Abstract
For recovering block-sparse signals with unknown block structures using compressive sensing, a block orthogonal matching pursuit- (BOMP-) like block generalized orthogonal matching pursuit (BgOMP) algorithm has been proposed recently. This paper focuses on support conditions of recovery of any K -sparse block signals incorporating BgOMP under the framework of restricted isometry property (RIP). The proposed support conditions guarantee that BgOMP can achieve accurate recovery block-sparse signals within k iterations.
Highlights
Where A ∈ RM1×M2 (M1 ≪ M2) is a sensing matrix with normalized columns, Y ∈ RM1×1 is a measurement vector, and the vector v represents a random noise
Signals with block property are frequently encountered in practical applications
Given any v2 ≤ ε, matrix A satisfies block RIP with the order Nk + N + |Ω| − k. It implies that the successful recovery can be guaranteed, and the support condition of the block generalized orthogonal matching pursuit (BgOMP) algorithm is satisfied. e following bound of RIP constant can be expressed as δNk+N+|Ω|−
Summary
X ∈ RM2×1 is a concatenation of blocks x[i] ∈ Rd, 1 ≤ i ≤ L
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