Compressed Sensing based Speech Enhancement

Compressed Sensing or Compressive Sampling (CS) is a newly developed method for simultaneously compression and sampling of the given signal. In this way, development of CS applications in speech processing is not an exception and advancements in these applications are an ongoing process. In this paper, we propose compressive sampling method to reconstruct the clean speech signal. The problem of speech signal reconstruction is formulated based on CS utilizing Basis Pursuit (BP) and Compressive Sampling Matching Pursuit (CoSaMP) algorithms. Furthermore, direct sparsity estimation is adopted to efficiently find the sparsity level. Ultimately, it is demonstrated that roughly both of methods are effective in reconstructing the signal of interest with high probability. In addition, the average output frame-based SNRs and the perceptual evaluation of speech quality (PESQ) of subjective listening quality (LQ) and objective quality score for each method are compared.