.

A regularized eigenmatrix method for unstructured sparse recovery

<p>The recently developed data-driven eigenmatrix method shows very promising reconstruction accuracy in sparse recovery for a wide range of kernel functions and random sample locations. However, its current implementation can lead to numerical instability if the threshold tolerance is not appropriately chosen. To incorporate regularization techniques, we have proposed to regularize the eigenmatrix method by replacing the computation of an ill-conditioned pseudo-inverse by the solution of an ill-conditioned least squares system, which can be efficiently treated by Tikhonov regularization. Extensive numerical examples confirmed the improved effectiveness of our proposed method, especially when the noise levels were relatively high.</p>

Data-Based Tampered-Data Recovery Strategy With Encoding Against Stealthy Attack for Unknown Discrete-Time Systems.

This study addresses a tampered-data recovery problem for linear discrete-time systems with completely unknown system dynamics under stealthy attacks. The basic idea is to identify the stealthy attack, that lies in any of attack-stealthy subspaces, and compensate for it. Different from the existing sparse recovery methods which are applicable to nonstealthy sparse attacks, a novel encoding scheme, where a set of subdecoding matrices is designed specifically for each 1-D attack-stealthy subspace, is developed so that the parameters of the stealthy attack can be identified via a subspace projection technique. A necessary and sufficient condition of determining the targeted subspace by using n parallel attack identification filters is established for this encoding scheme. Especially, a composite encoding matrix characterizes the lower and upper boundaries of the recovery error covariance's trace. A simulation example of a flight vehicle illustrates the efficiency of the proposed approach.

Adaptive integral alternating minimization method for robust learning of nonlinear dynamical systems from highly corrupted data

This paper proposes an adaptive integral alternating minimization method (AIAMM) for learning nonlinear dynamical systems using highly corrupted measured data. This approach selects and identifies the system directly from noisy data using the integral model, encompassing unknown sparse coefficients, initial values, and outlier noisy data within the learning problem. It is defined as a sparse robust linear regression problem. An adaptive threshold parameter selection method is proposed to constrain model fitting errors and select appropriate threshold parameters for sparsity. The robustness and accuracy of the proposed AIAMM are demonstrated through several numerical experiments on typical nonlinear dynamical systems, including the van der Pol oscillator, Mathieu oscillator, Lorenz system, and 5D self-exciting homopolar disc dynamo. The proposed method is also compared to several advanced methods for sparse recovery, with the results indicating that the AIAMM demonstrates superior performance in processing highly corrupted data.

An Efficient Two-Stage SPARC Decoder for Massive MIMO Unsourced Random Access

In this paper, we study a concatenate coding scheme based on sparse regression code (SPARC) and tree code for unsourced random access in massive multiple-input and multiple-output systems. Our focus is concentrated on efficient decoding for the inner SPARC with practical concerns. A two-stage method is proposed to achieve near-optimal performance while maintaining low computational complexity. Specifically, a one-step thresholding-based algorithm is first used for reducing large dimensions of the SPARC decoding, after which a relaxed maximum-likelihood estimator is employed for refinement. Adequate simulation results are provided to validate the near-optimal performance and the low computational complexity. Besides, for covariance-based sparse recovery method, theoretical analyses are given to characterize the upper bound of the number of active users supported when convex relaxation is considered, and the probability of successful dimension reduction by the one-step thresholding-based algorithm.

A robust adaptive-thresholding primal-dual sparse recovery for THz imaging

Terahertz time-domain spectroscopy (THz-TDS) system is a powerful tool in material spectral analysis and non-destructive testing (NDT). However, the data acquisition is time-consuming due to the point-by-point scanning process, which leads to limitations in THz imaging applications. In this paper, a robust adaptive-thresholding primal-dual sparse recovery (APSR) method is proposed to reconstruct high-resolution THz images and reduce the acquisition time. A sparsity averaging dictionary, which is a concatenate of multiple bases, is applied to improve the robustness and generalization. A reweighted scheme is also adopted to enhance the sparse solution. As a crucial consideration in the sparse recovery method, we propose a robust adaptive threshold estimator based on the median absolute deviation in the sense that the final threshold determines the reconstruction quality and the convergence rate. Meanwhile, together with the Nesterov acceleration technique, a large threshold can be applied at the beginning of the iteration to help accelerate the convergence. Numerical experiments demonstrate that the APSR method can reconstruct THz images with robustness even with low SNR (of 30 dB) and low sampling rate (of 30%) compared to conventional methods. In the real THz-TDS system, our proposed sparse imaging method can successfully recover a composite object with much fewer THz spectra and reduces the acquisition time to 30% at the cost of a relative error of 2.5%, demonstrating the efficiency of our proposed method and the penetrating ability of THz technology in the NDT applications.

Block sparse signal recovery via minimizing the block [formula omitted]-ratio sparsity

In this paper, we propose a method for block sparse signal recovery that minimizes the block q-ratio sparsity ‖z‖2,1/‖z‖2,qqq−1 with q∈[0,∞]. For the case of 1<q≤∞, we present the theoretical analyses and the computing algorithms for both cases of the ℓ2-bounded and ℓ2,∞-bounded noises. The corresponding unconstrained model is also investigated. Its superior performance in block sparse signal reconstruction is demonstrated by numerical experiments.

Improved analytical learning proximal operator method for sparse recovery

Sparse recovery (SR) has received considerable attention in the last decades. Various iterative algorithms have been proposed to solve the SR problem, but most of them are unsatisfactory in terms of convergence accuracy and speed. Recently, deep unfolding methods achieve a dramatic improvement in convergence by unfolding iterative SR algorithms into deep neural networks and learning their parameters from training data, e.g., Learning Proximal Operator Method (LePOM) and Analytical LePOM (ALePOM). However, according to theoretical analysis, the recovery error bound of ALePOM should be further reduced as its network parameters are learned to fit all training data. To solve this problem, we design a new network named Improved ALePOM (I-ALePOM) by introducing a Long Short-Term Memory (LSTM) cell into each layer of ALePOM, which helps to adaptively compute the thresholds and step-sizes for each training data. By doing so, the recovery error bound becomes tighter and higher sparse recovery performance can be achieved. Furthermore, we extend the proposed I-ALePOM from the 1-D vector form to the 2-D matrix form, reducing the memory and computation burdens for practical sparse matrix recovery applications. Various numerical simulations verify that the proposed method has a higher performance than the state-of-the-art methods in the literature.

Adaptive Grid Refinement Method for DOA Estimation via Sparse Bayesian Learning

In sparse signal recovery methods for direction of arrival (DOA) estimation, a set of uniform angular grid points is usually predefined. Dense grid points will improve the resolution and precision, but increase computational workload distinctly. To improve the efficiency and performance when using coarse initial grid points, an adaptive grid refinement (AGR) sparse Bayesian learning (SBL) method is proposed. The key idea of the proposed method is to adaptively insert new grid points based on the spatial spectrum learned from SBL iterations, as a result, grid points become denser and denser around the potential DOAs. The number of total grid points in the AGR process is much smaller than that of traditional uniform grid points, which enhances the computation efficiency. After the improved on-grid estimation of the AGR process, a post-processing DOA search procedure is implemented to reduce the off-grid DOA error. Furthermore, the proposed method is extended into the wideband case. Simulation results demonstrate that the proposed method has higher computation efficiency and precision than the classical off-grid SBL methods in scenarios of low SNR and limited snapshots. The effectiveness of the proposed method is also validated using the data of the SWellEx-96 ocean acoustic experiment.

Enhanced Tensor Low-Rank and Sparse Representation Recovery for Incomplete Multi-View Clustering

Incomplete multi-view clustering (IMVC) has attracted remarkable attention due to the emergence of multi-view data with missing views in real applications. Recent methods attempt to recover the missing information to address the IMVC problem. However, they generally cannot fully explore the underlying properties and correlations of data similarities across views. This paper proposes a novel Enhanced Tensor Low-rank and Sparse Representation Recovery (ETLSRR) method, which reformulates the IMVC problem as a joint incomplete similarity graphs learning and complete tensor representation recovery problem. Specifically, ETLSRR learns the intra-view similarity graphs and constructs a 3-way tensor by stacking the graphs to explore the inter-view correlations. To alleviate the negative influence of missing views and data noise, ETLSRR decomposes the tensor into two parts: a sparse tensor and an intrinsic tensor, which models the noise and underlying true data similarities, respectively. Both global low-rank and local structured sparse characteristics of the intrinsic tensor are considered, which enhances the discrimination of similarity matrix. Moreover, instead of using the convex tensor nuclear norm, ETLSRR introduces a generalized non-convex tensor low-rank regularization to alleviate the biased approximation. Experiments on several datasets demonstrate the effectiveness of our method compared with the state-of-the-art methods.

A neighborhood-based multiple orthogonal least square method for sparse signal recovery

Orthogonal least squares (OLS) is a popular greedy algorithm because of its simplicity and low complexity. To improve the reconstruction accuracy performance of OLS, the multiple orthogonal least squares (MOLS) algorithm selects multiple L indices per iteration. Compared with OLS, MOLS improves the reconstruction accuracy and reduces the running time. However, the MOLS algorithm ignores the situation that the correct atom is in the neighborhood of the selected multiple L indices. We propose a neighborhood-based MOLS (NMOLS) algorithm in this study. The NMOLS algorithm incorporates a neighborhood-based strategy to find the more matching atoms in each iteration. NMOLS selects the support from the candidate atoms by comparing their residual error. Simulation and image experimental results show that the proposed algorithm outperforms orthogonal matching pursuit (OMP), regularized OMP (ROMP), compressive sampling matching pursuit (CoSaMP), orthogonal least squares (OLS), and MOLS in terms of reconstruction accuracy.

Sparse Bayesian learning for sparse signal recovery using [formula omitted]-norm

Sparse signal recovery is an important technique for acoustic direction-of-arrival (DOA) estimation which is widely used in applications such as humanoid robots and voice control loudspeakers. However, the estimation accuracy performance is limited by the size of platform and the sound wavelength. To improve the accuracy performance, we propose a sparse signal recovery approach for acoustic DOA estimation based on a hierarchical formulation of the generalized Gaussian prior with a shape parameter q=1/2. Specifically, a sparse Bayesian learning (SBL) framework is built using ℓ1/2-norm priors to efficiently utilize the space sparsity nature of acoustic sources. The priors, built primarily based on a hierarchical structure with a couple of layers, are used for modeling the sparse signals. Then, an expectation–maximization algorithm is proposed for inference and parameter learning. The estimation accuracy performance of the proposed approach is verified in terms of sparse signal recovery and acoustic DOA estimation. The experimental results exhibit that the proposed method achieves the highest recovery accuracy performance and has the lowest root mean square error (RMSE) in contrast with the state-of-the-art sparse signal recovery methods.

Target Imaging Using Compressed Sampling in Synthetic Aperture Interferometric Radiometer

The target imaging application is significant to various sensing systems, such as radiometers, radars, and infrared. However, high system complexity impedes the application of interferometric radiometers to target imaging tasks to some extent. Specifically for an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> -element interferometric radiometer with aperture synthesis technique, complex correlators are of the order of O( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ), giving rise to the great difficulty of system hardware implementation. In this paper, we propose a new compressed interferometric radiometer (CIR) concept for target imaging applications, which exploits the sparsity property of targets in the spatial domain. The CIR target imaging framework mainly adopts the compressive measurement method to acquire partial visibility function samples in the spatial-frequency domain via a proper sparse sampling pattern. Then, these partially observed visibility samples are inverted to image the target contrast information by sparse recovery methods. For the above image recovery process, we propose two novel algorithms named local regional information-based reweighted <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> 1-norm minimization (LRRL1) and local regional convolution-based reweighted <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> 1-norm minimization (LRCRL1). The experiments using simulated and real data demonstrate the validity and effectiveness of the proposed CIR target imaging framework, showing superiority in both imaging performance and system complexity compared with conventional algorithms used in interferometric radiometers.

Variational Bayesian Inference for DOA Estimation Under Impulsive Noise and Non-Uniform Noise

Existing direction of arrival (DOA) estimation approaches are often only considering Gaussian noise or impulsive noise, leading to the performance degradation in the scenario that both noises exist simultaneously. Considering that ambient noise of underwater acoustic array may have different variances due to the large aperture, this paper proposes a robust sparse recovery method based on variational Bayesian inference (VBI) that considers the “heavy-tailed” characteristics of impulsive noise, and the non-uniformity of ambient noise. Student-t distribution and Bernoulli distribution are modeled as impulsive noise in the measurement, and then, the array observed signal is created as a mixture of desired signal, impulsive noise and non-uniform noise. A VBI scheme is constructed to estimate the desired sparse signal to implement DOAs. Results obtained from the numerical simulation and experimental data processing verify the superior performance of the proposed VBI promoting DOA estimation for dealing with impulsive noise and non-uniform noise.

A Novel Detector based on Compressive Sensing for Uplink Massive MIMO Systems

Massive multiple-input multiple-output is a promising technology in future communication networks where a large number of antennas are used. It provides huge advantages to the future communication systems in data rate, the quality of services, energy efficiency, and spectral efficiency. Linear detection algorithms can achieve a near-optimal performance in large-scale MIMO systems, due to the asymptotic orthogonal channel property. But, the performance of linear MIMO detectors degrades when the number of transmit antennas is close to the number of receive antennas (loaded scenario). Therefore, this paper proposes a series of detectors for large MIMO systems, which is capable of achieving promising performance in loaded scenarios. The main idea is to improve the performance of the detector by finding the hidden sparsity in the residual error of the received signal. At the first step, the conventional MIMO model is converted into the sparse model via the symbol error vector obtained from a linear detector. With the aid of the compressive sensing methods, the incorrectly detected symbols are recovered and performance improvement in the detector output is obtained. Different sparse recovery algorithms have been considered to reconstruct the sparse error signal. This study reveals that error recovery by imposing sparse constraint would decrease the bit error rate of the MIMO detector. Simulation results show that the iteratively reweighted least squares method achieves the best performance among other sparse recovery methods.

The Sufficient Conditions for Orthogonal Matching Pursuit to Exactly Reconstruct Sparse Polynomials

Orthogonal matching pursuit (OMP for short) is a classical method for sparse signal recovery in compressed sensing. In this paper, we consider the application of OMP to reconstruct sparse polynomials generated by uniformly bounded orthonormal systems, which is an extension of the work on OMP to reconstruct sparse trigonometric polynomials. Firstly, in both cases of sampled data with and without noise, sufficient conditions for OMP to recover the coefficient vector of a sparse polynomial are given, which are more loose than the existing results. Then, based on a more accurate estimation of the mutual coherence of a structured random matrix, the recovery guarantees and success probabilities for OMP to reconstruct sparse polynomials are obtained with the help of those sufficient conditions. In addition, the error estimation for the recovered coefficient vector is gained when the sampled data contain noise. Finally, the validity and correctness of the theoretical conclusions are verified by numerical experiments.

WiHGR: A Robust WiFi-Based Human Gesture Recognition System via Sparse Recovery and Modified Attention-Based BGRU

Gesture recognition is an essential part in the field of human–computer interaction (HCI) and Internet of Things system. Compared with the existing technologies based on wearable sensors and dedicated devices, approaches using WiFi channel state information (CSI) signals are more desirable for passive and fine-grained gesture recognition. However, the existing CSI-based gesture recognition systems usually suffer from high model complexity and low accuracy caused by environmental dynamics. To address these issues, we propose a robust gesture recognition system (WiHGR) in this article. The WiHGR starts with a sparse recovery method to find the dominant paths from the multipath effect introduced by the orthogonal frequency division multiplexing (OFDM) technology, i.e., the main propagation paths disturbed by a human gesture. Then, the phase difference matrix is constructed according to the phase differences between two adjacent receiving antennas from the dominant paths. We propose a modified attention-based bi-directional gate recurrent unit (ABGRU) network to learn and extract discriminative features automatically from the phase difference matrix. The proposed attention mechanism assigns higher weights to the more important features, thus achieving a better recognition performance. The experimental results show that the WiHGR not only has a high accuracy for gesture recognition in the training environment, but also has a remarkable performance in new environment settings without retraining.

Sparse and Incomplete Signal Dictionaries for Reconstruction of MR Images

Compressed Sensing(CS) is a mathematical approach for data acquisition in which the signals are compressible and sparse w.r.t. to an orthonormal basis. These sparse signals are reconstructed from very less measurements. CS technique Is widely used in Magnetic Resonance Imaging (MRI) where the doctors suggest the patients to undergo MRI scans for diagnosing their body parts. During the prolonged MRI Scan, the exact slice of the MRI cannot be achieved due to the difficulties faced by the patient or irregular changes in the body position of the patient. The idea is to reduce the exposure time of the patient’s body against the MRI scan by considering only fewer samples. Is it possible to Reconstruct the signal by making use of a fewer number of samples that are less than the Nyquist rate? Yes, it is possible to reconstruct the signal by making use of the Compressed Sensing or sampling Technique. Compressed sensing is a new framework for signal acquisition and representation in a compressible manner less below the Nyquist sampling rate. In this article, Sampling and reconstruction are dealt here thoroughly as part of the research activity. Compressive Sensing Matching pursuit (CoSaMP) is a novel technique for optimization. It is an iterative approximation method for sparse and incomplete signal recovery. CoSaMP method along with Different transform techniques is used for reconstruction. The FFT_CoSaMP, DCT_CoSaMP and DWT_CoSaMP are proposed methods for MR Image Reconstruction, where DWT-based CoSaMP along with different wavelet families give the best results when compared to other CS-based techniques w.r.t. PSNR, SSIM and RMSE analysis.

Unlimited dynamic range signal recovery for folded graph signals

Recovery of a graph signal from samples has many important applications in signal processing over networks and graph-structured data. To capture very high or even unlimited dynamic range signals, modulo sampling has been investigated. Folded signals are signals generated from a modulo operation. In this paper, we investigate the problem of recovering bandlimited graph signals from folded signal samples. We derive sufficient conditions to achieve successful recovery of the graph signal, which can be achieved via integer programming. To resolve the scalability issue of integer programming, we propose a sparse optimization recovery method for graph signals satisfying certain technical conditions. Such an approach requires a novel graph sampling scheme that selects vertices with small signal variation. The proposed algorithm exploits the inherent relationship among the graph vertices in both the vertex and time domains to recover the graph signal from folded samples. Simulations and experiments validate the feasibility of our proposed approach.