Sparse Signal Reconstruction Algorithm Research Articles

Time-varying neurodynamic optimization approaches with fixed-time convergence for sparse signal reconstruction

Convergence speed is one of the most considerable features for sparse signal reconstruction algorithms. This paper introduces several novel fast time-varying neurodynamic optimization approaches (TVNOAs) with fixed-time convergence for sparse signal reconstruction. It is demonstrated that these trajectories converge to solutions within a fixed-time from arbitrary initial conditions, exhibiting a faster convergence rate due to the selection of appropriate time-varying coefficients. The fixed-time convergence of the proposed TVNOAs is investigated using the Polyak–Lojasiewicz condition. Moreover, explicit upper bounds for the settling time of TVNOAs are provided. Additionally, the robustness under bounded noises is further examined. Numerical experiments on sparse signal reconstruction validate the superiority of the proposed neurodynamic approaches.

Evaluation on improved sparse signal reconstruction algorithm for trusted AI and DCS technology

The improved Sparse Signal Reconstruction (SR) algorithm for Trusted Artificial Intelligence (AI) and Distributed Compressed Sensing (DCS) technology was thoroughly investigated. The study verified its effectiveness and advantages in trusted AI and DCS systems, which have significant implications for enhancing the credibility, security, and performance of signal processing and AI algorithms. The reconstruction performance was evaluated using Orthogonal Matching Pursuit (OMP), Basis Pursuit (BP), and Least Absolute Shrinkage and Selection Operator (LASSO). The analysis primarily focused on runtime, refactoring errors, and the number of successful reconstruction attempts. When K = 4, K = 6, K = 8, and K = 10, OMP outperformed BP and LASSO in terms of successful reconstructions, demonstrating better performance and higher reconstruction precision.

A distributed neurodynamic algorithm for sparse signal reconstruction via [formula omitted]-minimization

This paper proposes a distributed neurodynamic algorithm for sparse signal reconstruction by addressing ℓ1-minimization problems. Firstly, a ℓ1-minimization problem is transformed into a distributed model, drawing support from multi-agent consensus theory. Secondly, to address this distributed model, a novel distributed neurodynamic algorithm is proposed by employing derivative feedback and projection operator. It is proved that the proposed neurodynamic algorithm is globally convergent by utilizing the properties of projection operator and set-valued system. Moreover, compared with the existing distributed neurodynamic algorithms, the proposed neurodynamic algorithm is inverse-free and does not involve any matrix decomposition. Finally, some experimental results on sparse signal reconstruction indicate the effectiveness of the proposed neurodynamic algorithm.

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.

A linearly convergent self-adaptive gradient projection algorithm for sparse signal reconstruction in compressive sensing

<abstract><p>For sparse signal reconstruction (SSR) problem in compressive sensing (CS), by the splitting technique, we first transform it into a continuously differentiable convex optimization problem, and then a new self-adaptive gradient projection algorithm is proposed to solve the SSR problem, which has fast solving speed and pinpoint accuracy when the dimension increases. Global convergence of the proposed algorithm is established in detail. Without any assumptions, we establish global $ R- $linear convergence rate of the proposed algorithm, which is a new result for constrained convex (rather than strictly convex) quadratic programming problem. Furthermore, we can also obtain an approximate optimal solution in a finite number of iterations. Some numerical experiments are made on the sparse signal recovery and image restoration to exhibit the efficiency of the proposed algorithm. Compared with the state-of-the-art algorithms in SSR problem, the proposed algorithm is more accurate and efficient.</p></abstract>

A Signal Dependent Analysis of Orthogonal Least Squares Based on the Restricted Isometry Property

The Orthogonal Least Squares (OLS) is a widespread greedy algorithm for sparse signal approximation or reconstruction. We here address the problem of sufficient condition for exact signal support recovery via OLS. Based on the generalized Wielandt inequality, new bounds on the OLS selection rule are provided that enable a simple approach of the Restricted Isometry Property based analysis of OLS. Since these new bounds naturally take the signal magnitude distribution into account, they allow a derivation of a new relaxed exact support recovery condition in the noise-free case. Moreover, we study their influence on the design of such new conditions in bounded noise and Gaussian noise cases.

Sparse Signal and Image Reconstruction Algorithm for Adaptive Dual Thresholds Matching Pursuit Based on Variable-step Backtracking Strategy

Sparse Signal and Image Reconstruction Algorithm for Adaptive Dual Thresholds Matching Pursuit Based on Variable-step Backtracking Strategy

Spatiotemporal optimization of groundwater monitoring networks using data-driven sparse sensing methods

Abstract. Groundwater monitoring and specific collection of data on the spatiotemporal dynamics of the aquifer are prerequisites for effective groundwater management and determine nearly all downstream management decisions. An optimally designed groundwater monitoring network (GMN) will provide the maximum information content at the minimum cost (Pareto optimum). In this study, PySensors, a Python package containing scalable, data-driven algorithms for sparse sensor selection and signal reconstruction with dimensionality reduction is applied to an existing GMN in 1D (hydrographs) and 2D (gridded groundwater contour maps). The algorithm first fits a basis object to the training data and then applies a computationally efficient QR algorithm that ranks existing monitoring wells (for 1D) or suitable sites for additional monitoring (for 2D) in order of importance, based on the state reconstruction of this tailored basis. This procedure enables a network to be reduced or extended along the Pareto front. Moreover, we investigate the effect of basis choice on reconstruction performance by comparing three types typically used for sparse sensor selection (i.e., identity, random projection, and SVD, respectively, PCA). We define a gridded cost function for the extension case that penalizes unsuitable locations. Our results show that the proposed approach performs better than the best randomly selected wells. The optimized reduction makes it possible to adequately reconstruct the removed hydrographs with a highly reduced subset with low loss. With a GMN reduced by 94 %, an average absolute reconstruction accuracy of 0.1 m is achieved, in addition to 0.05 m with a reduction by 69 % and 0.01 m with 18 %.

Sparse signal reconstruction via collaborative neurodynamic optimization

In this paper, we formulate a mixed-integer problem for sparse signal reconstruction and reformulate it as a global optimization problem with a surrogate objective function subject to underdetermined linear equations. We propose a sparse signal reconstruction method based on collaborative neurodynamic optimization with multiple recurrent neural networks for scattered searches and a particle swarm optimization rule for repeated repositioning. We elaborate on experimental results to demonstrate the outperformance of the proposed approach against ten state-of-the-art algorithms for sparse signal reconstruction.

Modified complex multitask Bayesian compressive sensing using Laplacian scale mixture prior

Bayesian compressive sensing (BCS) is an important sub-class of sparse signal reconstruction algorithms. In this paper, a modified complex multitask Bayesian compressive sensing (MCMBCS) algorithm using the Laplacian scale mixture (LSM) prior is proposed. The LSM prior is first introduced into the complex BCS framework by exploiting its better sparse characteristic and flexibility than traditional Laplacian prior. Furthermore, by integrating out the noise variance analytically, the MCMBCS algorithm significantly improves the signal recovery performance than the original CMBCS. More importantly, the authors not only present the iterative algorithm but also develop the sub-optimal fast implementation method based on the marginal likelihood maximisation, which dramatically reduce the computational complexity. Finally, sufficient numerical simulations validate the better performance of the proposed algorithm in reconstruction accuracy and computational effectiveness than existing work. It is revealed that the proposed algorithm has great potential in the complex-valued signal processing field.

Gohberg-Semencul Factorization-Based Fast Implementation of Sparse Bayesian Learning With a Fourier Dictionary

Sparse Bayesian learning (SBL) is a popular and robust algorithm for sparse signal reconstruction (SSR). Unfortunately, the SBL algorithm suffers from heavy computational complexity when it is implemented directly since the inversion and multiplying operations of the estimation of the covariance matrix are involved in each iteration, which is proportional to the cube of the observed data length and thus prevents it solving large-scale problems. In many applications, such as radar imaging and array signal processing, the signal to be recovered is sparse in the Fourier dictionary. In this article, we propose an efficient implementation method for the Fourier dictionary-based SBL (FD-SBL). In the case that the Fourier dictionary is adopted, the estimation of the covariance matrix is a Toeplitz matrix for 1-D data or a Toeplitz-block-Toeplitz (TBT) matrix for 2-D data during the FD-SBL iterations. By utilizing this property, we employ the Gohberg–Semencul (G-S)-type factorization to accelerate the implementation of FD-SBL. To be noted, there is no approximation in our proposed method, and the computational cost is reduced by several orders of magnitude compared with the direct implementation of SBL. Finally, the experimental results verify the effectiveness of the proposed method.

Off-Grid Error and Amplitude–Phase Drift Calibration for Computational Microwave Imaging With Metasurface Aperture Based on Sparse Bayesian Learning

Computational microwave imaging (CMI) based on the frequency diversity metasurface apertures (FDMAs) is an emerging technology and has attracted wide attention. FDMA based CMI (FDMA-CMI) can be considered as microwave compressive sensing imaging with the frequency diversity pattern of the FDMA being the sensing matrix and solved by sparse signal reconstruction algorithms. However, the imaging quality is affected by the sensing matrix error and off-grid error seriously. In this paper, we propose a novel algorithm for FDMA-CMI, referred to as OGSISBL, by taking both the off-grid error and sensing matrix error into account. Firstly, we establish the measurement model with both the off-grid error and sensing matrix error. Specifically, the off-grid error is represented as a set of parameters to be estimated in the measurement model and the sensing matrix error is represented as the amplitude-phase drift of the transceiver channels of the imaging system due to the principle of the FDMA. Then, under the framework of the sparse Bayesian learning, a robust imaging algorithm OGSISBL is developed via the variational Bayesian expectation maximization (VBEM), which can not only recover the amplitude and position of the return of the scattered, but also simultaneously calibrate the amplitude-phase drift of the transceiver channels and the off-grid error. The performance of the proposed algorithm is evaluated by both the simulation data and the measured data collected by the self-designed experimental FDMA-CMI system, and the results validate the effectiveness and robustness of the proposed method.

Time-Frequency Sparse Reconstruction of Non-Uniform Sampling for Non-Stationary Signal

We address the problem of the reconstruction of time-frequency characteristics of sparse multi-band signals by using the discrete multi-coset sampling (DMCS) model. In this article, the signal is characterized by complicated time-variable components. According to the feature of the short-time Fourier transform (STFT) analysis method, we obtain the rewritten matrix form of the discrete STFT. Then, an analysis method of the multi-coset sliding window (MCSW) is proposed, and the discrete multi-coset sampling sequence is locally windowed. The sparse signal reconstruction algorithm is used to obtain the optimal time-frequency reconstruction value of the original signal. Numerical simulations show the feasibility of this method. We simulate the effects of measurement noise, sampling rate, and time-frequency analysis parameters on the reconstruction accuracy. Our method can carry out time-frequency reconstruction for undersampled signals obtained from multi-coset sampling to ensure the time-varying feature of the original signals, which can well highlight the characteristics of signals. The method is of great significance to the research and development of the sub-Nyquist sampling technique.

A comparative study of multi-objective optimization algorithms for sparse signal reconstruction

A comparative study of multi-objective optimization algorithms for sparse signal reconstruction

A novel sparse reconstruction method based on multi-objective Artificial Bee Colony algorithm

Compressed sensing is a signal processing method that performs the compressing and sensing processes at the same time. Sparse signal reconstruction is one of the most important issues of compressed sensing. The developments in sparse signal reconstruction methods directly affect the performance of the compressed sensing process. Many sparse signal reconstruction methods have been proposed in the literature. In general, these algorithms are classified as convex optimization, non-convex optimization, and greedy algorithms. In addition, multi-objective optimization algorithms have started to be used in sparse signal reconstruction lately. A sparse signal reconstruction method based on a Multi-objective Artificial Bee Colony algorithm is proposed in this study. The proposed algorithm optimizes the sparsity and measurement error at the same time. Furthermore, it uses the iterative half thresholding algorithm to improve the convergence acceleration of the method. The proposed method was evaluated by using various test signals. Additionally, it was compared with other sparse signal reconstruction algorithms. According to the obtained results, the proposed method has some superiority over the compared algorithms.

A Neurodynamic Algorithm for Sparse Signal Reconstruction with Finite-Time Convergence

In this paper, a neurodynamic algorithm with finite-time convergence to solve $${L_{\mathrm{{1}}}}$$ -minimization problem is proposed for sparse signal reconstruction which is based on projection neural network (PNN). Compared with the existing PNN, the proposed algorithm is combined with the sliding mode technique in control theory. Under certain conditions, the stability of the proposed algorithm in the sense of Lyapunov is analyzed and discussed, and then the finite-time convergence of the proposed algorithm is proved and the setting time bound is given. Finally, simulation results on a numerical example and a contrast experiment show the effectiveness and superiority of our proposed neurodynamic algorithm.

Gradient Immune-based Sparse Signal Reconstruction Algorithm for Compressive Sensing

The reconstruction aspect is the main core of the compressive sensing theory, in which the sparse signal is reconstructed from an incomplete set of random measurements. The constraint of spare signal reconstruction is the minimization of l0-norm, especially under noise condition. Thus, this paper proposes a new method called Gradient Immune-based Sparse Signal Reconstruction Algorithm for Compressive Sensing (GISSRA-CS) to optimize the trade-off between the reconstruction error and the sparsity requirements. The principle of the GISSRA-CS method is embedding the Gradient Local Search (GLS) method in the evolutionary process of the Immune Algorithm (IA) for solving the sparsity problem. Here, the sparsity problem is formulated as a multi-objective problem (MOP) by combining l0 and l1-norms of a solution and l2-norm of a residual error in the same criterion to optimize the trade-off between the sparsity requirements and the error. This MOP problem is solved in a several subproblems manner by assigning different weights for each subproblem to increase the population diversity. For a long-term sparse signal, the window method is used to divide it into multiple short signals to improve the performance and computational complexity of the proposed method. Mathematical analysis and simulation experiments are presented to validate the performance and complexity of the GISSRA-CS method. Results of different simulation scenarios based on the benchmark and simulated signals show that the GISSRA-CS method outperforms the other methods in recovering the sparse signals with a small reconstruction error from noiseless and noisy measurements. Furthermore, the convergence of GISSRA-CS is faster than the other evolutionary recovery methods, but it is slower than the traditional recovery methods.

A novel multiobjective optimization algorithm for sparse signal reconstruction

Sparsity and reconstruction error are two main objectives to be optimized in sparse signal reconstruction. In this paper, sparse signals are reconstructed by optimizing these two objectives simultaneously. This reconstruction method mainly consists of three steps. First, a one-dimension-dominated method is used to find a uniformly distributed optimal compromise solution set between these two objectives. Second, the Iterative Half Thresholding method is employed to improve the sparsity. Third, a robust selection method is proposed to choose a final solution from the solution set. The proposed method is compared with eight sparse reconstruction algorithms on twelve sparse test instances. Experimental results show that the proposed algorithm is able to reconstruct both noisy and noiseless sparse signals. In addition, the effectiveness of the proposed algorithm is demonstrated in practical application instances.

Bayesian Matching Pursuit: A Finite-Alphabet Sparse Signal Recovery Algorithm for Quantized Compressive Sensing

In this letter, we consider the problem of detecting finite-alphabet sparse signals from noisy and coarsely quantized measurements. To solve this problem, we propose a greedy sparse signal detection algorithm referred to as Bayesian matching pursuit (BMP). The key idea of BMP is to identify the non-zero elements of a sparse signal that produce the largest a posteriori probabilities in an iterative fashion. Our simulation results show that the BMP algorithm outperforms the existing sparse signal reconstruction algorithms in terms of frame error rates even with a significantly reduced computational complexity.

Non-Negative Orthogonal Greedy Algorithms

Orthogonal greedy algorithms are popular sparse signal reconstruction algorithms. Their principle is to select atoms one by one. A series of unconstrained least-square subproblems of gradually increasing size is solved to compute the approximation coefficients, which is efficiently performed using a fast recursive update scheme. When dealing with non-negative sparse signal reconstruction, a series of non-negative least-squares subproblems have to be solved. Fast implementation becomes tricky since each subproblem does not have a closed-form solution anymore. Recently, non-negative extensions of the classical orthogonal matching pursuit and orthogonal least squares algorithms were proposed, using slow ( i.e. , non-recursive) or recursive but inexact implementations. In this paper, we revisit these algorithms in a unified way. We define a class of non-negative orthogonal greedy algorithms and exhibit their structural properties. We propose a fast and exact implementation based on the active-set resolution of non-negative least-squares and exploiting warm start initializations. The algorithms are assessed in terms of accuracy and computational complexity for a sparse spike deconvolution problem. We also present an application to near-infrared spectra decomposition.