An improved sparse reconstruction algorithm for speech compressive sensing using structured priors

This work addresses the issue of sparse reconstruction in compressive sensing (CS) for speech signals. We propose a novel sparse reconstruction algorithm based on the approximate message passing (AMP) framework, via exploiting the intrinsic structures of real-life speech signals in the modified discrete cosine transform (MDCT) domain. We use a Gaussian mixture model to characterize the marginal distribution of the MDCT coefficients, and employ a first order Markov chain model to capture the inter-dependencies between neighboring MDCT coefficients. The parameters of these two models are adaptively learned using an expectation-maximization (EM) learning procedure. Compared with several state-of-the-art algorithms, the new algorithm showed significantly better performance in reconstruction experiments on real speech signals.