基于改进l1范数最小化组合算法欠定盲源分离.docVIP

更多电子资料请登录赛微电子网 基于改进哈尔滨工业大学自动化测试与控制系哈尔滨 150080欠定盲TN911　　　文献标识码: A　　　国家标准学科分类代码: 510.40 Underdetermined blind source separation based on improved combinatorial algorithm for l1-norm minimization Fu Ning Peng Xiyuan (Dept. of Automatic Test and Control, Harbin Institute of Technology, Harbin 150080, China) Abstract: Under the sparse assumption, the problem of underdetermined blind source separation can be solved by l1-norm minimization algorithms such as the linear programming, the shortest-path algorithm, the combinatorial algorithm and so on. But these conventional algorithms rely on the high sparseness of the sources, so the recovery accuracy of the sources is not high enough. To overcome this disadvantage, an improved combinatorial algorithm for l1-norm minimization is proposed in this paper. First, the algorithm searches the second best solutions which are close to the minimum l1-norm solution according to a threshold, and then the weighted sum of these second best solutions and the minimum l1-norm solution is taken as the estimation of the sources. The experiments of sound sources show that the recovery accuracy of the sources can be increased by about 10% when the number of mixtures is not too small. Keywords: underdetermined blind source separation; sparse signals; l1-norm minimization; linear programming 1 引 言 近年来, 观测信号个数少于源信号个数的欠定盲源分离(underdetermined blind source separation, UBSS), 已成为盲源分离(blind source separation, BSS)领域的研究热点[1-7]。 考虑BSS的基本瞬时线性混合模型, (1) 式中: s(t) = [s1(t), s2(t),, sN(t)]T表示N维源信号向量, x(t) = [x1(t), x2(t),, xM(t)]T表示M维观测信号向量, A表示M×N维的混合矩阵, ai是A的列向量, t是离散时刻, T是观测信号点数。BSS的命题就是, 对任何t, 根据已知的x(t), 在A未知的条件下求未知的s(t)。当MN时, 这个问题就称为UBSS。 对于欠定盲源分离问题, 一般将求解过程分解为估计混合矩阵A和估计源信号s(t)两步[2]。目前很多文献集中研究如何估计混合矩阵A, 提出了很多有效的方法[3-5]。而对于如何估计源信号s(t), 缺乏十分有效的方法, 研究的也相对较少。本文在假定A已经估计出来的前提下, 集中研究如何估计源信号s(t)。 针对估计源信号s(t)的问题, 一般是在源信号服从稀疏分布的假设条件下, 将该问题转化为l1范数最小化问题。最经典的求解方法是线性规划法[4-6], 但线性规划法计算复杂度高, 求解速度很慢。为此, P. Bofill[2]等人提出了最短路径法, 大大提高了求解速度, 该方法的解与线性规划法的解等价, 但它仅适用于观测信号个