Abstract
This article focuses on obtaining sufficient conditions for block orthogonal greedy algorithm (BOGA) to recover block sparse signals via block restricted isometry property inherited from \(g\) -frames. Our analysis employs three essential terms: residual vector, match block vector, and match block matrix. We proved that if a \(g\) -frame satisfies the block-restricted isometry property of order \(K+1\) with isometry constant \(\rho<\dfrac{1}{3\sqrt{K}}\) , then BOGA can recover every block \(K\) -sparse signals in the at most \(K\) iterations. In addition, we discuss the recovery of strongly decaying block sparse signals with a relaxed bound on the isometry constant.
