摘要
盲源分离或盲信号分离（Blind Source/Signal Separation，BSS）已经成为信号和图像处理领域的一个强有力的工具，其目标是在没有任何或很少关于源信号和混合模型先验信息的条件下，从一组观测信号中恢复出原始的源信号。目前已经产生了许多关于BSS的理论和算法研究成果，但在应用上都有一定的局限性。本文主要针对复杂通信信号、具备时间结构的图像信号和欠定模式下的语音信号的盲分离进行了深入研究，设定了更加接近实际应用的仿真条件。信道编码盲识别技术在非协作通信的应用日益重要，本文还重点研究了RS码的盲识别算法，提高了识别性能。
本文在以下几个方面取得了研究成果：
（1）针对复杂通信信号的盲分离提出了一种基于超定模式下改进的自然梯度算法。
基于对独立分量分析（Independent Component Analysis，ICA）理论及其扩展和相关算法的详细阐述，通过仿真复杂通信信号的盲分离，分析了传统自然梯度（Natural Gradient，NG）算法在超定模式下趋于发散的原因，提出了一种改进的超定自然梯度算法，能够在超定模式和信源数目未知或动态变化的条件下，有效分离复杂通信信号。
（2）针对使用时间结构的图像信号提出了一种改进的快速不动点算法。
标准的ICA算法在分析并非统计独立的具备时间结构的信号时完全失效。本文在经典的AMUSE算法的基础上，提出了一种改进的快速不动点算法，给出了新的目标函数表示，采用时间点处的某种局估计来估计局部方差，利用方差的非平稳性来实现信号分离。通过仿真比较分析了所提算法和FastICA算法，结果证明改进算法能够实现4幅图像的盲分离。
（3）针对欠定模式下的语音信号盲分离提出了一种基于稀疏独立分量分析（Sparse Independent ComponentAnalysis，S-ICA）的改进算法。
欠定情况下的盲源分离问题是一个更符合实际情况、也更具有挑战性的问题。基于对经典的稀疏独立分量分析（S-ICA）的2阶段欠定盲分离算法缺点的分析，本文对其进行改进。在信源个数和混合矩阵估计阶段，提出了一种新的加权势函数；在信源的估计和恢复阶段，针对L1范数算法的缺点，提出了一种结合最小均方误差的分离方法。在只有两路观测信号的条件下，仿真实现了非平稳的4路语音信号的盲分离。
（4）提出了一种基于本原元的RS码快速盲识别算法。
针对现有RS码的盲识别算法的缺点，本文提出了一种RS码编码参数的盲识别新方法。该方法利用本原元的校检作用并行搜索码长和域，提高了盲识别的效率；略掉不符合本原元校检的码字，增强了码根搜寻的可靠性；利用码根的连续性采用前进-倒退法向前搜索生成多项式，简化了计算，提高了搜索速度。仿真结果表明，新算法在90%识别率的误比特率的上限值有明显提高。
Blind source/signal separation(BSS) has become a powerful tool in the areas ofsignal and image processing. The goal of BSS is to recover the original signals form aset of mixed signals with no or little a priori knowledge about the source and mixtures.There are many theories and algorithms results available, but which all have somelimitations in application.
The main part of the thesis are reserch on BSS problem in complex communicationsignals, image signals and sppech signals of under-determined mode, for which theconditions are set much closer to the actual applications. The blind recognitiontechnology of channel coding has been increasingly important in the non-cooperativecommunication, thus the blind identification of RS codes is also mainly studied in thethesis, which improves the recognition performace and fills a gap to a certain extent.
The thesis has made some achievements in the following aspects:
(1)An improved natural gradient algorithm of over-determinded mode is proposedon the BSS of complex communication signals
Based on the elaborate introduction of ICA(Independent Component Analysis)theory and its extension, and related algorithms, by the simulation of the BSS ofcomplex communication signals, the reason of the natural gradient algorithm’sdivergence is analyzed. An improved natural gradient algorithm of over-determindedmode is proposed, which can separate the complex communication signals onover-determinded mode and the unknown or dynamic changing source number.
(2)An improved fast fixed point algorithm is proposed on the BSS of image signalswith time structure
Standard ICA algorithm is a complete failure when used on the BSS of the signalswith time structure, which are not statistical independent usually. An improved fastfixed point algorithm is proposed based on the classical AMUSE algorithm. The newalgorithm can achieve the BSS by using the nonstationarity of variance, and a newobjective function is given. the proposed algorithm can separate four channels of imigesignals compared to FastICA.
(3) Based on the S-ICA(Sparse Independent Component Analysis), a newalgorithm is proposed on the BSS of speech signal on under-determined mode
The BSS problem on under-determined mode is more consistent with the actual situation and more challenging. Some improvements are made based on the two-stagealgorithm of S-ICA aftern the analyze of its defects. In the stage of source number andmixing matrix estimation, a new weighted potential function is deliverde. In the stage ofsource recovery, a method combined with MMSE(Minimum mean square error) isintroduced. The new algorithm can separate4channels of speech signals which arenonstationary.
(4) A Fast blind recognition algorithm of RS codes by primitive element is proposed
Based on the disvantages of available blind recognition of RS codes, A newalgorithm was presented to solve RS codes blind recognition problems. By searchingthe code length and the field parallelly based on the parith check function of primitiveelement, the recognition efficiency was improved. The reliability of roots’ searchingwas promoted by omitting error contained code words which did not accord with theprimitive element parith check. The generator polynomial was searched byforward-backward method using the continuity of roots to simplify calculations andaccelerate search speed. Simulation results indicate that new algorithm’s upper limit ofBER when correct recognition rate is90%has a significant increase.
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