Sparse signal recovery with unknown signal sparsity

In this paper, we proposed a detection-based orthogonal match pursuit (DOMP) algorithm for compressive sensing. Unlike the conventional greedy algorithm, our proposed algorithm does not rely on the priori knowledge of the signal sparsity, which may not be known for some application, e.g., sparse multipath channel estimation. The DOMP runs binary hypothesis on the residual vector of OMP at each iteration, and it stops iteration when there is no signal component in the residual vector. Numerical experiments show the effectiveness of the estimation of signal sparsity as well as the signal recovery of our proposed algorithm.