Newton Pursuit algorithm for sparse signal reconstruction in compressed sensing

A directional pursuit algorithm is proposed to reconstruct an unknown sparse signal from noisy measurements. The algorithm offered an iterative update direction for improving the reconstructive accuracy of compressive sensing. Unlike traditional directional pursuit methods which only select the atoms owning higher correlation with the residual signal, the proposed algorithm not only values the higher correlation atoms but also reserves the lower correlation atoms with the residual signal. In the lower correlation atoms, only a few are active which usually impact the reconstructive performance and decide the reconstruction dynamic range of directional pursuit methods. The others are inactive. In order to avoid redundant atoms impacting the reconstructive accuracy, Bayesian hypothesis testing model is used to identify active atoms and eliminate redundant ones. Simulation results of the proposed algorithm show that the reconstructive accuracy and reconstructive dynamic range can indeed be improved. Furthermore, better noisy immunity compared with the traditional directional pursuit methods can be obtained.

In traditional compressed sensing theory, the authors have to adopt a discretisation procedure to reduce the continuous parameter space to a finite set of grid points. The discretisation procedure will cause the off-grid effect, which result in the reconstruction result unstable. To solve this problem, an alternating iteration algorithm is proposed which is built on the greedy-like algorithms. Firstly, a multilayer first-order approximation model is proposed to approximate the true observation model in the off-grid model. Then, an alternating iteration algorithm is proposed to estimate the sparse signal and mismatch factor. Moreover, the computational complexities of the proposed algorithm with different greedy algorithms are discussed. Finally, simulations demonstrate the good performance of the proposed algorithm. Meanwhile, the performance of the proposed method will not be influenced by the correlation of dictionary matrix and mismatch matrix.

Common problem in signal processing is reconstruction of the missing signal samples. Missing samples can occur by intentionally omitting signal coefficients to reduce memory requirements, or to speed up the transmission process. Also, noisy signal coefficients can be considered as missing ones, since they have wrong values due to the noise. The reconstruction of these coefficients is demanding task, considered within the Compressive sensing area. Signal with large number of missing samples can be recovered, if certain conditions are satisfied. There is a number of algorithms used for signal reconstruction. In this paper we have analyzed the performance of iterative gradient-based algorithm for sparse signal reconstruction. The parameters influence on the optimal performances of this algorithm is tested. Two cases are observed: non-noisy and noisy signal case. The theory is proved on examples.

Sparse signal reconstruction methods are used in a wide range of applications such as compressive sensing, denoising, signal separation and general linear inverse problems. The numerical algorithms used for the sparse signal recovery frequently involve finding solutions to the least squares optimization problem with l1-norm regularization. As the l1-norm penalty is not differentiable, so it rules out the possibility of using the efficient optimization techniques that call for the derivative of the objective function. This paper presents a hyperbolic tangent based surrogate function to closely approximate the l1-norm regularization. Simultaneously, we also develop an iterative algorithm for sparse signal reconstruction using the gradient of the proposed smooth function. The algorithm can be used to recover the compressively sampled images from a reduced set of measurements. Various numerical and imaging experiments are used to illustrate the performance of the promising recovery method. It has been shown that the algorithm can be used to reconstruct the compressively sampled images from less number of acquired data, which makes fast imaging possible without compromising high spatial resolutions. The results are validated using phantom as well as original MR and microwave SAR images.

Traditional compressive sensing (CS) primarily assumes light-tailed models for the underlying signal and/or noise statistics. Nevertheless, this assumption is not met in the case of highly impulsive environments, where non-Gaussian infinite-variance processes arise for the signal and/or noise components. This drives the traditional sparse reconstruction methods to failure, since they are incapable of suppressing the effects of heavy-tailed sampling noise. The family of symmetric alpha-stable (SαS) distributions, as a powerful tool for modeling heavy-tailed behaviors, is adopted in this paper to design a robust algorithm for sparse signal reconstruction from linear random measurements corrupted by infinite-variance additive noise. Specifically, a novel greedy reconstruction method is developed, which achieves increased robustness to impulsive sampling noise by solving a minimum dispersion (MD) optimization problem based on fractional lower-order moments. The MD criterion emerges naturally in the case of additive sampling noise modeled by SαS distributions, as an effective measure of the spread of reconstruction errors around zero, due to the lack of second-order moments. The experimental evaluation demonstrates the improved reconstruction performance of the proposed algorithm when compared against state-of-the-art CS techniques for a broad range of impulsive environments.

Sparse signal reconstruction via collaborative neurodynamic optimization

For the sparse signal reconstruction problem in compressive sensing, we propose a projection-type algorithm without any backtracking line search based on a new formulation of the problem. Under suitable conditions, global convergence and its linear convergence of the designed algorithm are established. The efficiency of the algorithm is illustrated through some numerical experiments on some sparse signal reconstruction problem.

The orthogonal matching pursuit (OMP) algorithm is widely used because of its simple algorithmic structure, the linear magnitude of its computational complexity and other advantages. Algorithms of improved and extended OMP types are continually emerging. To make the OMP algorithm more suitable for the new transmission requirements of the fifth-generation (5G) network, the orthogonal matching pursuit with multiple users (OMP_mu) algorithm is proposed for cell-free massive multi-input multi-output (MIMO) networks with multiuser spatial index modulation. The OMP_mu algorithm considers the constraint condition for the sparsity of each user on the basis of each iterative search in the OMP algorithm until all users meet the constraint. The simulation results show that compared with the original OMP algorithm, the OMP_mu algorithm has a greatly improved demodulation performance. Compared with the orthogonal matching pursuit step-by-step (OMP_step) algorithm, which takes the user sparsity constraint condition into account in two steps, the OMP_mu algorithm greatly reduces the operation time and number of iterations while achieving a slightly better performance. The OMP_mu algorithm provides an effective reference for the application of spatial index modulation in cell-free massive MIMO networks.

FOMP algorithm for Direction of Arrival estimation

Traditional orthogonal matching pursuit (OMP) algorithms for direction of arrival (DOA) estimation suffer from poor angular resolution and noise suppression. In this paper, we analyze the reason why the OMP algorithm has difficulties in resolving closely separated DOAs and conclude that it lies in the rules of support detection. Moreover, we propose a solution to this problem via developing the connection between the sparse reconstruction class algorithm and the subspace algorithm from the structure of the redundant dictionary. Based on the framework of the matching pursuit (MP) algorithm, the effective information of the signal and noise subspaces is integrated, and a noise subspace reprojection orthogonal matching pursuit (NSRomp) algorithm for DOA estimation is proposed. By adopting signal subspaces to reconstruct the original signal, the proposed NSRomp can reduce both the influence of noise on the selection of the support set and the computing time. By implementing the minimum norm method to optimize the noise subspace into a vector, which corrects the selection rules of the support set during each iteration, the angular resolution of the proposed algorithm is improved. From the simulation results, when the signal to noise ratio (SNR) is lower than or near 0, the angular resolution can be improved by > 15° using OMP algorithms to by > 5° using the proposed NSRomp algorithm.

In this paper, a fast orthogonal matching pursuit (OMP) algorithm based on optimized iterative process is proposed for sparse time-varying underwater acoustic (UWA) channel estimation. The channel estimation consists of calculating amplitude, delay and Doppler scaling factor of each path using the received multi-path signal. This algorithm, called as OIP-FOMP, can reduce the computationally complexity of the traditional OMP algorithm and maintain accuracy in the presence of severe inter-carrier interference that exists in the time-varying UWA channels. In this algorithm, repeated inner product operations used in the OMP algorithm are removed by calculating the candidate path signature Hermitian inner product matrix in advance. Efficient QR decomposition is used to estimate the path amplitude, and the problem of reconstruction failure caused by inaccurate delay selection is avoided by optimizing the Hermitian inner product matrix. Theoretical analysis and simulation results show that the computational complexity of the OIP-FOMP algorithm is reduced by about 1/4 compared with the OMP algorithm, without any loss of accuracy.

In this paper, the estimation of doubly spread underwater acoustic (UWA) channels is investigated. The UWA channels are characterized by severe delay spread and significant Doppler effects, and can be well modeled as a multi-scale multi-lag (MSML) channel. Furthermore, exploiting the sparsity of UWA channels, MSML channel estimation can be transformed into the estimation of parameter sets (amplitude, Doppler scale factor, time delay). Based on this, the orthogonal matching pursuit (OMP) algorithm has been widely used. However, the estimation accuracy of OMP depends on the size of the dictionary, which is related with both delay spread and Doppler spread. Thus it requires high computational complexity. This paper proposes a new method, called wavelet transform (WT) based algorithm, for the UWA channel estimation. Different from OMP algorithm which needs to search in both time domain and Doppler domain, WT-based algorithm only needs to search in time domain by using the Doppler invariant characteristic of hyperbolic frequency modulation (HFM) signal. The performance of the proposed algorithm is evaluated by computer simulations based on BELLHOP. The simulation results show that WT-based algorithm performs slightly better than OMP algorithm in low signal to noise ratio (SNR) while can greatly reduce computational complexity.

Robust sensing matrix design for the Orthogonal Matching Pursuit algorithm in compressive sensing

Acoustic emission(AE) dynamic monitoring of HRB400 welding specimens during tension process will collect a large number of mixed noise data, increasing the storage space and transmission time of data. And the sparsity of the signal changes with the change of ambient noise, which affects the reconstruction performance of the orthogonal matching pursuit (OMP) algorithm under fixed sparse degree. An adaptive threshold piecewise weak orthogonal matching pursuit (SWOMP) algorithm is proposed to reconstruct the signal, which is solved the problem of data quantity and guarantees the quality of real-time monitoring and reconstruction. The simulation results show that the reconstruction error of SWOMP and OMP algorithm decreases with the increase of measurement value, and the reconstruction performance of SWOMP algorithm is obviously better than that of OMP algorithm. The reconstructed quality of OMP algorithm fluctuates greatly when reconstructing multi-segment signals, while the reconstructed error of SWOMP algorithm is stable at about 0.05, which can reconstruct signals effectively and has high adaptability.

Wearable ECG monitoring devices, often limited by power constraints, require efficient methods to reduce energy consumption and extend battery life for continuous health tracking. This work proposes a digital compressed sensing approach for ECG (DCS-ECG), featuring a suitable sensing matrix, effective sparse signal recovery algorithms, and an optimized number of bits for quantization (BM). The framework is designed to achieve high compression ratios (CR) with minimal signal distortion and parameter extraction without the reconstruction of the original signal. The following five sensing matrices are examined: deterministic block binary diagonal (DBBD) matrix, random binary (RBin) matrix, random Bernoulli (RBen) matrix, random Gaussian (RG) matrix, and random sparse fixed binary (RSB) matrix. These are paired with a sparsifying matrix (ψ), a hybrid of identity matrix (I), discrete sine transform matrix (S), and discrete cosine transform matrix (C) (i.e. ψ = [I S C]). The following five sparse reconstruction algorithms are evaluated: iterative hard thresholding (IHT) algorithm, orthogonal matching pursuit (OMP) algorithm, smoothed ℓ0 (SL0) algorithm, ℓ1 least square (L1LS) algorithm, and subspace matching pursuit (SMP) algorithm. The proposed DCS-ECG system was tested on ECG signals from the MIT-BIH arrhythmia database. The configuration using the DBBD sensing matrix and OMP recovery algorithm with the sparsifying matrix achieved a low average percentage of root mean square difference (PRD) of 3.75 ± 1.43% at CR = 12.5%, which also offers fast reconstruction. For CR = 12.5% and BM = 8, the CS measurement generation on the Arduino Due consumes 2.02 mJ, while reconstruction on the Raspberry Pi requires 1.13 J. The wireless transmission energy is 1.2973 J. Overall, the proposed CS-based system achieves an 86.24% total energy saving compared to the without CS approach, demonstrating its suitability for low-power IoT-enabled wearable edge ECG health monitoring applications.