Performance bound of multiple hypotheses classification in compressed sensing

Compressed sensing (CS) has been widely researched in the past decade due to its important contributions in sparse signal processing. In this paper, we study the problem of multiple hypotheses classification with sparse signals in compressed sensing. The performance of classifying sparse signals reconstructed with the underdetermined linear measurements under Gaussian random noise is considered. With the prior knowledge of the support set of a sparse signal, the theoretical classification bound with the recovered signal based on the oracle estimator and the restricted isometry property (RIP) of the sampling matrix is developed. The effectiveness of the proposed theoretical bound is demonstrated by the simulations results obtained by four representative reconstruction algorithms in CS.