Abstract
In this paper, we consider the block orthogonal matching pursuit (BOMP) algorithm and the block orthogonal multi-matching pursuit (BOMMP) algorithm respectively to recover block sparse signals from an underdetermined system of linear equations. We first introduce the notion of block restricted orthogonality constant (ROC), which is a generalization of the standard restricted orthogonality constant, and establish respectively the sufficient conditions in terms of the block RIC and ROC to ensure the exact and stable recovery of any block sparse signals in both noiseless and noisy cases through the BOMP and BOMMP algorithm. We finally show that the sufficient condition on the block RIC and ROC is sharp for the BOMP algorithm.
Highlights
Compressed sensing, which is a novel sampling theory, has many important practical applications including signal processing [48], medical imaging [32] and radar systems [1]
We first introduce the notion of block restricted orthogonality constant (ROC), which is a generalization of the standard restricted orthogonality constant, and respectively establish the sufficient conditions by using the block restricted isometry constant (RIC) and ROC to ensure the exact and stable recovery of any block sparse signals in both noiseless and noisy cases through the block orthogonal matching pursuit (BOMP) and block orthogonal multi-matching pursuit (BOMMP) algorithms
We show that the sufficient condition on the block RIC and ROC is sharp for the BOMP algorithm
Summary
Compressed sensing, which is a novel sampling theory, has many important practical applications including signal processing [48], medical imaging [32] and radar systems [1]. Y = Φx + e, where y ∈ Rm is a measurement signal, Φ ∈ Rm×n (usually m n) is a given sensing matrix, the vector x ∈ Rn is an unknown K-sparse signal (i.e., x has at most K nonzero entries) and e ∈ Rm is a vector of measurement errors Many efficient methods, such as convex optimization method [4]-[6] and [10, 23, 41], greedy algorithm [14, 20, 38, 39, 47] and iterative threshold algorithm [2, 3, 18, 21], have been developed to recover x based on the sensing matrix Φ and its measurements y.
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