Hypothesis testing for partial sparse recovery

Traditionally, sparse recovery pursues the objective of reconstructing an information source that has a sparse representation in an appropriate basis. In such situations, full recovery of the support of the sparse signal is necessary as missing any point in the support penalizes the quality of the reconstructed signal. In certain applications, however, the ultimate objective is not to reconstruct an information source, and is rather to recover the sparse support only partially. This paper provides a hypothesis-testing framework for recovering any desired fraction of the supper and offers some asymptotic performance limits for the proposed tests.