A Sampling And Reconstruction Approach For Audio Signals Based On Compressive Sensing

Compressive sensing is an emerging field that facilitates a new framework of data acquisition.According to the theory of CS,a signal can be exactly recovered from far less samples than required by the Shannon-Nyquist Theorem as long as it can be represented sparsely in some transform domain.For the multi-channel microphone array used for acquiring the sound field information,this technology can alleviate the pressure brought by the huge amount of data produced by the multi-channel microphone array on the sampling end.However,it is not so straightforward to apply the CS theory to audio signals due to the wide range of audio types and the inconsistency of sparsity.In order to solve this problem,in this article,we proposed an improved sparse reconstruction algorithm with high efficiency for audio compressive sensing using structured priors.In this algorithm,we use modified discrete cosine transform(MDCT)as the sparsity basis for audio signals and a Gaussian mixture model to characterize the marginal distribution of the MDCT coefficients.Moreover,we employ a first order Markov chain model to capture the inter-dependencies between neighboring MDCT coefficients,along both the time axis and frequency axis according to different types of audio structures.In order to improve the adaptability of the proposed algorithm,different hyper-parameters are used for different frame of signals and these hyper-parameters are learned in an online way using an expectation-maximization(EM)learning procedure.We further use the probability graph model to describe the proposed signal model.Based the recently proposed approximate message passing(AMP)algorithm framework,we derive the high efficient reconstruction algorithm via belief propagation between different nodes on a factor graph.Compared with several state-of-the-art algorithms,the proposed single-channel algorithm showed significantly better performance in reconstruction experiments on real audio signals,with a 3-5dB improvement on terms of reconstruction SNR.As for the CS problem for multi-channel audio signals,we use a Gaussian-Markov process to model the slowly varying property of the audio coefficients along the space dimension based on the proposed single-channel algorithm.Considering the discrepancy of correlation of two channels in different space region,we further partition the multi-channel audio signals into different groups based on the space correlation between two channels.Audio reconstruction are conducted independently between groups in a parallel way,while different channels of audio signals are reconstructed jointly within the same group.Sufficient experiments are conducted to investigate the influence of different grouping strategy on the reconstruction accuracy.Compared with non-joint reconstruction algorithm,the proposed joint reconstruction algorithm showed significant better performance with a 2-5dB improvement on terms of average SNR of all channels.