本文關(guān)鍵詞： 盲分離 獨(dú)立成分分析 負(fù)熵 峭度 快速固定點(diǎn)算法　出處：《上海交通大學(xué)》2015年碩士論文　論文類型：學(xué)位論文

【摘要】：目前信號(hào)處理領(lǐng)域中最熱點(diǎn)的研究問題之一就是盲源分離問題(BBS),它的主要研究工作就是,在對(duì)系統(tǒng)的源信號(hào)和混合系統(tǒng)都未知的情況下,處理一組以時(shí)間序列或者并行信號(hào)的形式表示的觀測(cè)變量,最終分離出想要求解的源信號(hào)。盲源分離的典型例子有很多:手機(jī)中的射頻干擾信號(hào)、傳感器記錄的腦電波以及麥克風(fēng)錄取的混合語音信號(hào)等。而處理這類問題最有效的方法就是獨(dú)立成分分析(ICA),它是隨著盲分離問題研究的不斷發(fā)展而引起廣泛關(guān)注的。ICA方法的基本思想是,首先通過傳感器采集到觀測(cè)信號(hào),再根據(jù)信號(hào)的統(tǒng)計(jì)特性尋找一個(gè)合適的目標(biāo)函數(shù),通過選取迭代算法對(duì)目標(biāo)函數(shù)優(yōu)化,得到最優(yōu)的解混信道,將觀測(cè)信號(hào)通過解混信道的處理就可以得到想要求解的源信號(hào)的估計(jì)。基于盲源分離問題的研究背景下,本文簡述了獨(dú)立成分分析的研究意義和發(fā)展歷史,通過對(duì)ICA基本原理的研究分析得到基本模型存在的不確定性以及約束條件:研究對(duì)象必須是非高斯信號(hào),并且滿足相互獨(dú)立的統(tǒng)計(jì)特性。ICA問題可以簡化為通過一定的優(yōu)化算法得到選定的目標(biāo)函數(shù)的最優(yōu)解,從而分離出待求解的源信號(hào),由此從理論上重點(diǎn)介紹了獨(dú)立成分分析的幾種典型的目標(biāo)函數(shù)和優(yōu)化算法。在ICA模型估計(jì)之前,必須要對(duì)測(cè)量信號(hào)作預(yù)處理,包括中心化和白化這兩個(gè)處理過程,本文從理論上說明了預(yù)處理可以有效地減少ICA中需要預(yù)估模型參數(shù)的數(shù)目�？焖俟潭c(diǎn)算法(FastICA)是獨(dú)立成分分析中最常用的一種快速算法,根據(jù)非高斯性的評(píng)價(jià)指標(biāo)的不同,本文介紹了兩種FastICA算法:基于峭度的FastICA算法和基于負(fù)熵的FastICA算法。本課題的核心研究工作在于,通過對(duì)兩種原有算法的原理分析,針對(duì)其存在的問題,分別提出了相應(yīng)的改進(jìn)方案。對(duì)于基于峭度的FastICA算法存在的收斂不穩(wěn)定問題,本文提出了通過共軛梯度法對(duì)原算法進(jìn)行改進(jìn),實(shí)驗(yàn)結(jié)果表明,改進(jìn)后的算法不僅分離效果更佳,而且改善了原算法收斂不穩(wěn)定的問題。對(duì)于基于負(fù)熵的FastICA算法,本文分別提出了通過最速下降法以克服原算法易受初始值影響的缺點(diǎn),用差商法代替求導(dǎo)以降低了原算法的復(fù)雜性。仿真實(shí)驗(yàn)結(jié)果表明,改進(jìn)后的算法不僅分離出的信號(hào)更逼近源信號(hào),而且解決了初始值的問題,算法速度也變得更快。最后,將本文中提出的兩種改進(jìn)的FastICA算法分別應(yīng)用于分離人工混合和實(shí)際混合的語音信號(hào),對(duì)分離結(jié)果進(jìn)行分析得出,基于峭度的改進(jìn)算法的分離效果更佳,而基于負(fù)熵的改進(jìn)算法的收斂速度更快,但由于兩種改進(jìn)算法的分離效果差距并不大,基于負(fù)熵的改進(jìn)算法以其收斂速度的優(yōu)勢(shì)更具有實(shí)用性。
[Abstract]:At present, one of the hottest research problems in the field of signal processing is the blind source separation (BSS) problem. Its main research work is that the source signal and hybrid system are unknown. Processing a set of observation variables in the form of a time series or a parallel signal, and finally separating the source signal to be solved. There are many typical examples of blind source separation: radio frequency interference signals in mobile phones, Brain waves recorded by sensors and mixed speech signals recorded by microphones, etc. The most effective way to deal with this kind of problems is independent component analysis (ICA), which has attracted wide attention with the development of blind separation research. The basic idea of the ICA approach is, First, the observed signals are collected by the sensor, then a suitable objective function is found according to the statistical characteristics of the signal, and the optimal unmixing channel is obtained by selecting the iterative algorithm to optimize the objective function. The estimation of the source signal to be solved can be obtained by processing the observed signal through the de-mixing channel. Based on the research background of blind source separation problem, the research significance and development history of independent component analysis (ICA) are briefly described in this paper. Based on the analysis of the basic principle of ICA, the uncertainty and constraint conditions of the basic model are obtained: the object of study must be non-#china_person0# signal, The ICA problem can be simplified to obtain the optimal solution of the selected objective function by a certain optimization algorithm, and the source signal to be solved can be separated. Therefore, several typical objective functions and optimization algorithms of independent component analysis (ICA) are introduced in theory. Before ICA model estimation, the measurement signal must be preprocessed, including centralization and whitening. In this paper, it is theoretically explained that preprocessing can effectively reduce the number of estimated model parameters in ICA. Fast fixed point algorithm (FastICA) is one of the most commonly used fast algorithms in independent component analysis (ICA), according to the difference of non-#china_person0# evaluation indexes. This paper introduces two kinds of FastICA algorithms: FastICA algorithm based on kurtosis and FastICA algorithm based on negative entropy. For the unsteady convergence of FastICA algorithm based on kurtosis, the conjugate gradient method is proposed to improve the original algorithm. The experimental results show that the improved algorithm not only has better separation effect. Moreover, the unsteady convergence of the original algorithm is improved. For the FastICA algorithm based on negative entropy, this paper proposes to overcome the shortcoming that the original algorithm is vulnerable to the influence of initial value by the steepest descent method. The difference quotient method is used instead of the derivative method to reduce the complexity of the original algorithm. The simulation results show that the improved algorithm not only approximates the source signal, but also solves the problem of initial value, and the speed of the algorithm becomes faster. The two improved FastICA algorithms proposed in this paper are applied to the separation of speech signals with manual mixing and actual mixing respectively. The analysis of the separation results shows that the improved algorithm based on kurtosis has better separation effect. The improved algorithm based on negative entropy has a faster convergence speed, but because the separation effect of the two improved algorithms is not big, the improved algorithm based on negative entropy is more practical because of its advantage of convergence speed.
【學(xué)位授予單位】：上海交通大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2015
【分類號(hào)】：TN912.3

【共引文獻(xiàn)】

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