scholarly journals A New Regularized Reconstruction Algorithm Based on Compressed Sensing for the Sparse Underdetermined Problem and Applications of One-Dimensional and Two-Dimensional Signal Recovery

Algorithms ◽  
2019 ◽  
Vol 12 (7) ◽  
pp. 126 ◽  
Author(s):  
Bin Wang ◽  
Li Wang ◽  
Hao Yu ◽  
Fengming Xin
Keyword(s):  
Compressed Sensing ◽  
Reconstruction Algorithm ◽  
Steepest Descent Method ◽  
Signal Recovery ◽  
Two Dimensional ◽  
Reconstruction Algorithms ◽  
Experimental Conditions ◽  
One Dimensional ◽  
Recovery Algorithm ◽  
Reconstruction Performance

The compressed sensing theory has been widely used in solving undetermined equations in various fields and has made remarkable achievements. The regularized smooth L0 (ReSL0) reconstruction algorithm adds an error regularization term to the smooth L0(SL0) algorithm, achieving the reconstruction of the signal well in the presence of noise. However, the ReSL0 reconstruction algorithm still has some flaws. It still chooses the original optimization method of SL0 and the Gauss approximation function, but this method has the problem of a sawtooth effect in the later optimization stage, and the convergence effect is not ideal. Therefore, we make two adjustments to the basis of the ReSL0 reconstruction algorithm: firstly, we introduce another CIPF function which has a better approximation effect than Gauss function; secondly, we combine the steepest descent method and Newton method in terms of the algorithm optimization. Then, a novel regularized recovery algorithm named combined regularized smooth L0 (CReSL0) is proposed. Under the same experimental conditions, the CReSL0 algorithm is compared with other popular reconstruction algorithms. Overall, the CReSL0 algorithm achieves excellent reconstruction performance in terms of the peak signal-to-noise ratio (PSNR) and run-time for both a one-dimensional Gauss signal and two-dimensional image reconstruction tasks.

scholarly journals Constrained Backtracking Matching Pursuit Algorithm for Image Reconstruction in Compressed Sensing

2021 ◽  
Vol 11 (4) ◽  
pp. 1435
Author(s):  
Xue Bi ◽  
Lu Leng ◽  
Cheonshik Kim ◽  
Xinwen Liu ◽  
Yajun Du ◽  
...  
Keyword(s):  
Image Reconstruction ◽  
Compressed Sensing ◽  
Matching Pursuit ◽  
Reconstruction Algorithm ◽  
Energy Criterion ◽  
Step Size ◽  
Relationship Analysis ◽  
Support Set ◽  
Reconstruction Performance ◽  
Sparsity Level

Image reconstruction based on sparse constraints is an important research topic in compressed sensing. Sparsity adaptive matching pursuit (SAMP) is a greedy pursuit reconstruction algorithm, which reconstructs signals without prior information of the sparsity level and potentially presents better reconstruction performance than other greedy pursuit algorithms. However, SAMP still suffers from being sensitive to the step size selection at high sub-sampling ratios. To solve this problem, this paper proposes a constrained backtracking matching pursuit (CBMP) algorithm for image reconstruction. The composite strategy, including two kinds of constraints, effectively controls the increment of the estimated sparsity level at different stages and accurately estimates the true support set of images. Based on the relationship analysis between the signal and measurement, an energy criterion is also proposed as a constraint. At the same time, the four-to-one rule is improved as an extra constraint. Comprehensive experimental results demonstrate that the proposed CBMP yields better performance and further stability than other greedy pursuit algorithms for image reconstruction.

scholarly journals Sparse Recovery Algorithm for Compressed Sensing Using Smoothed l0 Norm and Randomized Coordinate Descent

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 834
Author(s):  
Jin ◽  
Yang ◽  
Li ◽  
Liu
Keyword(s):  
Compressed Sensing ◽  
Image Denoising ◽  
Signal To Noise Ratio ◽  
Sparse Recovery ◽  
Coordinate Descent ◽  
Sparse Signal ◽  
Sparse Signal Recovery ◽  
Signal Recovery ◽  
Recovery Algorithm ◽  
Core Concepts

Compressed sensing theory is widely used in the field of fault signal diagnosis and image processing. Sparse recovery is one of the core concepts of this theory. In this paper, we proposed a sparse recovery algorithm using a smoothed l0 norm and a randomized coordinate descent (RCD), then applied it to sparse signal recovery and image denoising. We adopted a new strategy to express the (P0) problem approximately and put forward a sparse recovery algorithm using RCD. In the computer simulation experiments, we compared the performance of this algorithm to other typical methods. The results show that our algorithm possesses higher precision in sparse signal recovery. Moreover, it achieves higher signal to noise ratio (SNR) and faster convergence speed in image denoising.

scholarly journals WSNs Compressed Sensing Signal Reconstruction Based on Improved Kernel Fuzzy Clustering and Discrete Differential Evolution Algorithm

2019 ◽  
Vol 2019 ◽  
pp. 1-9
Author(s):  
Zhou-zhou Liu ◽  
Shi-ning Li
Keyword(s):  
Compressed Sensing ◽  
Differential Evolution ◽  
Fuzzy Clustering ◽  
Clustering Algorithm ◽  
Signal Reconstruction ◽  
Differential Evolution Algorithm ◽  
Reconstruction Algorithm ◽  
Reconstruction Algorithms ◽  
Evolution Algorithm ◽  
Discrete Differential Evolution

To reconstruct compressed sensing (CS) signal fast and accurately, this paper proposes an improved discrete differential evolution (IDDE) algorithm based on fuzzy clustering for CS reconstruction. Aiming to overcome the shortcomings of traditional CS reconstruction algorithm, such as heavy dependence on sparsity and low precision of reconstruction, a discrete differential evolution (DDE) algorithm based on improved kernel fuzzy clustering is designed. In this algorithm, fuzzy clustering algorithm is used to analyze the evolutionary population, which improves the pertinence and scientificity of population learning evolution while realizing effective clustering. The differential evolutionary particle coding method and evolutionary mechanism are redefined. And the improved fuzzy clustering discrete differential evolution algorithm is applied to CS reconstruction algorithm, in which signal with unknown sparsity is considered as particle coding. Then the wireless sensor networks (WSNs) sparse signal is accurately reconstructed through the iterative evolution of population. Finally, simulations are carried out in the WSNs data acquisition environment. Results show that compared with traditional reconstruction algorithms such as StOMP, the reconstruction accuracy of the algorithm proposed in this paper is improved by 36.4-51.9%, and the reconstruction time is reduced by 15.1-31.3%.

scholarly journals Compressed sensing for electrocardiogram acquisition in wireless body sensor network: A comparative analysis

2019 ◽  
Vol 15 (7) ◽  
pp. 155014771986488 ◽  
Author(s):  
Junxin Chen ◽  
Jiazhu Xing ◽  
Leo Yu Zhang ◽  
Lin Qi
Keyword(s):  
Compressed Sensing ◽  
Sensor Network ◽  
Low Cost ◽  
Reconstruction Algorithm ◽  
Signal Acquisition ◽  
Reconstruction Algorithms ◽  
Practical Applications ◽  
Body Sensor Network ◽  
The Past ◽  
Electrocardiogram Signals

In the past decades, compressed sensing emerges as a promising technique for signal acquisition in low-cost sensor networks. For prolonging the monitoring duration of biosignals, compressed sensing is also exploited for simultaneous sampling and compression of electrocardiogram signals in the wireless body sensor network. This article presents a comprehensive analysis of compressed sensing for electrocardiogram acquisition. The performances of involved important factors, such as wavelet basis, overcomplete dictionaries, and the reconstruction algorithms, are comparatively illustrated, with the purpose to give data reference for practical applications. Drawn from a bulk of comparative experiments, the potential of compressed sensing in electrocardiogram acquisition is evaluated in different compression levels, while preferred sparsifying basis and reconstruction algorithm are also suggested. Relative perspectives and discussions are also given.

scholarly journals Energy Preserved Sampling for Compressed Sensing MRI

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Yudong Zhang ◽  
Bradley S. Peterson ◽  
Genlin Ji ◽  
Zhengchao Dong
Keyword(s):  
Compressed Sensing ◽  
Cost Function ◽  
Computation Time ◽  
Reconstruction Algorithm ◽  
Simple Random Sampling ◽  
Variable Density ◽  
Reconstruction Algorithms ◽  
Iterative Thresholding ◽  
Thresholding Algorithm

The sampling patterns, cost functions, and reconstruction algorithms play important roles in optimizing compressed sensing magnetic resonance imaging (CS-MRI). Simple random sampling patterns did not take into account the energy distribution ink-space and resulted in suboptimal reconstruction of MR images. Therefore, a variety of variable density (VD) based samplings patterns had been developed. To further improve it, we propose a novel energy preserving sampling (ePRESS) method. Besides, we improve the cost function by introducing phase correction and region of support matrix, and we propose iterative thresholding algorithm (ITA) to solve the improved cost function. We evaluate the proposed ePRESS sampling method, improved cost function, and ITA reconstruction algorithm by 2D digital phantom and 2Din vivoMR brains of healthy volunteers. These assessments demonstrate that the proposed ePRESS method performs better than VD, POWER, and BKO; the improved cost function can achieve better reconstruction quality than conventional cost function; and the ITA is faster than SISTA and is competitive with FISTA in terms of computation time.

scholarly journals A Fast Sparse Recovery Algorithm for Compressed Sensing Using Approximate l0 Norm and Modified Newton Method

Materials ◽  
2019 ◽  
Vol 12 (8) ◽  
pp. 1227 ◽  
Author(s):  
Dingfei Jin ◽  
Yue Yang ◽  
Tao Ge ◽  
Daole Wu
Keyword(s):  
Compressed Sensing ◽  
Newton Method ◽  
Simulation Experiment ◽  
Sparse Recovery ◽  
Signal Recovery ◽  
Recovery Efficiency ◽  
Recovery Algorithm ◽  
Modified Newton Method ◽  
Computer Simulation Experiment ◽  
Recovery Algorithms

In this paper, we propose a fast sparse recovery algorithm based on the approximate l0 norm (FAL0), which is helpful in improving the practicability of the compressed sensing theory. We adopt a simple function that is continuous and differentiable to approximate the l0 norm. With the aim of minimizing the l0 norm, we derive a sparse recovery algorithm using the modified Newton method. In addition, we neglect the zero elements in the process of computing, which greatly reduces the amount of computation. In a computer simulation experiment, we test the image denoising and signal recovery performance of the different sparse recovery algorithms. The results show that the convergence rate of this method is faster, and it achieves nearly the same accuracy as other algorithms, improving the signal recovery efficiency under the same conditions.

scholarly journals Super-resolution reconstruction for a single image based on self-similarity and compressed sensing

2018 ◽  
Vol 12 (3) ◽  
pp. 234-244
Author(s):  
Qiang Yang ◽  
Huajun Wang
Keyword(s):  
Image Reconstruction ◽  
Compressed Sensing ◽  
Sparse Representation ◽  
Super Resolution ◽  
Reconstruction Algorithm ◽  
Single Image ◽  
Low Resolution ◽  
Self Similarity ◽  
Resolution Image ◽  
Reconstruction Performance

Super-resolution image reconstruction can achieve favorable feature extraction and image analysis. This study first investigated the image’s self-similarity and constructed high-resolution and low-resolution learning dictionaries; then, based on sparse representation and reconstruction algorithm in compressed sensing theory, super-resolution reconstruction (SRSR) of a single image was realized. The proposed algorithm adopted improved K-SVD algorithm for sample training and learning dictionary construction; additionally, the matching pursuit algorithm was improved for achieving single-image SRSR based on image’s self-similarity and compressed sensing. The experimental results reveal that the proposed reconstruction algorithm shows better visual effect and image quality than the degraded low-resolution image; moreover, compared with the reconstructed images using bilinear interpolation and sparse-representation-based algorithms, the reconstructed image using the proposed algorithm has a higher PSNR value and thus exhibits more favorable super-resolution image reconstruction performance.

Modified meta-heuristic-oriented compressed sensing reconstruction algorithm for bio-signals

2019 ◽  
Vol 17 (05) ◽  
pp. 1950031
Author(s):  
Ashok Naganath Shinde ◽  
Sanjay L. Lalbalwar ◽  
Anil B. Nandgaonkar
Keyword(s):  
Compressed Sensing ◽  
Signal Reconstruction ◽  
Sampling Rate ◽  
Reconstruction Algorithm ◽  
Haar Wavelet ◽  
Evaluation Procedure ◽  
Grey Wolf Optimizer ◽  
Reconstruction Algorithms ◽  
Swarm Optimization ◽  
Glowworm Swarm Optimization

In signal processing, several applications necessitate the efficient reprocessing and representation of data. Compression is the standard approach that is used for effectively representing the signal. In modern era, many new techniques are developed for compression at the sensing level. Compressed sensing (CS) is a rising domain that is on the basis of disclosure, which is a little gathering of a sparse signal’s linear projections including adequate information for reconstruction. The sampling of the signal is permitted by the CS at a rate underneath the Nyquist sampling rate while relying on the sparsity of the signals. Additionally, the reconstruction of the original signal from some compressive measurements can be authentically exploited using the varied reconstruction algorithms of CS. This paper intends to exploit a new compressive sensing algorithm for reconstructing the signal in bio-medical data. For this purpose, the signal can be compressed by undergoing three stages: designing of stable measurement matrix, signal compression and signal reconstruction. In this, the compression stage includes a new working model that precedes three operations. They are signal transformation, evaluation of [Formula: see text] and normalization. In order to evaluate the theta ([Formula: see text]) value, this paper uses the Haar wavelet matrix function. Further, this paper ensures the betterment of the proposed work by influencing the optimization concept with the evaluation procedure. The vector coefficient of Haar wavelet function is optimally selected using a new optimization algorithm called Average Fitness-based Glowworm Swarm Optimization (AF-GSO) algorithm. Finally, the performance of the proposed model is compared over the traditional methods like Grey Wolf Optimizer (GWO), Particle Swarm Optimization (PSO), Firefly (FF), Crow Search (CS) and Glowworm Swarm Optimization (GSO) algorithms.

RBF-network based sparse signal recovery algorithm for compressed sensing reconstruction

2015 ◽  
Vol 63 ◽  
pp. 66-78 ◽  
Author(s):  
Vidya L. ◽  
Vivekanand V. ◽  
Shyamkumar U. ◽  
Deepak Mishra
Keyword(s):  
Compressed Sensing ◽  
Sparse Signal ◽  
Sparse Signal Recovery ◽  
Signal Recovery ◽  
Rbf Network ◽  
Recovery Algorithm

Study on the Estimation Error Caused by Using One-Dimensional Model for the Evaluation of Dipole Tracer Test

2010 ◽  
Author(s):  
Yuji Ijiri ◽  
Yumi Naemura ◽  
Kenji Amano ◽  
Keisuke Maekawa ◽  
Atsushi Sawada ◽  
...  
Keyword(s):  
Estimation Error ◽  
Tracer Tests ◽  
Fracture Plane ◽  
Nuclear Waste Repository ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Transport Parameters ◽  
Experimental Conditions ◽  
One Dimensional ◽  
Longitudinal Dispersivity

In-situ tracer tests are a valuable approach to obtain parameters for a performance assessment of nuclear waste repository. A one-dimensional model is simple and is commonly used to identify radionuclide transport parameters by fitting breakthrough curves simulated using the model to those obtained from tracer tests. However, this method can increase uncertainty and introduce errors in the estimated parameters. In particular, such uncertainties and errors will be significant when evaluating parameters for tests conducted in a dipole (two-dimensional) flow field between injection and withdrawal wells. This paper describes a numerical analysis investigation into the effects of various experimental conditions on parameters estimated using a one-dimensional model for cases involving tracer tests in a two-dimensional fracture plane. Results show that longitudinal dispersivity tends to be overestimated by the one-dimensional model analysis. This overestimation is the result of several factors: smaller pumping rate, larger dipole ratio, stronger heterogeneity of the fracture hydraulic conductivity, and greater orthogonally-oriented background groundwater flow. Such information will help us to better plan and design tracer tests at underground research laboratories located in both Mizunami in central Japan and Horonobe in northern Japan. Understanding appropriate experimental conditions will help decrease the uncertainty in the results of tracer tests.

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