scholarly journals A Compressed Sensing Recovery Algorithm Based on Support Set Selection

Electronics ◽  
2021 ◽  
Vol 10 (13) ◽  
pp. 1544
Author(s):  
Wandi Liang ◽  
Zixiong Wang ◽  
Guangyu Lu ◽  
Yang Jiang
Keyword(s):  
Signal Processing ◽  
Compressed Sensing ◽  
Peak Frequency ◽  
Basis Pursuit ◽  
Nyquist Frequency ◽  
Analog To Digital ◽  
Recovery Algorithm ◽  
Support Set ◽  
Tone Signal ◽  
Set Up

The theory of compressed sensing (CS) has shown tremendous potential in many fields, especially in the signal processing area, due to its utility in recovering unknown signals with far lower sampling rates than the Nyquist frequency. In this paper, we present a novel, optimized recovery algorithm named supp-BPDN. The proposed algorithm executes a step of selecting and recording the support set of original signals before using the traditional recovery algorithm mostly used in signal processing called basis pursuit denoising (BPDN). We proved mathematically that even in a noise-affected CS system, the probability of selecting the support set of signals still approaches 1, which means supp-BPDN can maintain good performance in systems in which noise exists. Recovery results are demonstrated to verify the effectiveness and superiority of supp-BPDN. Besides, we set up a photonic-enabled CS system realizing the reconstruction of a two-tone signal with a peak frequency of 350 MHz through a 200 MHz analog-to-digital converter (ADC) and a signal with a peak frequency of 1 GHz by a 500 MHz ADC. Similarly, supp-BPDN showed better reconstruction results than BPDN.

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.

Construction of compressed sensing matrices for signal processing

2018 ◽  
Vol 77 (23) ◽  
pp. 30551-30574 ◽  
Author(s):  
Yingmo Jie ◽  
Cheng Guo ◽  
Mingchu Li ◽  
Bin Feng
Keyword(s):  
Signal Processing ◽  
Compressed Sensing ◽  
Compressed Sensing Matrices ◽  
Sensing Matrices

Review of Sparsity Known and Blind Sparsity Greedy Algorithms for Compressed Sensing

2013 ◽  
pp. 125-138
Author(s):  
Chun-Yan Zeng ◽  
Li-Hong Ma ◽  
Ming-Hui Du ◽  
Jing Tian
Keyword(s):  
Compressed Sensing ◽  
Compressive Sensing ◽  
Matching Pursuit ◽  
Greedy Algorithms ◽  
Diagrammatic Representation ◽  
Support Set ◽  
Exact Reconstruction ◽  
Signal Characteristics ◽  
Sparsity Level

Sparsity level is crucial to Compressive Sensing (CS) reconstruction, but in practice it is often unknown. Recently, several blind sparsity greedy algorithms have emerged to recover signals by exploiting the underlying signal characteristics. Sparsity Adaptive Matching Pursuit (SAMP) estimates the sparsity level and the true support set stage by stage, while Backtracking-Based Adaptive OMP (BAOMP) selects atoms by thresholds related to the maximal residual projection. This chapter reviews typical sparsity known greedy algorithms including OMP, StOMP, and CoSaMP, as well as those emerging blind sparsity greedy algorithms. Furthermore, the algorithms are analysed in structured diagrammatic representation and compared by exact reconstruction probabilities for Gaussian and binary signals distributed sparsely.

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