本文選題：聯(lián)合盲分離 + 張量對(duì)角化�。� 參考：《大連理工大學(xué)》2016年碩士論文

【摘要】：現(xiàn)代信號(hào)處理中,在眾多實(shí)際問(wèn)題的驅(qū)動(dòng)下,多數(shù)據(jù)集聯(lián)合盲分離已成為信號(hào)處理領(lǐng)域新的熱點(diǎn)。聯(lián)合盲分離能夠利用多數(shù)據(jù)集信號(hào)之間的統(tǒng)計(jì)特性,如組間相關(guān)性和組內(nèi)獨(dú)立性等,最終恢復(fù)出混合的源信號(hào)。而張量作為一種極具潛力的多維數(shù)據(jù)融合的工具,通過(guò)使用張量分解,(稀疏)非負(fù)矩陣／張量分解,凸優(yōu)化等數(shù)學(xué)工具,也可以更好地進(jìn)行盲信號(hào)的處理。若能將張量分解和聯(lián)合盲分離結(jié)合起來(lái),將大大地推動(dòng)張量信號(hào)處理、聯(lián)合盲分離等前沿技術(shù)在理論與方法上的發(fā)展�；趶埩繉�(duì)角化的聯(lián)合盲分離主要思想是構(gòu)造具有特定結(jié)構(gòu)的目標(biāo)張量,進(jìn)行代數(shù)擬合,辨識(shí)信號(hào)的混合機(jī)理,進(jìn)行聯(lián)合信號(hào)的處理,最終恢復(fù)出混合的源信號(hào)。目前基于張量分解的聯(lián)合盲分離正處于起步階段,本文主要開(kāi)展了基于張量對(duì)角化的聯(lián)合盲分離方法的研究,分別提出了基于Givens旋轉(zhuǎn)矩陣,LU分解和連續(xù)旋轉(zhuǎn)策略的三階及四階張量對(duì)角化算法,并將這些算法應(yīng)用至實(shí)際的聯(lián)合盲分離問(wèn)題中,具體成果如下：(1)針對(duì)三階正交的聯(lián)合盲分離問(wèn)題,提出了一種基于Givens旋轉(zhuǎn)矩陣的三階正交張量對(duì)角化算法。該算法求解一系列的Givens旋轉(zhuǎn)矩陣的解析解來(lái)交替更新每一個(gè)混合矩陣。仿真實(shí)驗(yàn)表明,該算法與現(xiàn)有的算法相比具有快速的收斂性以及較高的分離精度,并通過(guò)胎兒心電圖分離和語(yǔ)音信號(hào)分離的實(shí)驗(yàn),進(jìn)一步闡述了所提算法的性能。(2)針對(duì)四階正交的聯(lián)合盲分離問(wèn)題,提出了一種基于Givens旋轉(zhuǎn)矩陣的四階正交張量對(duì)角化算法。通過(guò)極分解,把多個(gè)參數(shù)優(yōu)化問(wèn)題分解為一系列簡(jiǎn)單的特征值分解問(wèn)題。仿真實(shí)驗(yàn)證明了該算法較優(yōu)的收斂性能、分離精度,并且將其應(yīng)用于解決胎兒心電信號(hào)的分離問(wèn)題上。(3)針對(duì)四階非正交的聯(lián)合盲分離問(wèn)題,提出了一種基于LU分解和連續(xù)旋轉(zhuǎn)的四階非正交張量對(duì)角化算法。該算法通過(guò)LU分解將復(fù)雜的整體優(yōu)化問(wèn)題轉(zhuǎn)化成L階段和U階段,將因子矩陣近似地由一系列簡(jiǎn)單的初等三角矩陣或酉矩陣代替。仿真實(shí)驗(yàn)證明了該算法的收斂性和分離精度,并將其應(yīng)用于解決胎兒心電信號(hào)的分離問(wèn)題中。
[Abstract]:In modern signal processing, driven by many practical problems, multi-dataset joint blind separation has become a new hotspot in the field of signal processing. Joint blind separation can recover the mixed source signals by using the statistical characteristics of multi-dataset signals such as inter-group correlation and intra-group independence. As a potential multidimensional data fusion tool, Zhang Liang can process blind signals better by using Zhang Liang decomposition (sparse) nonnegative matrix / Zhang Liang decomposition, convex optimization and other mathematical tools. If Zhang Liang decomposition can be combined with joint blind separation, it will greatly promote the development of the theory and method of Zhang Liang signal processing and joint blind separation. The main idea of joint blind separation based on Zhang Liang's diagonalization is to construct a special structure of the target Zhang Liang, to carry out algebraic fitting, to identify the mixing mechanism of the signal, to process the combined signal, and finally to recover the mixed source signal. At present, the joint blind separation based on Zhang Liang decomposition is in its infancy. In this paper, we mainly study the joint blind separation method based on Zhang Liang diagonalization. The third and fourth order Zhang Liang diagonalization algorithms based on Givens rotation matrix LU decomposition and continuous rotation strategy are proposed, and these algorithms are applied to the practical joint blind separation problem. The main results are as follows: 1) for the third order orthogonal joint blind separation problem, a third order orthogonal Zhang Liang diagonalization algorithm based on Givens rotation matrix is proposed. The algorithm solves a series of analytical solutions of Givens rotation matrix to update each hybrid matrix alternately. The simulation results show that the proposed algorithm has fast convergence and high separation accuracy compared with the existing algorithms. The experiments of fetal electrocardiogram separation and speech signal separation are carried out. Furthermore, the performance of the proposed algorithm is discussed. (2) aiming at the joint blind separation problem of fourth-order orthogonal, a quadrature Zhang Liang diagonalization algorithm based on Givens rotation matrix is proposed. By polar decomposition, multiple parameter optimization problems are decomposed into a series of simple eigenvalue decomposition problems. The simulation results show that the proposed algorithm has better convergence performance and better separation accuracy, and is applied to solve the separation of fetal ECG signals. (3) for the fourth order non-orthogonal joint blind separation problem, the proposed algorithm is applied to the separation of fetal ECG signals. A fourth order non-orthogonal Zhang Liang diagonalization algorithm based on LU decomposition and continuous rotation is proposed. The algorithm transforms the complex global optimization problem into L and U stages by LU decomposition and replaces the factor matrix by a series of simple elementary triangular or unitary matrices. Simulation results show that the algorithm is convergent and accurate, and it is applied to the separation of fetal ECG signals.
【學(xué)位授予單位】：大連理工大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2016
【分類(lèi)號(hào)】：TN911.7

【參考文獻(xiàn)】

相關(guān)碩士學(xué)位論文 前1條

1 王秀林;多集合信號(hào)聯(lián)合盲分離方法研究[D];大連理工大學(xué);2015年

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本文編號(hào)：1811194