【作者】 李飞；

【导师】 吴建华； 张烨；

【作者基本信息】 南昌大学 ， 信号与信息处理， 2010， 硕士

【摘要】 信号的盲分离就是从一组由未知源信号混合得到的观测信号中估计源信号的过程。近年来,盲分离技术在无线电通信、雷达与声纳技术、医学分析、图像增强以及语音识别等领域获得了广泛关注。由于传感器个数的限制,盲分离通常为源信号个数大于观测信号个数的过完备混合信号盲分离。对于过完备混合信号盲分离,现有的大部分算法大多要求源信号数目已知、源信号有充分稀疏性、观测信号不存在噪声污染及异常值。然而,实际应用中上述条件通常难以满足。因此,本文重点研究在源信号有非充分稀疏性(或源信号只在少部分采样点充分稀疏)、源信号数目未知、观测信号受噪声污染条件下的过完备混合信号盲分离。论文的主要工作概括如下：1、在源信号数目未知情况下,针对有加性噪声污染、源信号假设为非充分稀疏条件下的过完备混合信号盲分离问题,提出具有鲁棒性的过完备混合信号盲分离算法。首先,在传统的K-平面聚类中引入鲁棒竞争聚类算法的思想,提出鲁棒K-平面聚类算法估计超平面的法线向量,并利用该算法估计出的超平面的法线向量估计出混合矩阵。本算法改进传统算法对噪声点敏感的缺点,并解决了传统超平面聚类初始需要指定聚类数目的不足。其次,利用信号的稀疏性约束求解源信号。2、在源信号数目未知情况下,针对有加性噪声污染、源信号假设仅有少部分满足充分稀疏条件的过完备混合信号盲分离问题,提出一种基于新的柯西势函数辨识出过完备混合矩阵的算法。为增加算法的鲁棒性,本算法采用估计全局势函数极值点的方式代替传统的直接计算势函数值的方式。同时,文中对该算法的鲁棒性进行了分析。更多还原

【Abstract】 Blind sources separation (BSS) is process of estimating unknown source signals from observed signals which are mixtures of unknown source signals. Recently, the problem of blind source separation has received considerable attention, because of its wide application in various fields such as biomedical signal analysis, speech enhancement, image recognition, wireless communications, etc. In practical, the BSS with the number of observed signals is less than the number of sources because of the restriction on the number of sensors, referred to as overcomplete BSS. Recently, most of overcomplete BSS algorithms assume that the source number is known; the source signals are sufficiently sparse and observed signals are not contaminated by additive noise and including singular values. However, these conditions are usually absent. In this dissertation, we focus on investigating the problem of the overcomplete BSS with an unknown number of sources, the source signals are insufficiently sparse and observed signals are contaminated by additive noise. The main contributions of this dissertation are summarized blow:1. With unknown number of source signals, a robust algorithm for the overcomplete BSS is proposed when the source signals are insufficiently sparse and the observed signals are contaminated by additive noises. First, by introducing the robust competitive agglomeration algorithm into the K-plane clustering algorithm, a robust K-plane clustering algorithm is proposed to estimate the K-dimensional concentration hyperplanes, and then to estimate the mixing vectors using them. The robust K-plane clustering algorithm can reduce the sensitivity of the traditional K-plane clustering algorithm to noises and the predefined number of clustering is not necessary. Second, the source signals can be recovered by using the sparsity of source signals.2. Based on a novel Cauchy Potential Function, a new algorithm is proposed for estimating the mixing matrix in the overcomplete BSS when the number of sources is unknown; the source signals are insufficiently sparse (a small number of the source samples satisfy sufficiently sparse) and the mixture signals are contaminated by additive noise and outliers. By estimating the local maxim of a global Cauchy Potential Function instead of directly estimating the local maxim of the Cauchy Potential Function, the robustness of the proposed algorithm to the noise and sparsity of the sources can be increased. Meanwhile, the robustness of the algorithm is measured in the dissertation.更多还原