Abstract
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.
Highlights
Compressive sampling (CS) aims to recover a sparse signal from its far fewer samples than that required by the Nyquist–Shannon sampling theorem [1]
Methods having wide applications in signal sampling and processing. They are nearly compressible in certain conventional basis, such as fast Fourier transform, modified discrete cosine transform (MDCT) and time–frequency domain [6], and they should be exactly reconstucted from its CS samples theoretically
Considering the fact that the voiced sound takes a major part of signal energy, we assumed a Markov chain along the time axis in the support matrix
Summary
Compressive sampling (CS) aims to recover a sparse signal from its far fewer samples than that required by the Nyquist–Shannon sampling theorem [1]. Many CS methods, such as reweighted minimization [2], orthogonal matching pursuit [3], iteratively shrinkage-thresholding algorithm (ISTA) [4] and Bayesian CS [5], can successfully recover sparse signal from the CS samples under certain conditions. Many natural signals are sparse or compressible when represented in a proper basis. This makes CS methods having wide applications in signal sampling and processing. They are nearly compressible in certain conventional basis, such as fast Fourier transform, modified discrete cosine transform (MDCT) and time–frequency domain [6], and they should be exactly reconstucted from its CS samples theoretically. Traditional CS methods all can not achieve satisfactory performance when applied to speech signals
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