Minimum fourier measurements for stable recovery of block sparse signal

Model based sparse signal recovery requires fewer measurements and has attracted lots of attention recently. One prototypical sparsity model is block sparsity whose stability is guaranteed from block restricted isometry property (RIP). However, the existing block RIP methods in the l₂ norm space only consider Gaussian measurement case. In this paper, we extend the block RIP to the Fourier measurement case and demonstrate that the minimum number of measurements satisfying block RIP is as low as O (sd log q log(sd log q)log² s), where d is the block size, s represents the block sparsity, and N is the length of unknowns satisfying N = qd for some integer q.