平滑L0算法在语音压缩重构中的应用

Application of Smoothed L0 Algorithm in Compressed Sensing Reconstruction of Speech Signal

语音信号在频域和离散余弦变换域等都具有良好的稀疏特性,满足压缩感知的先验条件,因此可以基于压缩感知对语音信号进行处理。语音压缩感知主要包括三个方面:稀疏基、观测矩阵和重构算法。其中,重构算法直接影响着重构信号的质量,是最重要的一部分。传统的语音压缩感知常基于正交匹配追踪算法进行重构。正交匹配追踪算法要求已知信号稀疏度,增加了实现的难度。为了提高语音信号的重构质量、简化实现过程,提出了一种基于平滑L0算法的语音压缩重构模型。平滑L0算法是用平滑函数逼近L0范数,它不需要提前知道信号的稀疏度,具有计算量低、重构质量高等优点。此外,提出了一种新的平滑函数,并基于高斯函数和新的平滑函数来验证平滑L0算法在语音压缩重构中的优越性。实验结果表明,在相同的条件下,相比于正交匹配追踪算法,使用平滑L0算法对语音进行重构,不仅缩短了重构时间,而且大大提高了重构质量。

At present,speech signals have good sparsities in domains like frequency and Discrete Cosine Transformation （DCT） and so on,which satisfies the prerequisite for Compressed Sensing （CS）. Therefore,it can be treated by CS theory,which consists of sparse rep- resentation of the signal,design of the measurement matrix and the algorithms of reconstruction. Among them,the most important part is reconstruction algorithms which can influence the quality of reconstructed signals directly. The traditional compressed sensing reconstruc- tion of speech is usually based on Orthogonal Matching Pursuit （OMP） method. The orthogonal matching pursuit method needs to obtain sparse priors of the speech signal in advance, which makes the realization difficult. In order to improve the reconstruction quality of speech signal and simplify the implementation process, a compressed speech＇ s reconstruction method based on Smoothed L0 （SL0） algorithm has been proposed,in which the SL0 uses smooth function to approximate L0 norm without acquisition of sparse priors of the speech sig- nal in advance and with advantages of lower calculation capacity and higher quality of reconstruction. In addition, a new smooth function has been proposed. Ganssian function and the new smooth function are used to confirm the performance of the SLO. Simulation results demonstrate that the SLO algorithm has not only obtained a higher quality of reconstruction than the traditional OMP method, but also shorten the implementation time.