Abstract
In the compressed sensing (CS) reconstruction algorithms, the problems of overestimation and large redundancy of candidate atoms will affect the reconstruction accuracy and probability of the algorithm when using Sparsity Adaptive Matching Pursuit (SAMP) algorithm. In this paper, we propose an improved SAMP algorithm based on a double threshold, candidate set reduction, and adaptive backtracking methods. The algorithm uses the double threshold variable step-size method to improve the accuracy of sparsity judgment and reduces the undetermined atomic candidate set in the small step stage to enhance the stability. At the same time, the sparsity estimation accuracy can be improved by combining with the backtracking method. We use a Gaussian sparse signal and a measured shock wave signal of the 15psi range sensor to verify the algorithm performance. The experimental results show that, compared with other iterative greedy algorithms, the overall stability of the DBCSAMP algorithm is the strongest. Compared with the SAMP algorithm, the estimated sparsity of the DBCSAMP algorithm is more accurate, and the reconstruction accuracy and operational efficiency of the DBCSAMP algorithm are greatly improved.
Highlights
In recent years, Candes, Donoho, and Tao have proposed a new theory of signal acquisition and processing-compressed sensing (CS) [1, 2]. is theory states that as long as a signal is sparse or sparse in a specific transform domain, a projection matrix that is incoherent with the transform basis can be used to project the high-dimensional sparse signal onto a lowdimensional space
Many improved algorithms have appeared: Regularized Orthogonal Matching Pursuit (OMP) (ROMP) algorithm selects atoms carrying larger amounts of reconstruction information through a regularization process; Compressive Sampling Matching Pursuit (CoSaMP) algorithm selects 2K atomic indexes to update the candidate set in each iteration and discards redundant atomic indexes by pruning; Subspace Pursuit (SP) algorithm is similar to CoSaMP algorithm, but each iteration updates the candidate set with K atomic indexes
Gaussian sparse signals are random compared with shock wave signals. ey have controllable sparsity and the nonzero amplitude of the signals obeys the Gaussian distribution. ey are commonly used experimental signals when testing the stability of reconstruction algorithms
Summary
Candes, Donoho, and Tao have proposed a new theory of signal acquisition and processing-compressed sensing (CS) [1, 2]. is theory states that as long as a signal is sparse or sparse in a specific transform domain, a projection matrix that is incoherent with the transform basis can be used to project the high-dimensional sparse signal onto a lowdimensional space. E CS theory only uses a lower sampling rate to randomly sample and compress signals, breaking through the traditional sampling theorem It has great advantages in processing massive complex signals and is widely applied to various engineering practices. Sparsity Adaptive Matching Pursuit (SAMP) algorithm is one of the iterative greedy algorithms. Is algorithm solves the sparsity in signal reconstruction [6], breaking through the defect of using sparsity as prior information in traditional iterative greedy algorithms. E operational efficiency can be improved if the step-size is too large, but the overestimation that reduces the reconstruction accuracy is easy to occur. We propose an improved SAMP algorithm to enhance the stability and balance the accuracy of sparsity estimation and the efficiency
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