基于冗余字典的信号稀疏表示是一种新的信号表示理论,当前的理论研究主要集中在字典构造算法和稀疏分解算法两方面.该文提出一种新的基于自适应冗余字典的语音信号稀疏表示算法,该算法针对自相关函数为指数衰减的平稳信号,从K-L展开出发,建立了匹配信号结构的冗余字典,进而提出一种高效的基于非线性逼近的信号稀疏表示算法.实验结果表明冗余字典中原子的自适应性和代数结构使短时平稳语音信号稀疏表示具有较高的稀疏度和较好的重构精度,并使稀疏表示算法较好地应用于语音压缩感知理论.%The sparse representation based on overcomplete dictionary is a new signal representation theory. Recent activities in this field concentrate mainly on the study of dictionary design algorithm and sparse decomposition algorithm. In this paper, a novel speech signal sparse representation algorithm is proposed based on adaptive overcomplete dictionary. Considering stationary signal with autocorrelation function of exponential decay, an adaptive overcomplete dictionary is constructed in terms of the Karhunen-Loeve (K-L) expansion. Furthermore, an effective algorithm based on the nonlinear approximation is proposed to obtain sparse decomposition of signal with the adaptive dictionary. The experimental results indicate that short-term stationary speech signal sparse representation based on the adaptability and algebraic structure of atom in the overcomplete dictionary has higher sparsity and better reconstructive precision. The sparse representation algorithm can preferably be used in compressed sensing.
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