盲源分离的时频域算法研究
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摘要
盲源分离是指在不知道或无法获得源信号和混合方式的情况下仅由观测信号恢复源信号的过程。作为一种数据分析、信号处理强有力的工具，盲源分离具有非常重要的理论意义，并广泛应用于无线通信、语音信号处理、阵列信号处理、图像处理、生物信号处理、信号识别、地震勘探和计量经济学等领域。
本文围绕这一热点课题展开，讨论了盲源分离算法在非平稳信号中的应用问题。
对于非平稳信号，如语音信号、音乐信号、脑电信号等，时频联合分析JTFA（Joint Time-FrequencyAnalysis）不仅可以从频域的角度描述信号，还可以描述频率分量及信号的能量在时域中的分布，因此可以有效地提取非平稳信号的时变局部特征，比单一时域或频域表示有更好的“显微”优势。
在盲源分离中，引入双线性JTFA或线性JTFA，可以充分利用了源信号在时-频两域的多样性来分离信号。
1、本文分析了多分量信号自项、交叉项在Wigner-Ville平面、模糊平面的分布特性，根据两者的对应关系，设计了一种高性能的核函数，推导了其对应的时频分布、满足的性质和实现的算法。且以Boashash提出的时频性能指标为准则，分析了时频分布参数的选择方法。在此基础上，借鉴Belouchrani,A和Amin, M.G提出的时-频联合对角化思想，以该时频分布计算观测信号的时频谱，以自项点理论选择时频点进行Jacobi联合近似对角化求出酋矩阵，进而估计源信号和混合阵，提出了一种性能优越的双线性时频盲源分离算法。另外，本文从重排时频谱的角度，应用重排平滑伪Wigner-Ville分布来抑制双线性分布交叉项聚集的尖锋，提出了一种基于重排时频谱的盲源分离算法。上述算法能实现音乐信号、语音信号的盲源分离。
2、本文借鉴M.Puigt和Y.Deville提出的时频比思想，引入S变换(StockwellTransform)、或广义S变换来获得非平稳信号的多分辨率特性。通过S变换、或广义S变换将一维信号映射到二维时频平面，再构造不同观测信号的时频比矩阵，通过在时频比矩阵范围内搜索一个个单源分析域，以估计混合阵的每个元素，进而估计源信号，提出了一种具有多分辨率的线性时频盲源分离算法。该算法能避免双线性JTFA交叉项带来的干扰问题，并具有多分辨特性，适合分离同时含有多个高频分量和低频分量的混合信号。
3、由于现实世界中观测信号往往被各种各样的噪声污染，从而破坏了源信号的结构，因此如何抑制噪声，使盲源分离算法具有更好的鲁棒性是必须考虑的一个现实难题。本文针对噪声作为信号源之一的情况做了一点探讨，提出了一种基于Hough变换的盲源分离算法。该算法以Wigner-Ville分布计算观测信号的时频谱并将信号的时频谱看作图像，利用Hough变换将信号检测转换为在参数空间寻找局部极大值的问题，再运用自项点理论选择合适的矩阵进行联合近似对角化，求出酋矩阵，进而估计源信号和混合阵。该算法通过把噪声能量扩展到整个参数平面而只选择信号能量占主导的自项点进行对角化，对噪声具有一定的抑制能力。
Blind source separation (BSS) is to recover the sources form the observations only,without the information about the source signals or the mixing process. As a powerfuldata representation and signal processing tool, BSS has become a very important topicof research and development in many areas, especially wireless communications,speech signal processing, array signal processing, image processing, biological signalprocessing, signal recognition, exploration seismology, econometrics, etc.
Focusing on this theme, some BSS approaches for non-stationary signals arediscussed in this dissertation.
For non-stationary signals, such as speech signals, music signals and EEG, jointtime-frequency analysis(JTFA) can study these signals in both the time and frequencydomains simultaneously, using various t-f representations. This method, hence caneffectively extract the local time-varying characteristics of non-stationary signals andhas better “microscopic” advantage compared to the time domain or frequency domainrepresentation.
Based on the bilinear JTFA or linear JTFA, some BSS approaches exploiting thediversities in the t-f signatures of the sources can be obtained.
Firstly, the location features of auto-and cross-terms from the multi-componentssignals and their relationship between the Wigner-Ville distribution plane and ambiguityfunction plane are discussed in this dissertation. Then, a high performance kernel isstudied and its t-f distribution、its desirable properties and its calculation algorithm arederived. And, its parameter choice based on Boashash’ performance indicator isproposed. Moreover, a high-resolution t-f BSS approach is developed based on the t-fjoint diagonalization method, proposed by Belouchrani, A and Amin, M.G. Thisapproach includes first whitening mixed signals, then constructing a set of t-f matricesusing the proposed t-f distribution, finally a Jacobi joint diagonalization of a combinedset of t-f matrices to estimate the mixing matrix and the source signals. In addition, aBSS algorithm based on rearrangement t-f spectrum is proposed. This algorithmexploits the rearrangement spectrum mechanism and adopts smooth pseudo Wigner-Ville distribution to eliminate cross-terms interference. By use of the techniquesproposed in this dissertation, the improved performance of BSS of music signal, speechsignals has been achieved.
Secondly, a linear t-f BSS approach adopting Stockwell transform or generalizedStockwell transform to obtain multi-resolution characteristics are proposed. Thisapproach uses Stockwell transform or generalized Stockwell transform to derive t-fdistribution of mixed signals and then constructs different t-f ratio matrices, proposedby M.Puigt and Y.Deville. Then, it detects single source occurs to identify each elementof the mixing matrix and hence obtains the estimated signals. This approach can avoidthe cross-terms interference from bilinear t-f distributions and has the multi-resolutioncharacteristics. Therefore it may be more suitable to separate mixed-signals containingmany high-frequency components and low-frequency components simultaneously.
Thirdly, in real life, there is a variety of noise present in the observations. How toobtain better noise suppression and robustness is a real problem as the structure ofsignals are corrupted by noise. In this dissertation, source noise is discussed and a BSSapproach based on Hough transform is proposed. This approach is developed whichincludes firstly calculating the t-f distributions of observed signals by Wigner-Villedistribution, and using the Hough transform to convert the signals detection to find thelocal peak values in the parameter domain though considering this t-f distribution as animage, finally a joint-diagonalization of a combined set of t-f distributions chosen byauto-term theory to estimate the unitary matrix, the mixing matrix and the sourcesignals. The effect of spreading the noise power while localizing the source energy inthe parameter plane amounts to increasing the robustness of the proposed approach withrespect to noise.
本文围绕这一热点课题展开，讨论了盲源分离算法在非平稳信号中的应用问题。
对于非平稳信号，如语音信号、音乐信号、脑电信号等，时频联合分析JTFA（Joint Time-FrequencyAnalysis）不仅可以从频域的角度描述信号，还可以描述频率分量及信号的能量在时域中的分布，因此可以有效地提取非平稳信号的时变局部特征，比单一时域或频域表示有更好的“显微”优势。
在盲源分离中，引入双线性JTFA或线性JTFA，可以充分利用了源信号在时-频两域的多样性来分离信号。
1、本文分析了多分量信号自项、交叉项在Wigner-Ville平面、模糊平面的分布特性，根据两者的对应关系，设计了一种高性能的核函数，推导了其对应的时频分布、满足的性质和实现的算法。且以Boashash提出的时频性能指标为准则，分析了时频分布参数的选择方法。在此基础上，借鉴Belouchrani,A和Amin, M.G提出的时-频联合对角化思想，以该时频分布计算观测信号的时频谱，以自项点理论选择时频点进行Jacobi联合近似对角化求出酋矩阵，进而估计源信号和混合阵，提出了一种性能优越的双线性时频盲源分离算法。另外，本文从重排时频谱的角度，应用重排平滑伪Wigner-Ville分布来抑制双线性分布交叉项聚集的尖锋，提出了一种基于重排时频谱的盲源分离算法。上述算法能实现音乐信号、语音信号的盲源分离。
2、本文借鉴M.Puigt和Y.Deville提出的时频比思想，引入S变换(StockwellTransform)、或广义S变换来获得非平稳信号的多分辨率特性。通过S变换、或广义S变换将一维信号映射到二维时频平面，再构造不同观测信号的时频比矩阵，通过在时频比矩阵范围内搜索一个个单源分析域，以估计混合阵的每个元素，进而估计源信号，提出了一种具有多分辨率的线性时频盲源分离算法。该算法能避免双线性JTFA交叉项带来的干扰问题，并具有多分辨特性，适合分离同时含有多个高频分量和低频分量的混合信号。
3、由于现实世界中观测信号往往被各种各样的噪声污染，从而破坏了源信号的结构，因此如何抑制噪声，使盲源分离算法具有更好的鲁棒性是必须考虑的一个现实难题。本文针对噪声作为信号源之一的情况做了一点探讨，提出了一种基于Hough变换的盲源分离算法。该算法以Wigner-Ville分布计算观测信号的时频谱并将信号的时频谱看作图像，利用Hough变换将信号检测转换为在参数空间寻找局部极大值的问题，再运用自项点理论选择合适的矩阵进行联合近似对角化，求出酋矩阵，进而估计源信号和混合阵。该算法通过把噪声能量扩展到整个参数平面而只选择信号能量占主导的自项点进行对角化，对噪声具有一定的抑制能力。
Blind source separation (BSS) is to recover the sources form the observations only,without the information about the source signals or the mixing process. As a powerfuldata representation and signal processing tool, BSS has become a very important topicof research and development in many areas, especially wireless communications,speech signal processing, array signal processing, image processing, biological signalprocessing, signal recognition, exploration seismology, econometrics, etc.
Focusing on this theme, some BSS approaches for non-stationary signals arediscussed in this dissertation.
For non-stationary signals, such as speech signals, music signals and EEG, jointtime-frequency analysis(JTFA) can study these signals in both the time and frequencydomains simultaneously, using various t-f representations. This method, hence caneffectively extract the local time-varying characteristics of non-stationary signals andhas better “microscopic” advantage compared to the time domain or frequency domainrepresentation.
Based on the bilinear JTFA or linear JTFA, some BSS approaches exploiting thediversities in the t-f signatures of the sources can be obtained.
Firstly, the location features of auto-and cross-terms from the multi-componentssignals and their relationship between the Wigner-Ville distribution plane and ambiguityfunction plane are discussed in this dissertation. Then, a high performance kernel isstudied and its t-f distribution、its desirable properties and its calculation algorithm arederived. And, its parameter choice based on Boashash’ performance indicator isproposed. Moreover, a high-resolution t-f BSS approach is developed based on the t-fjoint diagonalization method, proposed by Belouchrani, A and Amin, M.G. Thisapproach includes first whitening mixed signals, then constructing a set of t-f matricesusing the proposed t-f distribution, finally a Jacobi joint diagonalization of a combinedset of t-f matrices to estimate the mixing matrix and the source signals. In addition, aBSS algorithm based on rearrangement t-f spectrum is proposed. This algorithmexploits the rearrangement spectrum mechanism and adopts smooth pseudo Wigner-Ville distribution to eliminate cross-terms interference. By use of the techniquesproposed in this dissertation, the improved performance of BSS of music signal, speechsignals has been achieved.
Secondly, a linear t-f BSS approach adopting Stockwell transform or generalizedStockwell transform to obtain multi-resolution characteristics are proposed. Thisapproach uses Stockwell transform or generalized Stockwell transform to derive t-fdistribution of mixed signals and then constructs different t-f ratio matrices, proposedby M.Puigt and Y.Deville. Then, it detects single source occurs to identify each elementof the mixing matrix and hence obtains the estimated signals. This approach can avoidthe cross-terms interference from bilinear t-f distributions and has the multi-resolutioncharacteristics. Therefore it may be more suitable to separate mixed-signals containingmany high-frequency components and low-frequency components simultaneously.
Thirdly, in real life, there is a variety of noise present in the observations. How toobtain better noise suppression and robustness is a real problem as the structure ofsignals are corrupted by noise. In this dissertation, source noise is discussed and a BSSapproach based on Hough transform is proposed. This approach is developed whichincludes firstly calculating the t-f distributions of observed signals by Wigner-Villedistribution, and using the Hough transform to convert the signals detection to find thelocal peak values in the parameter domain though considering this t-f distribution as animage, finally a joint-diagonalization of a combined set of t-f distributions chosen byauto-term theory to estimate the unitary matrix, the mixing matrix and the sourcesignals. The effect of spreading the noise power while localizing the source energy inthe parameter plane amounts to increasing the robustness of the proposed approach withrespect to noise.
引文
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