基于主分量分析的语音信号压缩感知

摘要

Compressed Sensing theory is a new research focus rising in recent years. Before Compressed Sensing theory is applied to speech signal processing field,a suitable sparse representation for speech signals must be found. Based on principal component analysis theory and a large number of block signals, features of the speech signal are extracted. Moreover, according to Compressed Sensing theory, the method of constructing the dictionary and the characteristics of the speech signal, a kind of redundant dictionary, the concatenation of some orthogonal bases, for the sparse representation of speech signal is presented in this paper. For more objective description of the advantages of such a sparse representation, the average gini index is applied to compare speech signals' sparsity in DCT,GABOR and this redundant dictionary respectively. And male and female speech signals and voiced and unvoiced speech signals are analysed. Simulation results show that whether male or female speech signals and whether voiced or unvoiced speech signals, sparsity of the speech signal in this redundant dictionary is greatly better than the DCT basis and close to the CABOR basis. However, with its number of atoms far less than CABOR basis and its low computational complexity and storage,this redundant dictionary is more applicable than CABOR basis to speech signal.%压缩感知理论是近年来兴起的一个新的研究热点.寻求适合于语音信号的稀疏基是压缩感知理论应用到语音信号处理领域的前提.本文基于主分量分析理论和大量的块数据,提取语音信号的特征信息,并根据压缩感知理论、字典构造的方法以及语音信号的特点,构造出一种适合于语音信号稀疏表示的冗余字典.该冗余字典是由多个正交基级联而成.为了更为客观的说明这种稀疏表示的优势,采用平均gini系数来比较语音信号在DCT基、GABOR基和该冗余字典下的稀疏性,并且分别对男女声语音信号和清浊音进行了分析.实验表明,无论是男声信号还是女声信号,清音还是浊音,在该冗余字典下的稀疏性均优于DCT基,与GABOR基相近,但是由于其原子数远少于GABOR基,其计算的复杂度和存储量均低于GABOR基,因而比GABOR基更具可用性.