Joint Sparse Recovery Algorithm Research Articles

A Sparse Recovery Algorithm for Suppressing Multiple Linear Frequency Modulation Interference in the Synthetic Aperture Radar Image Domain.

In synthetic aperture radar (SAR) signal processing, compared with the raw data of level-0, level-1 SAR images are more readily accessible and available in larger quantities. However, an amount of level-1 images are affected by radio frequency interference (RFI), which typically originates from Linear Frequency Modulation (LFM) signals emitted by ground-based radars. Existing research on interference suppression in level-1 data has primarily focused on two methods: transforming SAR images into simulated echo data for interference suppression, or focusing interference in the frequency domain and applying notching filters to reduce interference energy. However, these methods overlook the effective utilization of the interference parameters or are confined to suppressing only one type of LFM interference at a time. In certain SAR images, multiple types of LFM interference manifest bright radiation artifacts that exhibit varying lengths along the range direction while remaining constant in the azimuth direction. It is necessary to suppress multiple LFM interference on SAR images when original echo data are unavailable. This article proposes a joint sparse recovery algorithm for interference suppression in the SAR image domain. In the SAR image domain, two-dimensional LFM interference typically exhibits differences in parameters such as frequency modulation rate and pulse width in the range direction, while maintaining consistency in the azimuth direction. Based on this observation, this article constructs a series of focusing operators for LFM interference in SAR images. These operators enable the sparse representation of dispersed LFM interference. Subsequently, an optimization model is developed that can effectively suppress multi-LFM interference and reduce image loss with the assistance of a regularization term in the image domain. Simulation experiments conducted in various scenarios validate the superior performance of the proposed method.

Channel Estimation for Reconfigurable Intelligent Surface Aided Multi-User mmWave MIMO Systems

Channel acquisition is one of the main challenges for the deployment of reconfigurable intelligent surface (RIS) aided communication systems. This is because an RIS has a large number of reflective elements, which are passive devices with no active transmitting/receiving abilities. In this paper, we study the channel estimation problem for the RIS aided multi-user millimeter-wave (mmWave) multi-input multi-output (MIMO) system. Specifically, we propose a novel channel estimation protocol for the above system to estimate the cascaded channels, which are the products of the channels from the base station (BS) to the RIS and from the RIS to the users. Further, since the cascaded channels are typically sparse, this allows us to formulate the channel estimation problem as a sparse recovery problem using compressive sensing (CS) techniques, thereby allowing the channels to be estimated with less training overhead. Moreover, the sparse channel matrices of the cascaded channels of all users have a common block sparsity structure due to the common channel between the BS and the RIS. To take advantage of the common sparsity pattern, we propose a two-step multi-user joint channel estimation procedure. In the first step, we make use of the common column-block sparsity and project the received signals onto the common column subspace. In the second step, we make use of the row-block sparsity of the projected signals and propose a multi-user joint sparse matrix recovery algorithm that takes into account the common channel between the BS and the RIS.

Estimation of Time-Varying Channels in Virtual Angular Domain for Massive MIMO Systems

This paper is concerned with the problem of channel estimation in virtual angular domain in massive MIMO orthogonal frequency division multiplexing (OFDM) systems, in the presence of time varying channels. The proposed channel estimator is based on dichotomous coordinate decent joint sparse recovery (DCD-JSR) algorithm, which was well suited for massive MIMO systems with channels static over several OFDM symbols, but it is not accurate for time-varying channels. The estimator proposed in this paper exploits the basis expansion model (BEM) for approximation of the time-variation of the channel and the sparsity of the channel in the virtual angular domain with a common support over OFDM subcarriers and OFDM symbols for joint estimation of the BEM expansion coefficients. It is shown that, when using the Legendre polynomials as the BEM and depending on the normalized Doppler frequency, only a small number of expansion coefficients is required to provide accurate channel estimation.

A joint sparse recovery algorithm for coprime adjacent array synthetic aperture radar 3D sparse imaging

ABSTRACT In the linear array synthetic aperture radar (LASAR) three-dimensional (3D) imaging, the spacing between adjacent elements in the uniform linear array (ULA) must satisfy the Nyquist sampling theorem to avoid the grating lobes, which makes the number of elements in the ULA very large. To reduce the elements in the ULA, the coprime adjacent array (CAA) with the same aperture length as the ULA is used when conducting LASAR 3D sparse imaging by compressed sensing (CS) algorithms. However, due to the increased autocorrelation coefficient of the measurement matrix, there exists grating lobes interference in the CAA-SAR imaging results. To solve this problem, we propose a joint sparse recovery (JSR) algorithm for CAA-SAR 3D sparse imaging. Firstly, we conduct sparse imaging on the CAA and its two subarrays, respectively. Secondly, the imaging results of the CAA and its two subarrays are performed image segmentation by the OTSU algorithm to extract their target-areas’ imaging results. Finally, we perform the image fusion by the wavelet transform on the target-areas’ imaging results to obtain the final imaging results. Both simulation and experimental results indicate that the imaging quality and computational efficiency of the JSR algorithm are higher than the random sampling array (RSA) and CAA under the same number of array elements. Besides, under the same aperture length, the JSR algorithm improves the computational efficiency than the ULA without imaging-quality loss.

Low-rank and joint-sparse signal recovery using sparse Bayesian learning in a WBAN

Wireless body area networks (WBANs) will become increasingly important in future communication systems, especially in the area of wearable health monitoring systems, such as telemonitoring systems for the collection of electrocardiogram (ECG) data/electroencephalogram (EEG) data via WBANs for e-health applications. However, wearable devices usually require limited power consumption to ensure long battery life. Fortunately, compressed sensing (CS) has been proven to use less energy than traditional transform-coding-based methods. Because the spatial and temporal data collected by a WBAN have some closely correlated structures in certain transform domains (e.g., the discrete cosine transform (DCT) domain), we exploit these structures to propose a new low-rank and joint-sparse (L&S) signal recovery algorithm for recovering ECG/EEG data in the framework of CS. Using a simultaneously L&S signal model, we employ a Bayesian learning treatment. This treatment incorporates an L&S-inducing prior over the data and appropriate hyperpriors over all hyperparameters and thereby yields an effective reconstruction of L&S data. Simulation results with synthetic and real ECG/EEG data demonstrate that the proposed algorithm is superior to other state-of-the-art recovery algorithms in terms of reconstruction performance with comparable computational complexity.

Joint Sparse Recovery Using Signal Space Matching Pursuit

In this paper, we put forth a new joint sparse recovery algorithm called signal space matching pursuit (SSMP). The key idea of the proposed SSMP algorithm is to sequentially investigate the support of jointly sparse vectors to minimize the subspace distance to the residual space. Our performance guarantee analysis indicates that SSMP accurately reconstructs any row K -sparse matrix of rank r in the full row rank scenario if the sampling matrix $\mathbf {A}$ satisfies $\mathop{\mathrm{krank}}\limits (\mathbf {A}) \ge {K}+1$ , which meets the fundamental minimum requirement on $\mathbf {A}$ to ensure exact recovery. We also show that SSMP guarantees exact reconstruction in at most ${K}-{r}+\lceil \frac {{r}}{{L}} \rceil $ iterations, provided that $\mathbf {A}$ satisfies the restricted isometry property (RIP) of order ${L}({K}-{r})+{r}+1$ with $\delta _{{L}({K}-{r})+{r}+1} , where L is the number of indices chosen in each iteration. This implies that the requirement on the RIP constant becomes less restrictive when r increases. Such behavior seems to be natural but has not been reported for most of conventional methods. We also show that if ${r}=1$ , then by running more than K iterations, the performance guarantee of SSMP can be improved to $\delta _{\lfloor 7.8{K} \rfloor } \le 0.155$ . Furthermore, we show that under a suitable RIP condition, the reconstruction error of SSMP is upper bounded by a constant multiple of the noise power, which demonstrates the robustness of SSMP to measurement noise. Finally, from extensive numerical experiments, we show that SSMP outperforms conventional joint sparse recovery algorithms both in noiseless and noisy scenarios.

Simultaneous fast joint sparse recovery for WSN and IoT applications

Joint sparse recovery aims to recover a number of sparse signals having joint sparsity from multiple compressed measurements. Such a problem is finding increasing applications in wireless sensor networks (WSN) and Internet of Things (IoT) where multiple sensors collect measurements. However, existing algorithms lack both reconstruction accuracy and speed at the same time. In this study, the authors propose a joint sparse recovery algorithm, simultaneous fast matching pursuit (SFMP), which exploits some of the concepts developed for the fast matching pursuit (FMP) algorithm. SFMP achieves significant improvement in reconstruction time and speed compared to other related existing algorithms. In contrast to related algorithms, support selection is performed efficiently as the number of selected atoms is adapted from an iteration to another. Furthermore, signal estimation is performed avoiding large matrix inversion as in related algorithms. Moreover, simultaneously pruning the estimated signals, results in removing incorrectly selected ones. Due to the efficient selection strategy and the simultaneous pruning operation, the algorithm shows significant improvement in reconstruction accuracy from noisy measurements. SFMP achieves significant speed improvement over simultaneous orthogonal matching pursuit, and significant accuracy improvement over simultaneous compressive sampling matching pursuit, requiring a much smaller number of measurements.

Exploiting joint sparsity for far-field microphone array sound source localization

The presence of far-field noise and reverberation poses significant challenges to the conventional microphone array sound source localization approaches. Consider the sparsity contained in the source direction vector, source localization can be transformed into a compressed sensing (CS) problem by constructing the redundancy frequency domain room impulse response (RIR) matrix as CS measurement matrix. In this paper a new sparse recovery model is derived by decomposing the RIR into delay response term and reverberation response term to facilitate reverberation mitigation via frequency domain accumulation. Furthermore, as the source direction vector of adjacent speech frames tends to exhibit similar sparse pattern, namely, the direction of source can be assumed to keep static within this short period, thus there exists substantial correlation of spatial sparsity among adjacent speech frames. In this paper, under the framework of distributed compressed sensing (DCS), multiple source direction vectors are treated as sparse solutions with common spatial support to derive a joint sparse recovery algorithm for far-field source localization. The experimental results obtained in the context of a uniform circle array (UCA) show that the proposed algorithm is capable of yielding better estimation performance compared with the traditional algorithms.

Reconstruction of jointly sparse vectors via manifold optimization

In this paper, we consider the challenge of reconstructing jointly sparse vectors from linear measurements. Firstly, we show that by utilizing the rank of the output data matrix we can reduce the problem to a full column rank case. This result reveals a reduction in the computational complexity of the original problem and enables a simple implementation of joint sparse recovery algorithms for full-rank setting. Secondly, we propose a new method for joint sparse recovery in the form of a non-convex optimization problem on a non-compact Stiefel manifold. In our numerical experiments our method outperforms the commonly used ℓ2,1 minimization in the sense that much fewer measurements are required for accurate sparse reconstructions. We postulate this approach possesses the desirable rank aware property, that is, being able to take advantage of the rank of the unknown matrix to improve the recovery.

Enhancing the Accuracy and Robustness of a Compressive Sensing Based Device-Free Localization by Exploiting Channel Diversity.

As an emerging and promising technique, device-free localization (DFL) estimates target positions by analyzing their shadowing effects. Most existing compressive sensing (CS)-based DFL methods use the changes of received signal strength (RSS) to approximate the shadowing effects. However, in changing environments, RSS readings are vulnerable to environmental dynamics. The deviation between runtime RSS variations and the data in a fixed dictionary can significantly deteriorate the performance of DFL. In this paper, we introduce ComDec, a novel CS-based DFL method using channel state information (CSI) to enhance localization accuracy and robustness. To exploit the channel diversity of CSI measurements, the DFL problem is formulated as a joint sparse recovery problem that recovers multiple sparse vectors with common support. To solve this problem, we develop a joint sparse recovery algorithm under the variational Bayesian inference framework. In this algorithm, dictionaries are parameterized based on the saddle surface model. To adapt to the environmental changes and different channel characteristics, dictionary parameters are modelled as tunable parameters. Simulation results verified the superior performance of ComDec as compared with other state-of-the-art CS-based DFL methods.

Joint Sparsity With Partially Known Support and Application to Ultrasound Imaging

We investigate the benefits of known partial support for the recovery of joint-sparse signals and demonstrate that it is advantageous in terms of recovery performance for both rank-blind and rank-aware algorithms. We suggest extensions of several joint-sparse recovery algorithms, e.g., simultaneous normalized iterative hard thresholding, subspace greedy methods and subspace-augmented multiple signal classification techniques. We describe a direct application of the proposed methods for compressive multiplexing of ultrasound (US) signals. The technique exploits the compressive multiplexer architecture for signal compression and relies on joint-sparsity of US signals in the frequency domain for signal reconstruction. We validate the proposed algorithms on numerical experiments and show their superiority against state-of-the-art approaches in rank-defective cases. We also demonstrate that the techniques lead to a significant increase of the image quality on in vivo carotid images compared to reconstruction without partially known support. The supporting code is available on https://github.com/AdriBesson/spl2018_joint_sparse.

Compressive Sampling Rate Optimization for Multiple Measurement Vector Problems

Joint sparse recovery is a recently proposed signal processing approach which has become conventional due to its capability of solving a wide range of optimization problems. However, despite the appropriate performance of existing joint sparse recovery algorithms, all of them suffer from the same drawback: They collect pre-defined number of compressed measurements, which may be too small to precisely reconstruct the row support, or may be unnecessarily large which leads to the wastage of sampling resources. To address this issue and unlike the previous studies, this paper proposes a novel compressed sensing-based method to adaptively adjust the optimal sampling rate of joint sparse recovery problem. A data-driven approach based on Monte Carlo simulation is introduced to obtain the minimum number of samples which is required for precise row support estimation using several well-known joint sparse recovery techniques. Then, a sequential joint sparse recovery framework is developed where the first step predicts the optimal number of measurements and the second step reconstructs signal vectors applying the determined sampling rate. Numerical simulations investigate the effectiveness of suggested method to reduce both the required number of measurements and average algorithm runtime, without losing the recovery performance.

Joint sparse and low rank recovery algorithm for compressive hyperspectral imaging.

Compressive spectral imaging techniques encode and disperse a hyperspectral image (HSI) to sense its spatial and spectral information with few bidimensional (2D) multiplexed projections. Recovering the original HSI from the 2D projections is carried by traditional compressive sensing-based techniques that exploit the sparsity property of natural HSI as they are represented in a proper orthonormal basis. Nevertheless, HSIs also exhibit a low rank property inasmuch only a few numbers of spectral signatures are present in the images. Specifically, when an HSI is rearranged as a matrix whose columns represent vectorized 2D spatial images in a different wavelength, this matrix is said to be low rank. Therefore, this paper proposes an HSI recovering algorithm from compressed measurements involving a joint sparse and low rank optimization problem, which seeks to jointly minimize the ℓ2-, ℓ1-, and ℓ*-norm, leading the solution to fit the given projections, and be simultaneously sparse and low rank. Several simulations, along different data sets and optical sensing architectures, show that when the low rank property is included in the inverse problem formulation, the reconstruction quality increases up to four (dB) in terms of peak signal to noise ratio.

Adaptive joint sparse recovery algorithm based on Tabu Search

This paper introduces a novel metaheuristic methodology to address the Multiple Measurement Vectors problem using a well-known greedy search strategy. A modified version of Tabu Search algorithm is utilized to determine a precise estimation of row support and then joint sparse samples are reconstructed using MMSE criterion. The proposed approach is more robust to the sparsity order variations and noise uncertainty, in comparison with the conventional MMV problem solvers. Furthermore, to avoid wastage of the sampling resources and reduce the implementation costs, a two-step joint sparse recovery framework is developed which the first step predicts and adjusts the optimum sampling rate and the second one reconstructs signal vectors applying obtained sampling rate. Numerical simulations demonstrate the superiority of proposed technique for both improving the performance and reducing the computational complexity and sampling costs.

Exploiting joint sparsity for underwater acoustic MIMO communications

MIMO communication has been recognized as a potential solution for high speed underwater acoustic communication, which unfortunately encounters significant difficulties posed by simultaneous presence of multipath and Co-channel interference (CoI). Sparsity contained in the multipath structure of underwater acoustic channels offers an effective way for improving channel estimation quality and thus enhancing the communication performance in the form of time reversal or channel estimation based equalization. However, for MIMO channels with extensive multipath and CoI, the performance gain achieved by classic sparsity exploitation channel estimation methods such as orthogonal matching pursuit (OMP) is still not enough to yield satisfactory performance. Under quasi-stationary assumption, underwater acoustic channels of adjacent data blocks exhibit correlated multipath structure, namely, multipath arrivals with similar time delay but different magnitude, which has not been exploited. In this paper, a joint sparse recovery approach is proposed to exploit the sparse correlation among adjacent data blocks to improve the performance of channel estimation. Under the framework of distributed compressed sensing (DCS), a joint sparse model which treats the multipath arrivals as sparse solutions with common time support is adopted to derive a joint sparse recovery algorithm for efficient channel estimation, the results of which are used to initialize and periodly update a channel estimation based time reversal receiver. Finally, underwater MIMO communication experimental results obtained in a shallow water channel are provided to demonstrate the effectiveness of the proposed method, compared to the same type of receiver that do not exploit the joint sparse.

Exploiting multi-scale signal information in joint compressed sensing recovery of multi-channel ECG signals

Abstract Computational complexity and power consumption are prominent issues in wireless telemonitoring applications involving physiological signals. Compressed sensing (CS) has emerged as a promising framework to address these challenges because of its energy-efficient data reduction procedure. In this work, a CS-based approach is studied for joint compression/reconstruction of multi-channel electrocardiogram (MECG) signals. The MECG signals share spatially correlated cardiac information across the channels, which is exploited in a joint CS framework for improved signal recovery. Weighted mixed-norm minimization (WMNM)-based joint sparse recovery algorithms are proposed, which can successfully recover the signals from all the channels simultaneously by utilizing the joint sparsity of MECG signals in wavelet domain. The proposed algorithms exploit multi-scale signal information through a multi-scale weighting approach. Under this strategy, weights are designed based on the diagnostic information contents of each wavelet subband/scale. In particular, clinically relevant information is captured in the form of subband energy, entropy, and amplitude decay, and based on this weighting rules are defined at each wavelet scale. Such a weighting approach emphasizes nonzero wavelet coefficients having high diagnostic importance during joint CS reconstruction. Insignificant coefficients are deemphasized simultaneously, resulting in a sparser solution. Simulation results using Physikalisch-Technische Bundesanstalt (PTB), Common Standards for Electrocardiography (CSE) and Massachusetts Institute of Technology-Boston's Beth Israel Hospital (MIT-BIH) MECG databases show that the proposed methods can achieve superior reconstruction quality with a lower number of measurements compared to their non-weighted counterpart and other existing CS-based methods. Reduction in the required number of measurements reduces computational burden and directly translates into higher compression efficiency, resulting in low energy consumption in CS-based telemonitoring systems. The diagnostic reconstruction quality of the algorithm is validated using diagnostic distortion measures like wavelet energy-based diagnostic distortion (WEDD) and with a post-reconstruction classification task. It achieves a classification accuracy of 73.2% even when MECG signals are jointly reconstructed using only about 10% of compressed measurements, validating the diagnosability of the reconstructed signals even at very low data rates.

2-D DOA and mutual coupling coefficient estimation for arbitrary array structures with single and multiple snapshots

Direction-of-arrival (DOA) estimation for arbitrary array structures in the presence of mutual coupling (MC) is an important problem for antenna arrays. Previous methods in the literature are usually proposed for certain array geometries and show limited performance at low SNR or for small number of snapshots. In this paper, compressed sensing is used to exploit the joint-sparsity of the array model to estimate both DOA and MC coefficients with a single snapshot for an unstructured array where the antennas are placed arbitrarily in space. A joint-sparse recovery algorithm for a single snapshot (JSR-SS) is presented by embedding the source DOA angles and MC coefficients into a joint-sparse vector. A dictionary matrix is defined by considering the symmetricity of the MC matrix for the unstructured antenna array. The proposed method is extended to the multiple snapshots, and the joint-sparse recovery algorithm with multiple snapshots (JSR-MS) is developed. A new joint-sparsity structure, namely, joint-block-sparsity is introduced to take advantage of the structure in the composite matrix involving both DOA and MC coefficients. 1-D and 2-D DOA estimation performance of the proposed methods is provided in comparison to the conventional sparse recovery techniques, subspace methods, and the Cramer–Rao lower bound. It is shown that the proposed methods perform significantly better than the alternative methods.

Improving M-SBL for Joint Sparse Recovery Using a Subspace Penalty

The multiple measurement vector problem (MMV) is a generalization of the compressed sensing problem that addresses the recovery of a set of jointly sparse signal vectors. One of the important contributions of this paper is to reveal that the seemingly least related state-of-art MMV joint sparse recovery algorithms - M-SBL (multiple sparse Bayesian learning) and subspace-based hybrid greedy algorithms - have a very important link. More specifically, we show that replacing the $\log\det(\cdot)$ term in M-SBL by a rank proxy that exploits the spark reduction property discovered in subspace-based joint sparse recovery algorithms, provides significant improvements. In particular, if we use the Schatten-$p$ quasi-norm as the corresponding rank proxy, the global minimiser of the proposed algorithm becomes identical to the true solution as $p \rightarrow 0$. Furthermore, under the same regularity conditions, we show that the convergence to a local minimiser is guaranteed using an alternating minimization algorithm that has closed form expressions for each of the minimization steps, which are convex. Numerical simulations under a variety of scenarios in terms of SNR, and condition number of the signal amplitude matrix demonstrate that the proposed algorithm consistently outperforms M-SBL and other state-of-the art algorithms.

A Robust Algorithm for Joint Sparse Recovery in Presence of Impulsive Noise

This letter presents a robust solution for joint sparse recovery (JSR) under impulsive noise. The unknown measurement noise is endowed with the Student-t distribution, then a novel Bayesian probabilistic model is proposed to describe the JSR problem. To effectively recover the joint row sparse signal, variational Bayes (VB) method is introduced for Bayesian theory based JSR algorithms such that it overcomes the intractable integrations inherent. Simulation results verify that the proposed algorithm significantly outperforms the existing algorithms under impulsive noise.

Subsampled terahertz data reconstruction based on spatio-temporal dictionary learning

In this paper, the problem of terahertz pulsed imaging and reconstruction is addressed. It is assumed that an incomplete (subsampled) three dimensional THz data set has been acquired and the aim is to recover all missing samples. A sparsity-inducing approach is proposed for this purpose. First, a simple interpolation is applied to incomplete noisy data. Then, we propose a spatio-temporal dictionary learning method to obtain an appropriate sparse representation of data based on a joint sparse recovery algorithm. Then, using the sparse coefficients and the learned dictionary, the 3D data is effectively denoised by minimizing a simple cost function. We consider two types of terahertz data to evaluate the performance of the proposed approach: THz data acquired for a model sample with clear layered structures (e.g., a T-shape plastic sheet buried in a polythene pellet), and pharmaceutical tablet data (with low spatial resolution). The achieved signal-to-noise-ratio for reconstruction of T-shape data, from only 5% observation was 19 dB. Moreover, the accuracies of obtained thickness and depth measurements for pharmaceutical tablet data after reconstruction from 10% observation were 98.8%, and 99.9%, respectively. These results, along with chemical mapping analysis, presented at the end of this paper, confirm the accuracy of the proposed method.