Low rank sparse decomposition model based speech enhancement using gammatone filterbank and Kullback–Leibler divergence

Abstract

In speech enhancement systems, the key stage is to estimate noise which generally requires prior speech or noise models. However, it is difficult to obtain such prior models sometimes. This paper presents a speech enhancement algorithm which does not require prior knowledge of speech and noise, and is based on low-rank and sparse matrix decomposition model using gammatone filterbank and Kullback–Leibler divergence to estimate noise and speech by decomposing the input noisy speech magnitude spectra into low-rank noise and sparse speech parts, respectively. According to the proposed technique, noise signals are assumed as low-rank components because noise spectra within different time frames are usually highly correlated with each other; while the speech signals are considered as sparse components because they are relatively sparse in time–frequency domain. Based on these assumptions, we have developed an alternative speech enhancement algorithm to separate the speech and noise magnitude spectra by imposing rank and sparsity constraints, with which the enhanced time-domain speech can be constructed from sparse matrix The proposed technique is significantly different from existing speech enhancement techniques as it enhances noisy speech in an uncomplicated manner, without need of noise estimation algorithm to find noise-only excerpts for noise estimation. Moreover, it can obtain improved performance in low SNR conditions, and does not need to know the exact distribution of noise signals. Experimental results have showed that proposed technique can perform better than conventional techniques in many types of strong noise conditions, in terms of yielding less residual noise, lower speech distortion and better overall speech quality. An important improvement in terms of the PESQ, SNRSeg, SIG and BAK is observed with the proposed algorithm over baseline algorithms.