Sparse Signal Reconstruction Research Articles

Demystifying the Coherence Index in Compressive Sensing [Lecture Notes

The existence and uniqueness conditions are a prerequisite to ensure the reliable reconstruction of sparse signals from reduced sets of measurements within the compressive sensing (CS) paradigm. However, despite their underpinning role in practical applications, the existing uniqueness relations are either computationally prohibitive to implement [the restricted isometry property (RIP)] or involve mathematical tools that are beyond the standard background of engineering graduates (the coherence index). This may introduce conceptual and computational obstacles in the development of engineering intuition, design of suboptimal practical solutions, and understanding of theoretical and practical limitations of the CS framework.

Training prediction and athlete heart rate measurement based on multi-channel PPG signal and SVM algorithm

Athlete’s heart rate measurement has certain guiding significance for athlete training and competition intensity arrangement. At present, the accuracy and efficiency of the athlete’s heart rate measurement method cannot meet the actual training needs of athletes. In view of this, based on support vector machine, this research combines with improved algorithm to build athlete heart rate measurement model. Moreover, in this study, the denoising algorithm of multi-channel spectral matrix decomposition is used to eliminate the interference factors. The heart rate measurement algorithm based on support vector machine (Mix-SVM) proposed by this paper mainly includes the following parts: preprocessing, preliminary filtering of motion noise, sparse signal reconstruction model, spectral subtraction, and heart rate spectral peak tracking method based on SVM. In addition, in order to verify the effectiveness of the algorithm in this study, a control experiment is designed to verify the efficiency and accuracy of the algorithm proposed by this study. The research results show that the algorithm proposed by this paper has certain advantages in accuracy and efficiency.

An Efficient Projected Gradient Method for Convex Constrained Monotone Equations with Applications in Compressive Sensing

In this paper, a modified Polak-Ribière-Polyak conjugate gradient projection method is proposed for solving large scale nonlinear convex constrained monotone equations based on the projection method of Solodov and Svaiter. The obtained method has low-complexity property and converges globally. Furthermore, this method has also been extended to solve the sparse signal reconstruction in compressive sensing. Numerical experiments illustrate the efficiency of the given method and show that such non-monotone method is suitable for some large scale problems.

Source localization in reverberation environment based on improved equivalent sound source near-field acoustic holography algorithm

The compressive-equivalent source method near-field acoustic holography (C-ESM) is disturbed by reverberation in the enclosed space such as room and cabin, which leads to large reconstruction error and disturbs the judgment of sound source position. In order to solve this problem, an improved C-ESM algorithm based on room impulse response (RIR) is proposed to filter out reverberation interference in this paper. Different from the original equivalent source method, the improved algorithm constructs the transfer function through the room impulse response to establish the relationship between the equivalent source and the sound pressure on any plane in space, and the sparse signal reconstruction method of the compressive sensing technology is used to obtain the strength of the equivalent source. Then the transfer function to any plane of space is established according to the free field Green’s function, to eliminate the interference of reverberation and improve the effect of sound source location. The accuracy and effectiveness of the improved method are verified by preliminary numerical simulation. And the results show that compared with the original algorithm, this method has obvious advantages in sound source localization in a reverberant field.

Backtracking based Joint-Sparse Signal Recovery for Distributed Compressive Sensing

In Distributed Compressive Sensing (DCS), the Joint Sparsity Model (JSM) refers to an ensemble of signals being jointly sparse. In [4], a joint reconstruction scheme was proposed using a single linear program. However, for reconstruction of any individual sparse signal using that scheme, the computational complexity is high. In this paper, we propose a dual-sparse signal reconstruction method. In the proposed method, if one signal is known apriori, then any other signal in the ensemble can be efficiently estimated using the proposed method, exploiting the dual-sparsity. Simulation results show that the proposed method provides fast and efficient recovery.

Skin-conformal, soft material-enabled bioelectronic system with minimized motion artifacts for reliable health and performance monitoring of athletes

Recent advances in biosensors, bioelectronics, and system integration allow the development of wristband-type devices for health and performance monitoring of athletes. Although these devices provide adequate sensing outputs, they suffer from signal loss due to improper contact of a rigid sensor with the skin. In addition, when a rubber band tightly secures the sensor to the skin, the gap between sensor and skin causes inevitable motion artifacts, resulting in corrupted data. Consequently, the rigidity and bulky form factor of the existing devices are not suitable for a practical use since athletes typically go through strenuous activities during training and matches. Here, we introduce a soft, wearable flexible hybrid electronics (WFHE) with integrated flexible sensors and circuits in an ultrathin, low-modulus elastomer. The thin-film bioelectronic system avoids the use of bulky, rigid sensors, while providing negligible mechanical and thermal burdens to the wearer. Enabling conformal contact between sensor and skin minimizes undesired motion artifacts. A set of computational and experimental studies of soft materials, flexible mechanics, and system packaging provides key fundamental design factors for a comfortable, reliable, waterproof bioelectronic system. Skin conformal WFHE with sparse signal reconstruction enables reliable, continuous monitoring of photoplethysmogram, heart rate, and activities of athletes. Development of a quantitative analysis between impact force and impact velocity extracted from motion acceleration provides an objective assessment of an athletic punching force. Collectively, this study shows the first demonstration of a wireless, soft, thin-film electronics for a real-time, reliable assessment of athletic health and performance.

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.

An analog hardware solution for compressive sensing reconstruction using gradient-based method

This work proposes an analog implementation of gradient-based algorithm for compressive sensing signal reconstruction. Compressive sensing has appeared as a promising technique for efficient acquisition and reconstruction of sparse signals in many real-world applications. It starts from the assumption that sparse signals can be exactly reconstructed using far less samples than in standard signal processing. In this paper, we consider the gradient-based algorithm as the optimal choice that provides lower complexity and competitive accuracy compared with existing methods. Since the efficient hardware implementations of reconstruction algorithms are still an emerging topic, this work is focused on the design of hardware that will provide fast parallel algorithm execution for real-time applications, overcoming the limitations imposed by the large number of nested iterations during the signal reconstruction. The proposed implementation is simple and fast, executing 400 iterations in 1 ms which is sufficient to obtain highly accurate reconstruction results.

Improved Wavelet Denoising by Penalty Function and Regularization Parameter

Wavelet-based convex optimization in sparse signal processing has attracted extensive research interest in recent years. Research demonstrates that the penalty function promotes the sparsity and improves the accuracy better than L1 norm method in dealing with convex and sparse signal reconstruction issues. This paper presents an improved denoising model which utilizes a penalty function to induce stronger sparsity in wavelet domain. In this paper, we have redefined the relationship model between signal noise levels and the regularization parameter to enhance sparsity caused by penalty functions in a wavelet domain. And three penalty functions are employed for wavelet coefficients to induce strong sparse wavelet coefficients under the wavelet domain. We then apply the improved wavelet denoising algorithm for image denoising to get the values of the PSNR are analysed under different noise level conditions. Experimental results clearly show that the improved wavelet denoising model is strength in terms of both quantitative measure and structural similarity quality, and outperforms many widely used denoising algorithms.

Radar Imaging by Sparse Optimization Incorporating MRF Clustering Prior

Recent progress in compressive sensing underscores the importance of exploiting intrinsic structures in sparse signal reconstruction. In this letter, we propose a Markov random field (MRF) prior in conjunction with fast iterative shrinkage-thresholding algorithm (FISTA) for image reconstruction. The MRF prior is used to represent the support of sparse signals with clustered nonzero coefficients. The proposed approach is applied to the inverse synthetic aperture radar (ISAR) imaging problem. Simulations and experimental results are provided to demonstrate the performance advantages of this approach in comparison with the standard FISTA and existing MRF-based methods.

A smoothing neural network for minimization [formula omitted]-[formula omitted] in sparse signal reconstruction with measurement noises

This paper investigates a smoothing neural network (SNN) to solve a robust sparse signal reconstruction in compressed sensing (CS), where the objective function is nonsmooth l1-norm and the feasible set satisfies an inequality of lp-norm 2≥p≥1 which is used for measuring residual errors. With a smoothing approximate technique, the non-smooth and non-Lipschitz continuous issues of the l1-norm and the gradient of lp-norm can be solved efficiently. We propose a SNN which is modeled by a differential equation and give its circuit implementation. In this case, we prove the proposed SNN converges to the optimal of considered problem. Simulation results are discussed to demonstrate the efficiency of the proposed algorithm.

Sparse signal reconstruction via expanded subspace pursuit

Due to their low computational complexity, greedy pursuit algorithms are widely used in sparse signal reconstruction. An improved greedy iterative algorithm, called the expanded subspace pursuit, is proposed. By incorporating a simple backtracking technique, the proposed algorithm removes the mismatching atoms to refine the estimated support set effectively. Furthermore, the proposed algorithm can achieve blind sparse reconstruction even without the prior of the sparsity degree. Compared with other greedy algorithms, the proposed algorithm exhibits superior reconstruction accuracy and lower computational complexity. Finally, numerical results are presented to demonstrate the validity of the proposed algorithm.

VLSI Architecture for Enhanced Approximate Message Passing Algorithm

Compressed sensing (CS) enables the reconstruction of sparse signals from a small number of linear measurements. However, sparse signal recovery algorithms require significant computational effort, even for problems of moderate size, and make their hardware realization a highly challenging task. In this paper, we present a novel architecture for the reconstruction of the sparse signal using the recently proposed Enhanced Approximate Message Passing (EAMP) algorithm. The EAMP algorithm shows better performance in terms of convergence rate and sparsity measurement trade-off as compared to AMP, IST and IHT techniques. The execution time of the proposed design has been reduced by maximizing parallelism with an appropriate level of unfolding. It receives CS measurements (y) and the number of non-zero elements (K) in the input vector from the encoder. Depending on the value of K, one sensing matrix (Φ j ) is selected from the code book Φ. The reconstruction algorithm (EAMP) recovers the input vector (s) by using y and Φ. Bitonic sorting has been used to identify the thresholding value in the EAMP algorithm. The proposed architecture for EAMP algorithm has been synthesized using Synopsys design compiler with 65 nm technology CMOS standard cell libraries. It occupies 719.15 KGE and consumes 315.5 mW power at a frequency of 400 MHz. It is suitable for any arbitrary sparsity-based signal restoration and CS problems.

A Novel Block Sparse Reconstruction Method for DOA Estimation With Unknown Mutual Coupling

In this letter, we consider the direction-of-arrival (DOA) estimation in the presence of unknown mutual coupling in application to uniform linear arrays (ULAs). A novel method is proposed that treats the DOA estimation as a block sparse signal reconstruction problem with a modified array manifold matrix which utilizes the information of entire array output. A block smoothed $\ell _{0}$ norm approximation technique is introduced to solve the problem. Finally, an iterative proximal algorithm is proposed. Simulation results are presented that show the superiority of the proposed method against other known techniques.

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.

Compression Sensing Signal Detection Algorithm Based on Orthogonal Matching Pursuit

At present, most of the detection algorithms used in our country take the iteration process of feature as the research object. This detection method is only suitable for the presence of perceptual signals, but not for all the signal measurement work. This paper introduces the basic principle of signal compression sensing, the construction of measurement matrix and the orthogonal matching pursuit algorithm. The orthogonal matching pursuit algorithm is applied to compressed sensing reconstruction of sparse signals in one-dimensional time domain and transform domain, and the reconstruction performance of the orthogonal matching pursuit algorithm is analyzed. Compared with the detection algorithm based on matching pursuit, this algorithm based on the idea of orthogonal matching pursuit corrects the feature quantities as the basis of decision. When the signal of interest exists, the feature quantities with smaller fluctuations are obtained, and better detection results are obtained. The experimental results show that the OMP detection algorithm proposed in this paper has better performance in improving detection success rate, sampling points required, noise suppression and so on compared with MP detection algorithm.

Stage-Determined Matching Pursuit for Sparse Channel Estimation in OFDM Systems

As a sampling paradigm to recover the sparse or compressible signals from very few incoherent linear measurements, compressed sensing (CS) has spurred much interest in recent years. Since tractable recovery algorithm is a crucial and major issue of CS, the greedy pursuit (GP) algorithms are generally preferred to enable accurate reconstruction of sparse or compressible signals from very few noisy incoherent measurements. While selecting multiple “correct” indices per iteration to improve the running time of orthogonal matching pursuit algorithm, the chosen indices are usually not the optimal one due to the iterative short-sighted decisions. In this paper, since the demand for fast reconstruction algorithms-possibly operating in linear time-is of significant interest, an algorithm namely, stage-determined matching pursuit (SdMP) is proposed. The SdMP algorithm exploits the selection of few indices (below the target signal sparsity level) per iteration, and then combines a backtracking or pruning step in some later iterations-albeit after satisfying a sparsity level conditions to refine the selected set. Using the restricted isometry property, the theoretical analysis of the SdMP algorithm and the sufficient conditions (guarantees) for realizing an improved reconstruction performance are presented. Through numerical simulations, it is shown that SdMP outperforms many GP algorithms that select multiple indices per iteration in terms of reconstruction accuracy and the running speed.

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.

Multiband sparse signal reconstruction through direct one-bit sampling.

Compressive sensing (CS) aims at decreasing sampling rate to reduce the needed number of samples. On the other hand, the one-bit CS is proposed to reduce the quantization bit. In this paper, we proposed a one-bit CS system aiming at acquiring the multiband sparse signal which is a very popular signal model in wireless communication, especially in cognitive radio. This proposed system, called direct one-bit sampler (DOS), is simple in hardware implementation, and it consists of only a comparator working at Nyquist rate. In the stage of signal reconstruction, it can be equivalent to a special multicoset sampler which is a popular scheme in CS. Moreover, we propose an enhanced binary iterative hard thresholding (BIHT), a popular one-bit recovery algorithm, to deal with the multiple measurement vectors in the one-bit CS framework. Both the theoretical model and experimental results demonstrate that the proposed DOS, with the help of the enhanced BIHT, can not only accurately recover the positions of active subbands of the multiband sparse signal but also roughly estimate the power of each active subband.