Spectral Compressive Sensing with Model Selection

The performance of existing approaches to the recovery of frequency-sparse signals from compressed measurements is limited by the coherence of required sparsity dictionaries and the discretization of frequency parameter space. In this paper, we adopt a parametric joint recovery-estimation method based on model selection in spectral compressive sensing. Numerical experiments show that our approach outperforms most state-of-the-art spectral CS recovery approaches in fidelity, tolerance to noise and computation efficiency.Comment: 5 pages, 2 figures, 1 table, published in ICASSP 201

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

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