Abstract:  It is difficult to reconstruct speech signal after compressive sampling because coefficients of the signal in transforming domain aren’t sparse enough. In this paper the speech signal was recovered from compressed samples in the frequency domain using structural features. Two hidden variables, amplitude and state, are defined for each modified discrete cosine transforming (MDCT) coefficient of the speech signal. The probability density function of the amplitude of the MDCT coefficient is represented using a Gaussian mixture model, and the continuity of the states along the frequency axis is modeled through a first order Markov chain，the continuity of the amplitude along the frequency axis is modeled through GaussMarkov process. The joint posterior distribution of coefficient, amplitude and state is represented by the factor graph, on which the posterior mean of the coefficient is obtained using Turbo message passing method, and then the speech can be reconstructed. After compressive sampling the MDCT coefficients of a speech segment, we reconstructed the signal using our proposed algorithm and other stateoftheart algorithms for comparison. The results showed that our proposed algorithm achieved best reconstruction quality under different frames and compressive ratios. The spectrogram showed that the energy distribution of reconstructed signal using our algorithm was the most similar to the original signal’s energy distribution. It can be seen that better reconstruction accuracy can be obtained using the continuity along frequency axis and Turbo message passing method.

Key words:  speech signal, compressive sensing, Gaussian mixture model, Markov chain, message passing