scholarly journals Conjugate Gradient Hard Thresholding Pursuit Algorithm for Sparse Signal Recovery

Algorithms ◽  
2019 ◽  
Vol 12 (2) ◽  
pp. 36 ◽  
Author(s):  
Yanfeng Zhang ◽  
Yunbao Huang ◽  
Haiyan Li ◽  
Pu Li ◽  
Xi’an Fan
Keyword(s):  
Convergence Rate ◽  
Conjugate Gradient ◽  
Selection Strategy ◽  
Convergence Criterion ◽  
Signal Recovery ◽  
Hard Thresholding ◽  
Step Size ◽  
Iterative Hard Thresholding ◽  
Reconstruction Performance ◽  
Gaussian Signal

We propose a new iterative greedy algorithm to reconstruct sparse signals in Compressed Sensing. The algorithm, called Conjugate Gradient Hard Thresholding Pursuit (CGHTP), is a simple combination of Hard Thresholding Pursuit (HTP) and Conjugate Gradient Iterative Hard Thresholding (CGIHT). The conjugate gradient method with a fast asymptotic convergence rate is integrated into the HTP scheme that only uses simple line search, which accelerates the convergence of the iterative process. Moreover, an adaptive step size selection strategy, which constantly shrinks the step size until a convergence criterion is met, ensures that the algorithm has a stable and fast convergence rate without choosing step size. Finally, experiments on both Gaussian-signal and real-world images demonstrate the advantages of the proposed algorithm in convergence rate and reconstruction performance.

scholarly journals Iterative Hard Thresholding with Combined Variable Step Size & Momentum-Based Estimator for Wireless Communication Systems with Dynamic Sparse Channels

Electronics ◽  
2021 ◽  
Vol 10 (7) ◽  
pp. 842
Author(s):  
Olutayo Oyeyemi Oyerinde ◽  
Adam Flizikowski ◽  
Tomasz Marciniak
Keyword(s):  
Computational Complexity ◽  
Wireless Communication ◽  
Variable Step Size ◽  
Hard Thresholding ◽  
Step Size ◽  
Channel Estimator ◽  
Iterative Hard Thresholding ◽  
Variable Step ◽  
Complexity Cost ◽  
Sparse Channel

The channel of the broadband wireless communications system can be modeled as a dynamic sparse channel. Such a channel is difficult to reconstruct by using linear channel estimators that are normally employed for dense channels’ estimation because of their lack of capacity to use the inherent channel’s sparsity. This paper focuses on reconstructing this type of time-varying sparse channel by extending a recently proposed dynamic channel estimator. Specifically, variable step size’s mechanism and variable momentum parameter are incorporated into traditional Iterative Hard Thresholding-based channel estimator to develop the proposed Iterative Hard Thresholding with Combined Variable Step Size and Momentum (IHT-wCVSSnM)-based estimator. Computer simulations carried out in the context of a wireless communication system operating in a dynamic sparse channel, show that the proposed IHT-wCVSSnM-based estimator performs better than all the other estimators significantly. However, the computational complexity cost of the proposed estimator is slightly higher than the closely performing channel estimator. Nevertheless, the inherent complexity cost of the proposed estimator could be compromised in a situation where the system’s performance is of higher priority when compared with the computational complexity cost.

scholarly journals Convergence rate analysis of an iterative algorithm for solving the multiple-sets split equality problem

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Shijie Sun ◽  
Meiling Feng ◽  
Luoyi Shi
Keyword(s):  
Convergence Rate ◽  
Iterative Algorithm ◽  
Sufficient Conditions ◽  
Linear Convergence ◽  
Regularity Property ◽  
Step Size ◽  
Bounded Linear ◽  
Split Equality Problem ◽  
Linear Convergence Rate ◽  
Equality Problem

Abstract This paper considers an iterative algorithm of solving the multiple-sets split equality problem (MSSEP) whose step size is independent of the norm of the related operators, and investigates its sublinear and linear convergence rate. In particular, we present a notion of bounded Hölder regularity property for the MSSEP, which is a generalization of the well-known concept of bounded linear regularity property, and give several sufficient conditions to ensure it. Then we use this property to conclude the sublinear and linear convergence rate of the algorithm. In the end, some numerical experiments are provided to verify the validity of our consequences.

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 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.

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