scholarly journals Improved Stochastic Gradient Matching Pursuit Algorithm Based on the Soft-Thresholds Selection

2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
Zhao Liquan ◽  
Hu Yunfeng
Keyword(s):  
Least Squares ◽  
Matching Pursuit ◽  
Signal Reconstruction ◽  
Stochastic Gradient ◽  
Selection Strategy ◽  
Index Set ◽  
Least Squares Solution ◽  
Matching Pursuit Algorithm ◽  
Sparsity Level ◽  
Better Than

The preliminary atom set exits redundant atoms in the stochastic gradient matching pursuit algorithm, which affects the accuracy of the signal reconstruction and increases the computational complexity. To overcome the problem, an improved method is proposed. Firstly, a limited soft-threshold selection strategy is used to select the new atoms from the preliminary atom set, to reduce the redundancy of the preliminary atom set. Secondly, before finding the least squares solution of the residual, it is determined whether the number of columns of the measurement matrix is smaller than the number of rows. If the condition is satisfied, the least squares solution is calculated; otherwise, the loop is exited. Finally, if the length of the candidate atomic index set is less than the sparsity level, the current candidate atom index set is the support atom set. If the condition is not satisfied, the support atom index set is determined by the least squares solution. Simulation results indicate that the proposed method is better than other methods in terms of the reconstruction probability and shorter running time than the stochastic gradient matching pursuit algorithm.

scholarly journals Stochastic Gradient Matching Pursuit Algorithm Based on Sparse Estimation

Electronics ◽  
2019 ◽  
Vol 8 (2) ◽  
pp. 165 ◽  
Author(s):  
Liquan Zhao ◽  
Yunfeng Hu ◽  
Yulong Liu
Keyword(s):  
Prior Information ◽  
Matching Pursuit ◽  
Stochastic Gradient ◽  
Least Square ◽  
Improved Method ◽  
Step Size ◽  
Sparse Estimation ◽  
Practical Applications ◽  
Matching Pursuit Algorithm ◽  
Better Than

The stochastic gradient matching pursuit algorithm requires the sparsity of the signal as prior information. However, this prior information is unknown in practical applications, which restricts the practical applications of the algorithm to some extent. An improved method was proposed to overcome this problem. First, a pre-evaluation strategy was used to evaluate the sparsity of the signal and the estimated sparsity was used as the initial sparsity. Second, if the number of columns of the candidate atomic matrix was smaller than that of the rows, the least square solution of the signal was calculated, otherwise, the least square solution of the signal was set as zero. Finally, if the current residual was greater than the previous residual, the estimated sparsity was adjusted by the fixed step-size and stage index, otherwise we did not need to adjust the estimated sparsity. The simulation results showed that the proposed method was better than other methods in terms of the aspect of reconstruction percentage in the larger sparsity environment.

scholarly journals Filtering-Based Regularized Sparsity Variable Step-Size Matching Pursuit and Its Applications in Vehicle Health Monitoring

2021 ◽  
Vol 11 (11) ◽  
pp. 4816
Author(s):  
Haoqiang Liu ◽  
Hongbo Zhao ◽  
Wenquan Feng
Keyword(s):  
Health Monitoring ◽  
Matching Pursuit ◽  
Signal Reconstruction ◽  
Superior Performance ◽  
Sparse Signal ◽  
Variable Step Size ◽  
Step Size ◽  
Signal Sampling ◽  
Reconstruction Performance ◽  
Sparsity Level

Recent years have witnessed that real-time health monitoring for vehicles is gaining importance. Conventional monitoring scheme faces formidable challenges imposed by the massive signals generated with extremely heavy burden on storage and transmission. To address issues of signal sampling and transmission, compressed sensing (CS) has served as a promising solution in vehicle health monitoring, which performs signal sampling and compression simultaneously. Signal reconstruction is regarded as the most critical part of CS, while greedy reconstruction has been a research hotspot. However, the existing approaches either require prior knowledge of the sparse signal or perform with expensive computational complexity. To exploit the structure of the sparse signal, in this paper, we introduce an initial estimation approach for signal sparsity level firstly. Then, a novel greedy reconstruction algorithm that relies on no prior information of sparsity level while maintaining a good reconstruction performance is presented. The proposed algorithm integrates strategies of regularization and variable adaptive step size and further performs filtration. To verify the efficiency of the algorithm, typical voltage disturbance signals generated by the vehicle power system are taken as trial data. Preliminary simulation results demonstrate that the proposed algorithm achieves superior performance compared to the existing methods.

scholarly journals A Matching Pursuit Algorithm for Backtracking Regularization Based on Energy Sorting

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 231 ◽  
Author(s):  
Hanfei Zhang ◽  
Shungen Xiao ◽  
Ping Zhou
Keyword(s):  
Energy Distribution ◽  
Matching Pursuit ◽  
Signal Reconstruction ◽  
Selection Criterion ◽  
Critical Factor ◽  
Maximum Energy ◽  
Orthogonal Matching Pursuit ◽  
Support Set ◽  
Reconstruction Efficiency ◽  
Matching Pursuit Algorithm

The signal reconstruction quality has become a critical factor in compressed sensing at present. This paper proposes a matching pursuit algorithm for backtracking regularization based on energy sorting. This algorithm uses energy sorting for secondary atom screening to delete individual wrong atoms through the regularized orthogonal matching pursuit (ROMP) algorithm backtracking. The support set is continuously updated and expanded during each iteration. While the signal energy distribution is not uniform, or the energy distribution is in an extreme state, the reconstructive performance of the ROMP algorithm becomes unstable if the maximum energy is still taken as the selection criterion. The proposed method for the regularized orthogonal matching pursuit algorithm can be adopted to improve those drawbacks in signal reconstruction due to its high reconstruction efficiency. The experimental results show that the algorithm has a proper reconstruction.

Signal Reconstruction Based on a Fusion Compressed Sensing Frame

2013 ◽  
Vol 785-786 ◽  
pp. 1315-1323
Author(s):  
Xu Hua Li ◽  
Yue Li Chen ◽  
Nan Jun Hu ◽  
Wei Li ◽  
Tian Jun Yuan ◽  
...  
Keyword(s):  
Compressed Sensing ◽  
Matching Pursuit ◽  
Signal To Noise Ratio ◽  
Signal Reconstruction ◽  
Greedy Algorithms ◽  
Reconstruction Error ◽  
Reconstruction Accuracy ◽  
Support Sets ◽  
Reconstruction Effects ◽  
Better Than

Greedy algorithms represented by orthogonal matching pursuit (OMP) and subspace pursuit (SP) algorithms are practically used in image processing based upon compressed sensing theory. However, there are two disadvantages: 1)Relatively poor signal reconstruction accuracy; 2) High computation complexity and measurements time. This paper proposes a frame of greedy algorithms obtaining a novel fusion of matching pursuit (FMP), combining the OMP and SP algorithms. FMP unites the two support sets from OMP and SP selecting the most appropriate atoms to achieve secondary screening of the original two support sets, finally realizing the accurate signal reconstruction. Using same test conditions, image reconstruction experiments and stability of Frame, the proposed FMP algorithm can effectively improve signal-to-noise ratio (SNR) with improved reconstruction error. Reconstruction effects using proposed FMP are better than separately using other two greedy algorithms for both high and low resolution images.

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