Sparse Signal Research Articles

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.

A Lorentzian-[formula omitted] norm regularization based algorithm for recovering sparse signals in two types of impulsive noise

In this paper, we present a Lorentzian-ℓp(0<p<1) optimization for recovering sparse signals from measurements corrupted by two types of impulsive noise. A smoothing strategy for nonconvex ℓp norm is employed and an efficient Lorentzian based iterative algorithm is developed for solving the resulting optimization problem. We describe the detailed process of the algorithm and establish the convergence of the proposed algorithm. Numerical results show that our proposed algorithm performs effectively in recovering sparse signals from impulsive measurement noise compared with the state-of-the-art methods.

Compressed Sensing of Traction Motor Bearing Vibration Signals based on Discrete Fourier Transform and Generalized Orthogonal Matching Pursuit Algorithm

For the bogie traction motor bearings of rail vehicles under road transportation conditions, its vibration signal full-time domain data acquisition data volume, storage pressure, subsequent data analysis difficulties, and other problems. This study proposes a data compression acquisition and data reconstruction method for bearing vibration signals based on compressed sensing (CS), which can achieve compressed sampling, transmission, and storage of the original signal with fewer observations, and restore the original signal by combining reconstruction algorithms to achieve low error reconstruction. We study the effects of different sparse transform methods on signal sparsity, as well as the signal sparse performance based on different sparse transforms and the signal reconstruction effect of different reconstruction algorithms, and propose a sparse representation method based on the discrete Fourier transform (DFT) and the generalized orthogonal matching pursuit (gOMP) algorithm for CS. Through simulation and experimental comparison, it is concluded that the method can restore and reconstruct the original high-dimensional signal with small reconstruction error, and solve the problems of massive data, inconvenient transmission, and difficult data analysis in engineering.

Impact of antenna directivity on compressed sensing-based DOA estimation employing UCA antenna

This letter investigates the impact of the antenna element directivity on compressed sensing (CS)-based direction of arrival (DOA) estimation employing the uniform circular array (UCA) antenna. In the CS-based approach, the reconstruction accuracy of sparse signals is determined by a sensing matrix, which depends on the array antenna configuration in the DOA estimation. In our study, we analyze the cross-correlation between column vectors of the sensing matrix and clarify the estimation accuracy for various antenna element radiation patterns.

Compressed Sensing Σ-Δ Modulators and a Recovery Algorithm for Multi-Channel Wireless Bio-Signal Acquisition

Compressed sensing (CS) exploits signal sparsity in some domain to enable sub-Nyquist sampling which increases the energy efficiency of analog-to-digital conversion (ADC) and downstream data processing circuits–the sampling frequency is determined by the information rate, not the usual Nyquist rate. CS techniques for wireless multi-channel bio-signal recording applications based on sigma-delta modulation (SDM) are detailed and used to validate a multi-channel recovery algorithm. The SDM topology allows the required dot product calculations between the measurement and signal vectors to be performed in conjunction with its inherent integration using minimal additional circuitry. It eliminates opamp output saturation concerns and benefits directly from still ongoing Moore’s Law CMOS technology scaling. Finally, a sparse sensing matrix and recovery algorithm are described that exploit similar sparse signatures across multiple channels to improve both signal recovery accuracy and chip area efficiency. Simulation results validate the concepts.

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.

An improved fast adaptive complex approximation message passing algorithm

To solve the problem of reconstructing complex sparse signals from linear measurements of additive white Gaussian noise (AWGN) under the condition of unknown sparse signal distribution, this paper proposes a fast adaptive complex approximate message passing (CAMP) algorithm with significantly reduced mean square error and adaptive to parameter selection. First, we establish a complex sparse signal distribution model. Secondly, the unknown parameters of the distribution model are estimated in each iteration, and the estimated values are used as prior information to obtain the complex shrinkage function with minimum mean square error (MMSE). Finally, an improved fast adaptive CAMP algorithm is obtained by combining the updated shrinkage function with the CAMP. The algorithm has the advantages of fast convergence, low computational complexity, small mean square error, and good robustness. Theoretical analysis and simulation verify the effectiveness of the proposed algorithm.

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.

Low-Cost COTS GNSS Interference Monitoring, Detection, and Classification System

Interference signals cause position errors and outages to global navigation satellite system (GNSS) receivers. However, to solve these problems, the interference source must be detected, classified, its purpose determined, and localized to eliminate it. Several interference monitoring solutions exist, but these are expensive, resulting in fewer nodes that may miss spatially sparse interference signals. This article introduces a low-cost commercial-off-the-shelf (COTS) GNSS interference monitoring, detection, and classification receiver. It employs machine learning (ML) on tailored signal pre-processing of the raw signal samples and GNSS measurements to facilitate a generalized, high-performance architecture that does not require human-in-the-loop (HIL) calibration. Therefore, the low-cost receivers with high performance can justify significantly more receivers being deployed, resulting in a significantly higher probability of intercept (POI). The architecture of the monitoring system is described in detail in this article, including an analysis of the energy consumption and optimization. Controlled interference scenarios demonstrate detection and classification capabilities exceeding conventional approaches. The ML results show that accurate and reliable detection and classification are possible with COTS hardware.

Underdetermined Blind Source Separation Method for Speech Signals Based on SOM-DPC and Compressed Sensing

Underdetermined blind source separation has received increasing attention in recent years as an effective method for speech-signal processing. Hence, a self-organizing mapping-density peak clustering and compressed sensing approach, which is a two-step approach, is proposed herein to improve the accuracy of underdetermined blind source separation. The approach features the following two aspects: (1) A mixing matrix estimation method based on self-organizing mapping and density peak clustering, which can intuitively determine the number of source signals, remove outliers, and determine the column vector of the mixing matrix based on local density; (2) a compressed sensing-based source signal reconstruction method, which can exploit the sparsity of signals in the frequency domain and use a hierarchical coupling method to reconstruct the source signal accurately and efficiently under the premise that the prior knowledge of the signal is unknown. The proposed method does not require the number of source signals and exhibits excellent performance under different noise conditions. Theoretical analysis and experimental results demonstrate the effectiveness of the proposed method.

Granger causality for compressively sensed sparse signals.

Compressed sensing is a scheme that allows for sparse signals to be acquired, transmitted, and stored using far fewer measurements than done by conventional means employing the Nyquist sampling theorem. Since many naturally occurring signals are sparse (in some domain), compressed sensing has rapidly seen popularity in a number of applied physics and engineering applications, particularly in designing signal and image acquisition strategies, e.g., magnetic resonance imaging, quantum state tomography, scanning tunneling microscopy, and analog to digital conversion technologies. Contemporaneously, causal inference has become an important tool for the analysis and understanding of processes and their interactions in many disciplines of science, especially those dealing with complex systems. Direct causal analysis for compressively sensed data is required to avoid the task of reconstructing the compressed data. Also, for some sparse signals, such as for sparse temporal data, it may be difficult to discover causal relations directly using available data-driven or model-free causality estimation techniques. In this work, we provide a mathematical proof that structured compressed sensing matrices, specifically circulant and Toeplitz, preserve causal relationships in the compressed signal domain, as measured by Granger causality (GC). We then verify this theorem on a number of bivariate and multivariate coupled sparse signal simulations which are compressed using these matrices. We also demonstrate a real world application of network causal connectivity estimation from sparse neural spike train recordings from rat prefrontal cortex. In addition to demonstrating the effectiveness of structured matrices for GC estimation from sparse signals, we also show a computational time advantage of the proposed strategy for causal inference from compressed signals of both sparse and regular autoregressive processes as compared to standard GC estimation from original signals.

Compressive Sensing via Variational Bayesian Inference under Two Widely Used Priors: Modeling, Comparison and Discussion.

Compressive sensing is a sub-Nyquist sampling technique for efficient signal acquisition and reconstruction of sparse or compressible signals. In order to account for the sparsity of the underlying signal of interest, it is common to use sparsifying priors such as Bernoulli-Gaussian-inverse Gamma (BGiG) and Gaussian-inverse Gamma (GiG) priors on the components of the signal. With the introduction of variational Bayesian inference, the sparse Bayesian learning (SBL) methods for solving the inverse problem of compressive sensing have received significant interest as the SBL methods become more efficient in terms of execution time. In this paper, we consider the sparse signal recovery problem using compressive sensing and the variational Bayesian (VB) inference framework. More specifically, we consider two widely used Bayesian models of BGiG and GiG for modeling the underlying sparse signal for this problem. Although these two models have been widely used for sparse recovery problems under various signal structures, the question of which model can outperform the other for sparse signal recovery under no specific structure has yet to be fully addressed under the VB inference setting. Here, we study these two models specifically under VB inference in detail, provide some motivating examples regarding the issues in signal reconstruction that may occur under each model, perform comparisons and provide suggestions on how to improve the performance of each model.

Inertial projection neural network for nonconvex sparse signal recovery with prior information

Inertial projection neural network for nonconvex sparse signal recovery with prior information

Sparse signal reconstruction via Hager–Zhang-type schemes for constrained system of nonlinear equations

In this article, two Hager–Zhang (HZ) type projection algorithms are presented for large-dimension nonlinear monotone problems and sparse signal recovery in compressed sensing. This goal is attained by conducting singular value analysis of a nonsingular HZ-type search direction matrix as well as applying the idea by Piazza and Politi [J Comput Appl Math. 2002;143(1):141–144] and minimizing the Frobenius norm of an orthornormal matrix. The paper attempts to fill the gap in the work of Hager and Zhang [Pac J Optim. 2006;2(1):35–58], Waziri et al. [Appl Math Comput. 2019;361:645–660], Sabi'u et al. [Appl Numer Math. 2020;153:217–233] and Babaie-Kafaki [4OR-Q J Oper Res. 2014;12:285-292], where the sufficient descent or global convergence condition is not satisfied when the HZ parameter is in the interval . The proposed schemes are also suitable for solving non-smooth nonlinear problems. Also, by employing some mild conditions, global convergence of the schemes are established, while numerical comparison with four effective HZ-type methods show that the new methods are efficient. Furthermore, to illustrate their practical application, both methods are applied to solve the -norm regularization problems to recover a sparse signal in compressive sensing. The experiments conducted in that regard show that the methods are promising and perform better than two other methods in the literature.

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 Reconstruction Algorithm of Wireless Sensor Network Based on BFGS Quasi-Newton Method

Aiming at the problems of low reconstruction rate and poor reconstruction precision when reconstructing sparse signals in wireless sensor networks, a sparse signal reconstruction algorithm based on the Limit-Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) quasi-Newton method is proposed. The L-BFGS quasi-Newton method uses a two-loop recursion algorithm to find the descent direction dk directly by calculating the step difference between m adjacent iteration points, and a matrix Hk approximating the inverse of the Hessian matrix is constructed. It solves the disadvantages of BFGS requiring the calculation and storage of Hk, reduces the algorithm complexity, and improves the reconstruction rate. Finally, the experimental results show that the L-BFGS quasi-Newton method has good experimental results for solving the problem of sparse signal reconstruction in wireless sensor networks.

Framework for Segmented threshold [formula omitted] gradient approximation based network for sparse signal recovery

Signal reconstruction from compressed sensed data need iterative methods since the sparse measurement matrix is analytically non invertible. The iterative thresholding and ℓ0 function minimization are of special interest as these two operations provide sparse solution. However these methods need an inverse operation corresponding to the measurement matrix for estimating the reconstruction error. The pseudo-inverse of the measurement matrix is used in general for this purpose. Here a sparse signal recovery framework using an approximate inverse matrix Q and iterative segment thresholding of ℓ0 and ℓ1 norm with residue addition is presented. Two recovery algorithms are developed using this framework. The ℓ0 based method is later developed to a basis function dictionary based network for sparse signal recovery. The proposed framework enables the users experiment with different inverse matrix to achieve better efficiency in sparse signal recovery and implement the algorithm in computationally efficient way.

Sparse signals on hypergraphs

AbstractSignals with a sparse representation in a given basis as well as Laplacian eigenvectors of graphs play a big role in signal processing and machine learning. We put these topics together and look at signals on graphs that have a sparse representation in the basis of eigenvectors of the Laplacian matrix, which may appear after convolution with an unknown sparse filter. We give explicit algorithms to recover those sums by sampling the signal only on few vertices, i.e., the number of required samples is independent of the total size of the graph and takes only local properties of the graph into account. We generalize these methods to simplicial complexes.

TRUE: A Correlation Analysis Approach for Conducting Optimal Routing Metrics in VANETs

In vehicular networks, especially in urban scenarios, road topology-based routing shows great advantages in dealing with the problems of broken links and long delays originating from sparse connections and signal attenuation. However, how road status affect data transmission performance on various routing metrics is still an intricate and vague problem. Concerned with this problem, we propose a correlation analysis approach between road network features and routing metrics (TRUE) to assist in the construction of optimal routing metrics in road-based hierarchical inter-vehicle routing. Simulation results show that TRUE has a strong ability to optimize intermediate road selection.

Unsupervised Deep Learning of Sparse Signals against Low-Rank Backgrounds with Application to Online Lung Sound Separation

Unsupervised Deep Learning of Sparse Signals against Low-Rank Backgrounds with Application to Online Lung Sound Separation