本文選題：概率密度函數(shù)估計(jì) + 欠定混合模型��； 參考：《江南大學(xué)》2014年博士論文

【摘要】：盲信號(hào)分離（Blind Signal Separation，BSS）是指僅通過(guò)對(duì)傳感器上獲取的一組觀測(cè)信號(hào)進(jìn)行分析和處理，從而在并不了解混合系統(tǒng)先驗(yàn)信息的情況下恢復(fù)出無(wú)法直接觀測(cè)的多維源信號(hào)。盲信號(hào)分離在無(wú)線通信，語(yǔ)音的識(shí)別和增強(qiáng)，圖像的重構(gòu)和特征提取等方面都有著廣泛而重要的應(yīng)用價(jià)值，使得其已成為近年來(lái)人工神經(jīng)網(wǎng)絡(luò)，統(tǒng)計(jì)學(xué)以及信號(hào)處理等相關(guān)科研領(lǐng)域所研究的一個(gè)熱點(diǎn)問(wèn)題。本文圍繞多種混合模型情況下的盲信號(hào)分離問(wèn)題，，做了以下幾個(gè)方面的工作： 首先，對(duì)于線性適定混合模型，即源信號(hào)數(shù)目與觀測(cè)信號(hào)數(shù)目相等的情況，基于最小化互信息原理，分別提出了兩種自適應(yīng)BSS方法。針對(duì)傳統(tǒng)的梯度類BSS算法在實(shí)時(shí)計(jì)算中收斂速度較慢的問(wèn)題，提出了一種基于動(dòng)量項(xiàng)技術(shù)的BSS算法。該算法采用分離信號(hào)的互信息量作為代價(jià)函數(shù)，并將動(dòng)量項(xiàng)融入到了優(yōu)化該代價(jià)函數(shù)的自然梯度學(xué)習(xí)規(guī)則中，推導(dǎo)了搜索期望分離矩陣的自適應(yīng)算法。為了使得所提算法能夠分離出包含不同統(tǒng)計(jì)特性的源信號(hào)，在分離算法的每一步迭代更新中，使用了基于Gram-Charlier展開(kāi)式的分離信號(hào)評(píng)價(jià)函數(shù)的估計(jì)算法。仿真結(jié)果驗(yàn)證了所提BSS算法在收斂速度上的優(yōu)越性，以及在源信號(hào)中同時(shí)包含超高斯和亞高斯信號(hào)時(shí)的分離性能。 鑒于共軛梯度算法在神經(jīng)網(wǎng)絡(luò)學(xué)習(xí)中所表現(xiàn)出的卓越性能，提出了一種基于共軛梯度的自適應(yīng)盲信號(hào)分離算法。該算法在傳統(tǒng)的隨機(jī)梯度和自然梯度算法的基礎(chǔ)上，結(jié)合互信息準(zhǔn)則，將共軛梯度搜索原理引入到了最優(yōu)分離矩陣的求解中。即分離矩陣總是沿著與當(dāng)前搜索方向共軛的方向進(jìn)行更新。作為算法成功與否的關(guān)鍵點(diǎn)，采用核概率密度估計(jì)方法來(lái)估計(jì)分離信號(hào)的概率密度，進(jìn)而直接估計(jì)出對(duì)應(yīng)的評(píng)價(jià)函數(shù)，而不是依據(jù)經(jīng)驗(yàn)來(lái)選取單一的非線性函數(shù)。仿真結(jié)果驗(yàn)證了基于共軛梯度的BSS算法的有效性。 對(duì)于傳感器接收的觀測(cè)信號(hào)數(shù)目多于源信號(hào)，且混合矩陣為列滿秩矩陣的情形，提出了一種快速收斂的超定盲信號(hào)分離方法。該方法從對(duì)分離矩陣進(jìn)行奇異值分解入手，引入了超定BSS的代價(jià)函數(shù)。然后依據(jù)該代價(jià)函數(shù)，利用共軛梯度搜索原理推導(dǎo)了迭代計(jì)算分離矩陣的學(xué)習(xí)算法。并在算法的每一步計(jì)算中，利用隨機(jī)變量概率密度函數(shù)的核密度估計(jì)法估計(jì)分離信號(hào)的評(píng)價(jià)函數(shù)。在計(jì)算機(jī)仿真中，通過(guò)與隨機(jī)梯度算法和自然梯度算法相比較，驗(yàn)證了所提超定BSS算法的性能。 針對(duì)欠定混合模型中觀測(cè)信號(hào)數(shù)量不足的問(wèn)題，研究了在欠定混合條件下的非稀疏信號(hào)的BSS問(wèn)題，提出了一種基于局部平均分解的欠定混合BSS方法。該方法的基本思想是首先通過(guò)對(duì)混合信號(hào)進(jìn)行局部平均分解處理，生成若干乘積函數(shù)。按照一定的標(biāo)準(zhǔn)挑選出足夠數(shù)目的乘積函數(shù)，進(jìn)而構(gòu)造出一組額外的混合信號(hào)。將該組信號(hào)加入到原來(lái)的混合信號(hào)中，使得欠定盲分離模型轉(zhuǎn)變?yōu)檫m定或超定盲分離模型以便于處理。對(duì)于新的混合信號(hào)和新的混合模型，使用兩種高效的盲分離算法分離出源信號(hào)。理論上，局部平均分解算法的應(yīng)用對(duì)于信號(hào)的類別是沒(méi)有限制的。因此，所提的欠定盲分離算法可以打破大多數(shù)方法中存在的稀疏性約束，適用范圍更廣。另一方面，所提算法直接計(jì)算源信號(hào)，而不用預(yù)先估計(jì)出欠定混合矩陣，免去了不必要的計(jì)算。仿真結(jié)果驗(yàn)證了算法的性能。 除了上述線性混合模型以外，對(duì)于非線性混合模型，提出了一種基于感知器網(wǎng)絡(luò)的非線性盲信號(hào)分離方法。該方法采用感知器網(wǎng)絡(luò)構(gòu)建非線性分離系統(tǒng)來(lái)分離源信號(hào)，以最大輸出信息熵原理作為分離準(zhǔn)則調(diào)整非線性分離系統(tǒng)的參數(shù)，利用共軛梯度優(yōu)化算法計(jì)算分離感知器的隱層和輸出層連接權(quán)矩陣。算法中的Sigmoid函數(shù)選為分離信號(hào)的概率分布函數(shù)，并采用一種自適應(yīng)參數(shù)化概率密度估計(jì)方法對(duì)其進(jìn)行估計(jì)。仿真結(jié)果驗(yàn)證了所提算法的有效性。 最后，提出了一種用于線性卷積混合信號(hào)盲分離的聯(lián)合對(duì)角化方法。當(dāng)信號(hào)的混合過(guò)程并不是瞬時(shí)完成，也就是在將源信號(hào)到傳感器的傳輸過(guò)程中的延時(shí)也考慮進(jìn)去的時(shí)候，盲信號(hào)分離問(wèn)題的混合模型就變成了一個(gè)多維信號(hào)的卷積混合模型。所提的BSS方法首先將卷積混合模型變換為瞬時(shí)混合模型，得到新的瞬時(shí)混合信號(hào)，然后對(duì)變換后的模型應(yīng)用聯(lián)合對(duì)角化技術(shù)求取分離矩陣。同時(shí)，仿真結(jié)果表明該方法可成功實(shí)現(xiàn)線性卷積混合信號(hào)的盲分離。
[Abstract]:Blind signal separation ( BSS ) is a kind of multi - dimensional source signal which can ' t be observed directly by analyzing and processing a set of observation signals acquired on the sensor . The blind signal separation has a wide and important application value in the fields of wireless communication , speech recognition and enhancement , image reconstruction and feature extraction .

In order to make the proposed algorithm able to separate the source signals containing different statistical characteristics , this algorithm uses the mutual information amount of the separated signals as the cost function , and integrates the momentum items into the natural gradient learning rules which optimizes the cost function . In order to make the proposed algorithm separate out the source signals containing different statistical characteristics , the estimation algorithm of the separation signal evaluation function based on the Gram - Charlier expansion is used in every step iteration update of the separation algorithm . The simulation results verify the superiority of the proposed BSS algorithm on the convergence speed and the separation performance when the super - Gaussian and sub - Gaussian signals are simultaneously included in the source signal .

In view of the excellent performance of conjugate gradient algorithm in neural network learning , a self - adaptive blind signal separation algorithm based on conjugate gradient is proposed .

Based on the cost function , the cost function of the super - definite BSS is introduced . Then , according to the cost function , the evaluation function of the separation signal is estimated by using the kernel density estimation method of the probability density function of the random variable . In the computer simulation , the performance of the proposed super - fixed BSS algorithm is verified by comparing with the random gradient algorithm and the natural gradient algorithm .

In this paper , we study the BSS problem of non - sparse signal under the under - definite mixing condition , and put forward a method of sub - definite mixed BSS based on local average decomposition . The basic idea of this method is to select a sufficient number of product functions by means of local average decomposition of mixed signal .

In addition to the above - mentioned linear mixed model , a nonlinear blind signal separation method based on the perceptron network is proposed for nonlinear mixed model . The method adopts a perceptron network to construct a nonlinear separation system to separate the source signal , and the maximum output information entropy principle is used as the separation criterion to adjust the parameters of the nonlinear separation system . The Sigmoid function in the algorithm is selected as the probability distribution function of the separation signal , and an adaptive parametric probability density estimation method is adopted to estimate it . The simulation results verify the validity of the proposed algorithm .

In the end , a method for blind separation of linear convolution mixed signal is proposed . When the mixing process of the signal is not instantaneous and the time delay in the transmission process of the source signal to the sensor is taken into account , the mixed model of the blind signal separation problem is transformed into a multi - dimensional signal convolution mixed model . The proposed BSS method firstly transforms the convolution mixed model into a transient mixed model , obtains a new instantaneous mixed signal , and then applies a joint to the transformed model application to obtain a separation matrix .

【學(xué)位授予單位】：江南大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2014
【分類號(hào)】：TN911.7

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本文編號(hào)：1780457