Speech Compressive Sampling Using Approximate Message Passing and a Markov Chain Prior

• Published in: Sensors (Basel, Switzerland) Switzerland), 2020-08, Vol.20 (16), p.4609
• Main Authors: Jia, Xiaoli, Liu, Peilin, Jiang, Sumxin
• Format: Article
• Language: English
• Subjects: Algorithms; approximate message passing; compressive sampling; Data Compression; Dictionaries; Discrete cosine transform; Markov analysis; Markov chain; Markov Chains; MDCT; Methods; Noise; Sampling; Signal to noise ratio; Speech; Speech processing; speech spectrogram; Variables
• ISSN: 1424-8220; 1424-8220
• DOI: 10.3390/s20164609

By means of compressive sampling (CS), a sparse signal can be efficiently recovered from its far fewer samples than that required by the Nyquist-Shannon sampling theorem. However, recovering a speech signal from its CS samples is a challenging problem, as it is not sparse enough on any existing canonical basis. To solve this problem, we propose a method which combines the approximate message passing (AMP) and Markov chain that exploits the dependence between the modified discrete cosine transform (MDCT) coefficients of a speech signal. To reconstruct the speech signal from CS samples, a turbo framework, which alternately iterates AMP and belief propagation along the Markov chain, is utilized. In addtion, a constrain is set to the turbo iteration to prevent the new method from divergence. Extensive experiments show that, compared to other traditional CS methods, the new method achieves a higher signal-to-noise ratio, and a higher perceptual evaluation of speech quality (PESQ) score. At the same time, it maintaines a better similarity of the energy distribution to the original speech spectrogram. The new method also achieves a comparable speech enhancement effect to the state-of-the-art method.