Abstract
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.
Highlights
Compressive sensing (CS) [1,2], a framework to solve the under-determined system, has drawn great research attention in recent years
This method forms generalized likelihood ratio test (GLRT) for each iteration to test if signal component exists in the residual vector
We envision that the detection-based method can be apply to other greedy algorithms for iteration stopping rules
Summary
Compressive sensing (CS) [1,2], a framework to solve the under-determined system, has drawn great research attention in recent years. In OMP and its variant, e.g., ROMP, the signal sparsity k must be specified so that the computation stops after k iterations Other greedy algorithm such as subspace pursuit (SP) [7] needs to know the value of k so that exact k candidate atoms could be selected at each iteration. We proposed the detection-based orthogonal match pursuit (DOMP) algorithm which systematically provides the stop threshold based on the signal detection criteria. This is a more general threshold finding approach for stopping the OMP than the threshold proposed in [14].
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