Sparse Recovery Algorithm Research Articles

DOA estimation of noncircular signals with direction-dependent mutual coupling

In this paper, a reweighted sparse recovery algorithm based on the optimal weighted subspace fitting (WSF) for non-circular signals in direction-dependent mutual coupling (MC) is proposed. Firstly, a new augmented model is constructed by leveraging the characteristics of non-circular signals. Next, a new direction matrix without mutual coupling coefficients is obtained by a novel transformation method. Then, two sparse recovery models are constructed by utilizing the WSF technique, and the sparsity of the solution is increased by constructing a weighted matrix. Finally, the direction of arrival (DOA) is achieved by a sparse recovery approach. For both coherent and incoherent signals, the developed approach can achieve precise DOA estimation in the case of direction-dependent MC. The robustness and advantage of the developed approach are testified by various experiments.

An Efficient Sparse Recovery STAP Algorithm for Airborne Bistatic Radars Based on Atomic Selection under the Bayesian Framework

The traditional sparse recovery (SR) space-time adaptive processing (STAP) algorithms are greatly affected by grid mismatch, leading to poor performance in airborne bistatic radar clutter suppression. In order to address this issue, this paper proposes an SR STAP algorithm for airborne bistatic radars based on atomic selection under the Bayesian framework. This method adopts the idea of atomic selection for the process of Bayesian inference, continuously evaluating the contribution of atoms to the likelihood function to add or remove atoms, and then using the selected atoms to estimate the clutter support subspace and perform sparse recovery in the clutter support subspace. Due to the inherent sparsity of clutter signals, performing sparse recovery in the clutter support subspace avoids using a massive number of atoms from an overcomplete space-time dictionary, thereby greatly improving computational efficiency. In airborne bistatic radar scenarios where significant grid mismatch exists, this method can mitigate the performance degradation caused by grid mismatch by encrypting grid points. Since the sparse recovery is performed in the clutter support subspace, encrypting grid points does not lead to excessive computational burden. Additionally, this method integrates out the noise term under a new hierarchical Bayesian model, preventing the adverse effects caused by inaccurate noise power estimation during iterations in the traditional SR STAP algorithms, further enhancing its performance. Our simulation results demonstrate the high efficiency and superior clutter suppression performance and target detection performance of this method.

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.

Binary Least Squares: An Algorithm for Binary Sparse Signal Recovery

Binary Least Squares: An Algorithm for Binary Sparse Signal Recovery

A High-Resolution Imaging Method for Multiple-Input Multiple-Output Sonar Based on Deterministic Compressed Sensing.

Differences between conventional sonar and Multiple-Input Multiple-Output (MIMO) sonar systems arise in achieving high angular and range resolution. MIMO sonar uses Matched Filtering (MF) with well-correlated transmitted signals to enhance spatial resolution by obtaining virtual arrays. However, imperfect correlation characteristics yield high sidelobe values, which hinder accurate target localization in underwater imagery. To address this, a Compressed Sensing (CS) method is proposed by reconstructing echo signals to suppress correlation noise between orthogonal waveforms. A shifted dictionary matrix and a deterministic Discrete Fourier Transform (DFT) measurement matrix are used to multiply received echo signals to yield compressed measurements. A sparse recovery algorithm is applied to optimize signal reconstruction before joint transmit-receive beamforming forms a 2D sonar image in the angle-range domain. Numerical simulations and lake experimental results confirm the effectiveness of the proposed method, by obtaining a lower sidelobe sonar image under sub-Nyquist sampling rates as compared with other approaches.

Sufficient condition based on nearly optimal order RIC for IHT algorithm

Iterative hard thresholding (IHT) is one class of sparse signal recovery algorithms widely used in compressed sensing. The well-known restricted isometry constant (RIC) is one of the most popular frameworks used to ensure the convergence of recovery algorithms. In previous literature, sufficient conditions to guarantee the recovery performance of the IHT algorithm have usually been established based on RICs with orders 3 s and 2 s , while no such condition in terms of RIC with order less than 2 s has been reported yet. In this study, based on the theoretical optimal step-length, we develop the RIC condition γ < ( 5 − 1 ) / 8 ≈ 0.1545 for successful recovery via the IHT algorithm. Here, γ = δ s if s is an even number, otherwise γ = δ s + 1 . To the best of our knowledge, this is the first result based on RIC with nearly optimal order for the IHT algorithm.

Robust Sparse Recovery Based Vehicles Location Estimation in Intelligent Transportation System

An architecture for vehicle position estimation is introduced in this paper to tackle the issue of vehicles positioning in traffic congestion of intelligent transportation system (ITS). The introduced architecture is related to three unmanned aerial vehicles (UAVs) equipped with uniform linear array (ULA), ITS center and the terminal of position estimation, in which the UAV collect data from the ULA, the ITS center store data and the terminal is responsible for executing the corresponding direction of arrival (DOA) estimation algorithm to estimate the vehicle position. In the introduced architecture, DOA estimation is the crucial issue, hence a robust sparse recovery framework based on the optimal weighted subspace fitting is put forward for DOA estimation in the presence of direction-dependent unknown mutual coupling. Firstly, a data model can be obtained by a new transformation approach. Then, a sparse recovery algorithm based on the weighted subspace fitting is used to estimate the desired DOAs. The proposed DOA estimation algorithm can achieve superior performance in both coherent and incoherent signals in the environment of direction-dependent mutual coupling, and this environment often occurs in traffic congestion. Based on the DOA estimation results obtained from the proposed efficient regularized sparse recovery algorithm, the position of vehicles is final estimated by a weighted three-points cross-positioning method. The results of various simulation experiments fully demonstrate the robustness and superiority of the proposed architecture and algorithm.

Hard threshold acceleration algorithms for sparse signal recovery

Hard threshold acceleration algorithms for sparse signal recovery

Bayesian Algorithms for Kronecker-structured Sparse Vector Recovery With Application to IRS-MIMO Channel Estimation

Bayesian Algorithms for Kronecker-structured Sparse Vector Recovery With Application to IRS-MIMO Channel Estimation

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.

A ReLU-based hard-thresholding algorithm for non-negative sparse signal recovery

In numerous applications, such as DNA microarrays, face recognition, and spectral unmixing, we need to acquire a non-negative K-sparse signal x from an underdetermined linear model y=Ax+v, where A is a sensing matrix and v is a noise vector. In this paper, we first propose a ReLU-based hard-thresholding algorithm (RHT) to recover x by taking advantage of its non-negative sparsity. Two sufficient conditions for stable recovery with RHT are then developed, which are respectively based on the restricted isometry property (RIP) and mutual coherence of the sensing matrix A. As far as we know, these two sufficient conditions are the best for hard-thresholding-type algorithms. Numerical experiments show that RHT has better overall recovery performance in the recovery non-negative sparse signals than the non-negative least squares (NNLS) algorithm, some hard-thresholding-type algorithms including the iterative hard-thresholding (IHT) algorithm, hard-thresholding pursuit (HTP), Newton-step-based iterative hard-thresholding algorithm (NSIHT), and Newton-step-based hard-thresholding pursuit (NSHTP), several non-negative sparse recovery approaches including non-negative orthogonal matching pursuit (NNOMP), fast NNOMP (FNNOMP), non-negative orthogonal least squares (NNOLS), and non-negative regularization (NNREG) method. In terms of efficiency, RHT has a similar performance to IHT, and is much more efficient than other tested algorithms.

A truncated approximate difference algorithm for sparse signal recovery

In this paper, we study the regularization lp-norm minimization problem to recover the sparse signals. We first prove that every global optimal solution to the regularization lp-norm minimization problem also solves the l0-norm minimization problem if the certain conditions are satisfied, and then generate a truncated approximated difference algorithm to recover the sparse signals. At last, we provide some numerical simulations to test the performance of the truncated approximated difference algorithm, and the numerical results show that the proposed algorithm performs effectively in recovering the sparse signals compared with some state-of-art methods.

A Sparse Recovery Algorithm Using the Neurodynamic System With Predefined Time Convergence

Compressed sensing aims to compress sparse signals losslessly into significantly smaller samples and recover them if needed. One of the most critical approaches to recovering the sparse signal is minimizing l1-norm, the convex relaxation of l0-norm with the limit of linear measurement. However, sometimes such as the recovery of piecewise constant sparse signal, the need for controlling the convergence time has become an inevitable problem to solve. To solve this problem, the predefined time pseudo-inverse locally competitive algorithm (PPLCA) based on a nonlinear neurodynamic system is proposed in this paper, which is exceptionally effective if the signal is piecewise constant. Further, under the restricted isometry property (RIP), the predefined-time convergence rate of the proposed PPLCA is proven using Lyapunov’s stability theory. Finally, the numerical simulations show that the PPLCA could converge to the stationary point within the predefined time.

Fast acquisition method using modified PCA with a sparse factor for burst DS spread-spectrum transmission

To improve the acquisition speed and inbound capacity of the ground station in a burst direct-sequence (DS) spread-spectrum transmission system, an acquisition method based on a modified parallel code-phase acquisition (PCA) scheme is proposed. By taking advantage of the sparsity of the acquisition result with PCA in the time domain, we introduce the sparse factor to handle the signals via sparsification and apply the sparse recovery algorithm to search and estimate the acquisition result. The computational complexity, mean acquisition time, and relationship between the inbound capacity and acquisition performance are provided. We theoretically analyse the effect of the sparse factor on the acquisition performance. The estimation errors verify our analysis, and simulations show that the acquisition time of our proposed method outperforms that of advanced PCA by 1.2–4.0 times; additionally, the inbound capacity increases by 6.2–36.7%.

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.

Compressed channel estimation for RIS-assisted wireless systems: An efficient sparse recovery algorithm

The reconfigurable intelligent surface (RIS) technology plays an essential role in controlling the propagation environment of wireless systems, specifically millimeter wave (mmWave) communication systems. However, a considerable number of pilot signals should be provided at the base station (BS) side for channel estimation due to the significant passive elements installed in the RIS. In this paper, we propose a novel sparse recovery algorithm by exploiting the row, common, and individual sparse elements of the channel in a new way. Furthermore, as an essential presumption of real environments, a sparse channel with unknown parameters is considered. Then a halting method is introduced to stop the proposed algorithm at the best time. The numerical results demonstrate that the proposed algorithm can alleviate the pilot overhead problem substantially while the mean square error (MSE) still approaches the performance bound.

Logistic Regression Matching Pursuit algorithm for text classification

Text classification is a challenging problem due to the high dimensionality of the text, which can limit classification performance. The orthogonal matching pursuit (OMP) algorithm is one of the most popular sparse recovery algorithms. An OMP based text classification algorithm, called the Logistic-OMP algorithm, was recently proposed by Skianis et al.. Simulation tests indicate that Logistic-OMP has excellent performance in text dimensionality reduction. This paper optimizes the Logistic-OMP algorithm, and proposes a new text classification algorithm called the Logistic Regression Matching Pursuit (LRMP) algorithm. The LRMP algorithm defines a new loss function and residual update function. It requires only one iteration to solve the negative log likelihood minimization problem, and its classification performance is guaranteed by the strong Wolfe condition, which makes it optimizes the classification accuracy while significantly speeding up the training speed. Simulation tests on topic classification and sentiment analysis from 20Newsgroups, Amazon product reviews, and movie reviews datasets show that the LRMP algorithm has a shorter computation time of a single iteration than the Logistic-OMP algorithm, with a total training time of 8.08%–21.16% shorter than that of the Logistic-OMP algorithm, and the memory usage is 3.20%–6.21% lower than that of the Logistic-OMP algorithm. Furthermore, the average Accuracy and F1-Score of the LRMP algorithm are improved by 1.61%–26.55% and 1.83%–25.46%, respectively, compared with the benchmark classifier. Compared with the advanced classifiers (including Logistic-OMP), the average Accuracy and F1-Score of the LRMP algorithm are improved by 0.46%–8.97% and 0.57%–9.40%, respectively.

A gradient set matching pursuit algorithm with anti-base mismatch ability for sparse reconstruction under low SNR

This paper is concerned with designing an effective algorithm for recovering mismatched sparse signals from noise underdetermined measurements. The sparse recovery problem is formulated as the gradient optimization model of the residual cost function in a multidimensional continuous parameter space. The mismatched atoms of the discrete dictionary matrix are recovered as the accurate target sparse coefficient by solving a gradient descent algorithm with a hyperparameters joint adaptive adjustment function. To estimate the target parameters of frequency agile radar, we propose a gradient set matching pursuit algorithm. The algorithm uses the prior knowledge of resolution of the two-dimensional ambiguity function to build a discrete dictionary and obtains the support set according to the orthogonal matching pursuit principle. We divide the gradient set space in the neighborhood of the support set and calculate the mean gradient as the judgment direction and iteration step of the initial optimization process to overcome the residual function distortion and gradient error caused by random noise. The iterative convergence process of the proposed algorithm in the support set vector space is more robust, and the problem of falling into local optimum is avoided. Compared with the conventional sparse recovery algorithm and gradient descent algorithm, the proposed algorithm boosts its reconstruction performance of target parameters in the scenario of low SNR and mismatch of multiple scattering points. Simulation results show the effectiveness of the proposed algorithm.

Graph Sparsification by Universal Greedy Algorithms

Graph sparsification is to approximate an arbitrary graph by a sparse graph and is useful in many applications, such as simplification of social networks, least squares problems, numerical solution of symmetric positive definite linear systems and etc. In this paper, inspired by the well-known sparse signal recovery algorithm called orthogonal matching pursuit (OMP), we introduce a deterministic, greedy edge selection algorithm called universal greedy approach (UGA) for graph sparsification. For a general spectral sparsification problem, e.g., positive subset selection problem from a set of $m$ vectors from $\mathbb{R}^n$, we propose a nonnegative UGA algorithm which needs $O(mn^2+ n^3/\epsilon^2)$ time to find a $\frac{1+\epsilon/\beta}{1-\epsilon/\beta}$-spectral sparsifier with positive coefficients with sparsity $\le\lceil\frac{n}{\epsilon^2}\rceil$, where $\beta$ is the ratio between the smallest length and largest length of the vectors. The convergence of the nonnegative UGA algorithm will be established. For the graph sparsification problem, another UGA algorithm will be proposed which can output a $\frac{1+O(\epsilon)}{1-O(\epsilon)}$-spectral sparsifier with $\lceil\frac{n}{\epsilon^2}\rceil$ edges in $O(m+n^2/\epsilon^2)$ time from a graph with $m$ edges and $n$ vertices under some mild assumptions. This is a linear time algorithm in terms of the number of edges that the community of graph sparsification is looking for. The best result in the literature to the knowledge of the authors is the existence of a deterministic algorithm which is almost linear, i.e. $O(m^{1+o(1)})$ for some $o(1)=O(\frac{(\log\log(m))^{2/3}}{\log^{1/3}(m)})$. Finally, extensive experimental results, including applications to graph clustering and least squares regression, show the effectiveness of proposed approaches.

Two Choice Hard Thresholding Pursuit (TCHTP) for Delay-Doppler Channel Estimation in OTFS

In this work, we develop a low complexity fast greedy sparse recovery algorithm known as Two Choice Hard Thresholding Pursuit (TCHTP) to estimate delay-Doppler locations and the associated channel state information (DDLCSI) for orthogonal-time-frequency-space (OTFS) systems, without the explicit knowledge of the number of delay-Doppler (DD) paths. Unlike the existing greedy algorithms, the proposed scheme simultaneously estimates the DDLCSI as well as the number of DD paths. Furthermore, we perform computational complexity calculations for the proposed TCHTP and the state-of-the-art technique, and observe that the proposed method enjoys reduced computational complexity along with fast convergence speed compared to the state-of-the-art technique. Numerical simulations validate the superiority of the proposed TCHTP algorithm in terms of mean squared error of the DDLCSI estimate, estimate of the number of DD paths, bit-error-rate, computational complexity and execution time.