In traditional framework of Compressive Sensing (CS), only sparse prior on the property of signals in time or frequency domain is adopted to guarantee the exact inverse recovery. Other than sparse prior, structures on the sparse pattern of the signal have also been used as an additional prior, called modelbased compressive sensing, such as clustered structure and tree structure on wavelet coefficients. In this paper, the cluster structured sparse signals are investigated. Under the framework of Bayesian Compressive Sensing, a hierarchical Bayesian model is employed to model both the sparse prior and cluster prior, then Markov Chain Monte Carlo (MCMC) sampling is implemented for the inference. Unlike the state-of-the-art algorithms which are also taking into account the cluster prior, the proposed algorithm solves the inverse problem automatically -prior information on the number of clusters and the size of each cluster is unknown. The experimental results show that the proposed algorithm outperforms many state-of-the-art algorithms.

This paper proposes a novel approach for speech enhancement based on compressed sensing (CS) theory. Each frame of noisy speech signal is sparsified firstly by using discrete cosine transform (DCT). Then we divide each frame into the noisy sub-frame and the clear sub-frame with a soft thresholding method to obtain the threholded DCT coefficients of the noisy sub-frames. After that, the partial Hadamard ensemble is used as a sensing matrix to achieve compressive measurement of the DCT coefficients of noisy sub-frame. Finally, We use the orthogonal matching pursuit in order to recover the de-noised speech signal from noisy sub-frame. Both objective and subjective experiments are employed to compare the proposed approach with the subspace method and the spectral subtraction method. Experimental results shows that proposed method outperforms other methods with the highest PESQ, ABX and MOS score for Gaussian white noise and most kinds of colour noise.