Sparse Signal Recovery Algorithm Research Articles

Binary Least Squares: An Algorithm for Binary Sparse Signal Recovery

Binary Least Squares: An Algorithm for Binary Sparse Signal Recovery

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.

Hard threshold acceleration algorithms for sparse signal recovery

Hard threshold acceleration algorithms for sparse signal recovery

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 Pseudo-Inverse-Based Hard Thresholding Algorithm for Sparse Signal Recovery

A Pseudo-Inverse-Based Hard Thresholding Algorithm for Sparse Signal Recovery

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.

Heavy-ball-based hard thresholding algorithms for sparse signal recovery

The hard thresholding technique plays a vital role in the development of algorithms for sparse signal recovery. By merging this technique and heavy-ball acceleration method which is a multi-step extension of the traditional gradient descent method, we propose the so-called heavy-ball-based hard thresholding (HBHT) and heavy-ball-based hard thresholding pursuit (HBHTP) algorithms for signal recovery. It turns out that the HBHT and HBHTP can successfully recover a k-sparse signal if the restricted isometry constant of the measurement matrix satisfies δ3k<0.618 and δ3k<0.577, respectively. The guaranteed success of HBHT and HBHTP is also shown under the conditions δ2k<0.356 and δ2k<0.377, respectively. Moreover, the finite convergence of HBHTP and stability of the two algorithms are also established in this paper. Simulations on random problem instances are performed to compare the performance of the proposed algorithms and several existing ones. Empirical results indicate that the HBHTP performs very comparably to a few existing algorithms and it takes less average time to achieve the signal recovery than these existing methods.

Performance analysis of compressive sensing and reconstruction by LASSO and OMP for audio signal processing applications

Audio signal processing is used in acoustic IoT sensor nodes which have limitations in data storage, computation speed, hardware size and power. In most audio signal processing systems, the recovered data constitutes far less fraction of the sampled data providing scope for compressive sensing (CS) as an efficient way for sampling and signal recovery. Compressive sensing is a signal processing technique in which a sparse approximated signal is reconstructed at the receiving node by a signal recovery algorithm, using fewer samples compared to traditional sampling methods. It has two main stages: sparse approximation to convert the signal into a sparse domain and reconstruction through sparse signal recovery algorithms. Recovery algorithms involve complex matrix multiplication and linear equations in sampling and reconstruction, increasing the computational complexity and leading to highly resourceful hardware implementations. This work reconstructs the sparse audio signal using LASSO and orthogonal matching pursuit (OMP) algorithm. OMP is an iterative greedy algorithm involving least square method that takes a compressed signal as input and recovers it from the sparse approximation, while LASSO is L1 norm based with a controlled L2 penalty. The paper reviews the reconstruction and study of sparsity and error obtained for reconstructing an audio signal by OMP and LASSO.

Target parameter estimation for OTFS radar using sparse signal processing

In this paper, we consider a monostatic radar receiver for a joint communication and radar (JCR) system that transmits orthogonal time frequency space (OTFS) frames for target detection and parameter estimation. The circular prolate pulse shape (CPPS) is employed over the OTFS signal as it has lower out-of-band (OoB) power radiation in comparison with the rectangular pulse shaped (RPS) OTFS. The PAPR of CPPS OTFS signal shows lowest value for larger frame duration and hence the signal can be considered to be a good candidate for JCR system. In the Delay-Doppler (DD) domain, the radar channel is sparse and therefore, we model the target detection problem as a sparse recovery problem to generate target profiles with higher peak-to-sidelobe ratio (PSLR). The target detection is carried out in the DD domain, the time–frequency (TF) domain, and in the time domain (TD). Sparse signal recovery algorithms like the orthogonal matching pursuit (OMP) algorithm, the subspace pursuit (SP) algorithm, and the sparse Bayesian learning (SBL) based algorithm are used in target parameter estimation. The performance of these algorithms are compared in terms of their computational complexity, the root mean squared error (RMSE) in the estimates of range and velocity and PSLR value in the target profiles. Simulation results validate that the proposed CPPS OTFS based radar system could detect the targets accurately in all the three domains and produce target profiles with almost zero side lobes.

Improved Sufficient Conditions Based on RIC of Order 2s for IHT and HTP Algorithms

Reconstructing an s-sparse signal x from an un- derdetermined noisy linear model arises in many applications. The iterative hard thresholding (IHT) and hard thresholding pursuit (HTP) algorithms are two popular sparse signal recovery algorithms. Since their recovery performances can be theoreti- cally characterized by their sufficient conditions of stable sparse signal recovery, it is essential to establish less restrictive sufficient conditions. This work develops δ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2s</sub> -based sufficient conditions for stable recovery with IHT and HTP. The two new sufficient conditions are significantly less restrictive than the state-of-the- art ones for IHT and HTP.

Convolutional Sparse Support Estimator Network (CSEN): From Energy-Efficient Support Estimation to Learning-Aided Compressive Sensing.

Support estimation (SE) of a sparse signal refers to finding the location indices of the nonzero elements in a sparse representation. Most of the traditional approaches dealing with SE problems are iterative algorithms based on greedy methods or optimization techniques. Indeed, a vast majority of them use sparse signal recovery (SR) techniques to obtain support sets instead of directly mapping the nonzero locations from denser measurements (e.g., compressively sensed measurements). This study proposes a novel approach for learning such a mapping from a training set. To accomplish this objective, the convolutional sparse support estimator networks (CSENs), each with a compact configuration, are designed. The proposed CSEN can be a crucial tool for the following scenarios: 1) real-time and low-cost SE can be applied in any mobile and low-power edge device for anomaly localization, simultaneous face recognition, and so on and 2) CSEN's output can directly be used as "prior information," which improves the performance of sparse SR algorithms. The results over the benchmark datasets show that state-of-the-art performance levels can be achieved by the proposed approach with a significantly reduced computational complexity.

Parallel Greedy Search for Random Access in Wireless Networks

We consider the random access problem in wireless networks such as cellular networks and massive machine type communication networks, where a large number of devices/users are connected to a base station. In order to establish communication with the base station, as a part of the random access procedure, active users select and transmit codes (pilot sequences) randomly from a codebook. Since the active users are typically a small fraction of the total users, sparse signal recovery algorithms are employed to detect the transmitted codes. In this paper, we use multiple measurement vector model for the received signal and develop a parallel greedy search algorithm and it’s stopping criteria to detect the active users. We show through simulations that the proposed scheme, compared with the existing greedy algorithms, gives better detection performance at lower false alarms levels. We study how the code length and the code word size need to be chosen in order to detect a given number of active users. We also address the scenario when there are different timing offsets for signals received from different users.

Sensing matrix design for wideband channel estimation in millimeter‐wave hybrid multiple‐input multiple‐output system

AbstractHybrid analog/digital multiple‐input multiple‐output (MIMO) system is proposed to support low complexity multi‐stream communication in millimeter‐wave (mmWave) frequencies. The main idea of channel estimation methods for mmWave hybrid MIMO systems is based on leveraging the sparsity nature of the channel in the angle and delay domain. Sparse signal recovery algorithms have been used to reconstruct the channel coefficients. Due to the lack of information about the angle of arrival and angle of departure before channel estimation, random values are common choices for precoders and combiners. Moreover, the training pilot symbols are considered to be random variables. In this article, we propose sequential time domain sensing matrix design and sequential frequency domain sensing matrix design algorithms to design these variables in order to enhance sparse signal recovery performance and consequently the channel estimation accuracy. Our methods are based on reducing the correlation between the sensing matrix columns, which is defined in the sparse formulation of the channel estimation problem. We design the training radio frequency precoders/combiners phase angle values and pilot symbol vectors with the aid of a sequential procedure that has a reasonable complexity. Simulation results show that utilizing the designed values instead of random variables increased the performance of the channel estimation, especially when we deal with a higher number of variables.

Natural Thresholding Algorithms for Signal Recovery With Sparsity

The algorithms based on the technique of optimal <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula>-thresholding (OT) were recently proposed for signal recovery, and they are very different from the traditional family of hard thresholding methods. However, the computational cost for OT-based algorithms remains high at the current stage of their development. This stimulates the development of the so-called natural thresholding (NT) algorithm and its variants in this paper. The family of NT algorithms is developed through the first-order approximation of the so-called regularized optimal <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula>-thresholding model, and thus the computational cost for this family of algorithms is significantly lower than that of the OT-based algorithms. The guaranteed performance of NT-type algorithms for signal recovery from noisy measurements is shown under the restricted isometry property and concavity of the objective function of regularized optimal <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula>-thresholding model. Empirical results indicate that the NT-type algorithms are robust and very comparable to several mainstream algorithms for sparse signal recovery.

Compressive hard thresholding pursuit algorithm for sparse signal recovery

&lt;abstract&gt;&lt;p&gt;Hard Thresholding Pursuit (HTP) is one of the important and efficient algorithms for reconstructing sparse signals. Unfortunately, the hard thresholding operator is independent of the objective function and hence leads to numerical oscillation in the course of iterations. To alleviate this drawback, the hard thresholding operator should be applied to a compressible vector. Motivated by this idea, we propose a new algorithm called Compressive Hard Thresholding Pursuit (CHTP) by introducing a compressive step first to the standard HTP. Convergence analysis and stability of CHTP are established in terms of the restricted isometry property of a sensing matrix. Numerical experiments show that CHTP is competitive with other mainstream algorithms such as the HTP, Orthogonal Matching Pursuit (OMP) and Subspace Pursuit (SP) algorithms both in the sparse signal reconstruction ability and average recovery runtime.&lt;/p&gt;&lt;/abstract&gt;

Distributed Signal Processing Algorithms for Wireless Sensor Networks

Wireless Body Area Networks (WBAN), in particular in the field of wearable health monitoring system (WMB), such as electromagnetic cardiograms (ECG) data collecting system via WBANs in e-health applications, is becoming increasingly important for future communication systems. Compressive sensing (CS), on the other hand, has been shown to consume less power compared classic transform-coding-based approaches. We propose a new low-rank sparse deep signal recovery algorithm for recovering ECG data in the context of CS (Compressive sensing) because the spatial and temporal data collected by a WBAN have some closely correlated structures in certain wavelet domains e.g., the discrete wavelet transform (DWT) domain

A fast algorithm for joint sparse signal recovery in 1-bit compressed sensing

In this letter, a new algorithm is proposed for fast 1-bit compressed sensing (CS) recovery from multiple measurement vectors (MMV). The proposed algorithm is based on the adaptive outlier pursuit-flip (AOP-f), which adaptively locates and corrects potential sign flips from the measurement vectors. To improve the performance, we introduce an erasure method to the proposed algorithm by setting ambiguous sign flips as erasures. Additionally, we present a new stopping criterion, which significantly reduces the time complexity of the proposed algorithm. Numerical results show that the proposed algorithm performs better than existing ones in terms of reconstruction performance and time complexity.

A convergence analysis for iterative sparsification projection with soft-thresholding

The recently proposed iterative sparsification projection (ISP), a fast and robust sparse signal recovery algorithm framework, can be classified as smooth-ISP and nonsmooth-ISP. However, no convergence analysis has been established for the nonsmooth-ISP in the previous works. Motivated by this absence, the present paper provides a convergence analysis for ISP with soft-thresholding (ISP-soft) which is an instance of the nonsmooth-ISP. In our analysis, the composite operator of soft-thresholding and proximal projection is viewed as a fixed point mapping, whose nonexpansiveness plays a key role. Specifically, our convergence analysis for the sequence generated by ISP-soft can be summarized as follows: 1) For each inner loop, we prove that the sequence has a unique accumulation point which is a fixed point, and show that it is a Cauchy sequence; 2) for the last inner loop, we prove that the accumulation point of the sequence is a critical point of the objective function if the final value of the threshold satisfies a condition, and show that the corresponding objective values are monotonically nonincreasing. A numerical experiment is given to validate some of our results and intuitively present the convergence.

Learning-based accelerated sparse signal recovery algorithms

In this paper, we propose an accelerated sparse recovery algorithm based on inexact alternating direction of multipliers. We formulate a sparse recovery problem with a concave regularizer and solve it with the relaxed and accelerated alternating method of multipliers (R-A-ADMM). We introduce learnable parameters to optimize the algorithm with given data sets. The derived algorithm is an accelerated version of LISTA-AT that controls the threshold for each entry according to the previously recovered estimate. Numerical results show that the proposed Accel-LISTA-AT algorithm converges much faster and recovers the sparse signals with lower mean squared errors than the other learning-based sparse recovery algorithms.