Abstract
Compressive sampling matching pursuit (CoSaMP) is an efficient reconstruction algorithm for sparse signal. When the signal is block sparse, i.e., the non-zero elements are presented in clusters, some block sparse reconstruction algorithms have been proposed accordingly. In this paper, we present a new block algorithm based on CoSaMP, called block compressive sampling matching pursuit (BlockCoSaMP). Compared with CoSaMP algorithm, the proposed algorithm shows improved performance when sparse signal is presented in block form. Restricted isometry property (RIP) of measurement matrix is an effective tool for analyzing the performance of the CS algorithm, and Block restricted isometry property (Block RIP) is the extension of traditional RIP. Based on the Block RIP, we derive the sufficient condition to guarantee the convergence of Block-CoSaMP algorithm. In addition, the number of required iterations is obtained. Finally, simulation experiments show that with the increase of block length, the performance of Block-CoSaMP algorithm approaches to that of block subspace pursuit (Block-SP) algorithm. When the block length and sparsity are small, the performance of Block-CoSaMP algorithm is better than that of the CoSaMP, l 2 /l 1 norm and block orthogonal matching pursuit (BOMP) algorithms. Especially, when compared with CoSaMP and l 2 /l 1 norm algorithms, the proposed algorithm exhibits more obvious performance gain.
Highlights
Compressed sensing (CS) [1] is an efficient sampling method
To observe the performance of Block-Compressive sampling matching pursuit (CoSaMP) algorithm, the frequency of successful reconstruction is used as the evaluation metric, where the ‘‘success’’ is declared when the following error is less than a fixed threshold 10−6
It is shown that if the measurement matrix D satisfies the block Restricted isometry property (RIP) of order 4dK with a block isometry constant δ4dK < 0.5, Block-CoSaMP algorithm can converge so that the original signal can be exactly recovered in finite number of iterations
Summary
Compressed sensing (CS) [1] is an efficient sampling method. By exploiting the sparse nature of the signal, CS can obtain the discrete samples of the signal through random sampling at a rate far less than Nyquist sampling rate. In [22], it is shown that if the measurement matrix D has a small block RIP, l2/l1-norm algorithm can recover any block sparse signal x. As shown in [24], Block-SP algorithm exhibits perfect recovery performance for block sparse signal, but the RIP condition of the measurement matrix is very strict. Based on block RIP, the recovery performance of the proposed algorithm is analyzed It shows that if the block RIC of the measurement matrix D satisfies δ4dK < 0.5, Block-CoSaMP can exactly recover the block sparse signal in finite iterations. This sufficient condition is more relaxed than those of BOMP and Block-SP algorithms.
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