欠定松弛稀疏信号的盲分离研究
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摘要
欠定盲分离是指观测信号数目少于源信号的线性混叠问题,通常用基于信号稀疏表示的两步法来解决,第一步是估计混叠矩阵,第二步分离源信号。松弛稀疏是指混叠信号不完全满足稀疏性条件。论文正是针对松弛稀疏条件下的欠定的盲信号分离问题,旨在改善欠定盲信号分离的效果,提高恢复信号的信噪比。论文主要有如下四个方面的贡献。
第一,在欠定的盲信号分离算法的基础之上,考虑语音信号与高斯噪声的混叠,该问题也属于语音去噪的范畴。当语音信号与噪声混叠后,信号并不具有稀疏性,但可以视为松弛稀疏性的条件。根据松弛稀疏性,我们提出了基于稀疏性的双通道的语音去噪算法,该算法将该算法利用语音增强中的门限,将观测信号所在的时频域划分为两个区域：非交错区(JA)和交错区(DA)。在两个区域采取了不同的去噪策略。在非交错区,它丢弃所有信号；在交错区,它删除在散落图中“十字架”上的噪声,并用平滑滤波来补偿失真。
第二,稀疏性的条件是一个严格的条件,松弛稀疏性是一个宽松的条件,更加符合实际情况。时频掩码的方法是根据稀疏性确立的,与实际情况有较大的区别,为了能够获得更好的源信号恢复效果,我们提出了经时频掩码的盲提取算法,算法针对两个观测信号,融合了非完全稀疏信号的盲提取算法和DUET算法,它利用估计的混叠矩阵,计算源信号的提取矢量和源方向的法矢量,并经线性变换更新混叠信号和混叠矩阵,后采用时频掩码方法恢复源信号。算法在理论上增加了一定的计算复杂度,但在非完全稀疏的情况下,它的性能明显优于DUET算法。
第三,在经时频掩码的盲提取算法上,我们进一步的研究旋转变换和DUET算法的关系,分析松弛稀疏性对源信号恢复的影响,提出一个改进的DUET算法。算法用混叠矩阵的任意两列作为旋转矩阵,先旋转接收信号和混叠矩阵,后执行DUET算法。因为DUET算法在不同的旋转变换下有不同的结果,所以该算法将估计信号进行相加,弥补DUET算法的失真,改善了源信号的信噪比。
第四,在基于超平面法矢量聚类的基础上,我们针对k-SCA条件,提出了稀疏元分析的矩阵估计算法。算法仍然基于超平面法矢量的欠定盲信号分离算法,给出了k元区间的定义和检测方法。该算法的目的是寻找真正满足k-SCA条件的数据点和估计矩阵。
以上四个方面的研究是本论文的主要工作,最后,我们也利用大量的实验仿真证实所提出的理论和算法。
Underdetermined Blind signal separation is the linear mixing problem that the number of the observed signals is less than one of the sources. It is usually resolved using the two-step method based on sparse representation of the signal. The first step is to estimate the marix and the second step is to estimate the sources. Relaxed sparse condition doesn't completely satisfy the sparse condition. It is relaxed sparse and underdetermined blind source separation that is studied in this thesis. Its purpose is to improve the SNR of the estimated sources and to obtain the good sources. There are four contributions in this thesis.
Firstly, the mixing of the speech and Gaussian noise, which is belonged to speech denoising, is considered based on underdetermined blind source separation. The mixtures are not sparse but they are relaxed sparse when the speech is mixed into the noises. We propose a speech denoising based on sparsity according to the relaxed sparse. By the threshold in speech enhancement, the algorithm splits the time frequency domain of the observed signals into two areas that is in Non-Disjoint areas (NON-DA) and disjoints Area (DA). The algorithm adopts the different denoising strategies. In the NON-DA, it throws away the signals. In the DA, it deletes the noise on the "cross" and uses the smooth filter to compensate the distortion.
Secondly, the sparsity is a strick condition and the relaxed sparsity is a relaxed condition which is near to the actual case. Time-frequency mask method is far away the real circumvent as it uses the sparse condition. To obtain a good result, a blind extraction algorithm via time-frequency mask is proposed. The algorithm combines the non-completely sparse blind extraction with the DUET. It can compute the extraction vector of the source and the normal vector of the source direction; it also renews the mixtures and the mixing matrix using a linear transform. Subsequently, the source is recovered using time-frequency mask. Although it has higher computation complexity theoretically, its performance is obviously better than the DUET.
Thirdly, based on the blind extraction via time-frequency mask, we continuly study the relation between the rotatotion transform and the DUET algorithm. An improved DUET algorithm is proposed in this thesis. The algorithm rotates the mixtures and mixing matrix using a rotation matrix, which is formed by any two columns in the mixing matrix, and then do DUET algorithm. Because the results are different in DUET algorithms under different rotations, the algorithm sums the estimated signal to improve the distortion.
Finally, a matrix estimation of sparse component analysis is proposed for k-SCA condition based on the normal vector of hyperplain. The algithm is the extention of the underdetermined BSS based on the normal vector of hyper plain. It gives a definition of k-component interval and the method to identify it. The algorithm is to detect the samples of k-SAC and estimate the matrix.
The above four works are main contributions of this thesis. We also do many experiments to testify our theory and algorithms in this thesis.
第一,在欠定的盲信号分离算法的基础之上,考虑语音信号与高斯噪声的混叠,该问题也属于语音去噪的范畴。当语音信号与噪声混叠后,信号并不具有稀疏性,但可以视为松弛稀疏性的条件。根据松弛稀疏性,我们提出了基于稀疏性的双通道的语音去噪算法,该算法将该算法利用语音增强中的门限,将观测信号所在的时频域划分为两个区域：非交错区(JA)和交错区(DA)。在两个区域采取了不同的去噪策略。在非交错区,它丢弃所有信号；在交错区,它删除在散落图中“十字架”上的噪声,并用平滑滤波来补偿失真。
第二,稀疏性的条件是一个严格的条件,松弛稀疏性是一个宽松的条件,更加符合实际情况。时频掩码的方法是根据稀疏性确立的,与实际情况有较大的区别,为了能够获得更好的源信号恢复效果,我们提出了经时频掩码的盲提取算法,算法针对两个观测信号,融合了非完全稀疏信号的盲提取算法和DUET算法,它利用估计的混叠矩阵,计算源信号的提取矢量和源方向的法矢量,并经线性变换更新混叠信号和混叠矩阵,后采用时频掩码方法恢复源信号。算法在理论上增加了一定的计算复杂度,但在非完全稀疏的情况下,它的性能明显优于DUET算法。
第三,在经时频掩码的盲提取算法上,我们进一步的研究旋转变换和DUET算法的关系,分析松弛稀疏性对源信号恢复的影响,提出一个改进的DUET算法。算法用混叠矩阵的任意两列作为旋转矩阵,先旋转接收信号和混叠矩阵,后执行DUET算法。因为DUET算法在不同的旋转变换下有不同的结果,所以该算法将估计信号进行相加,弥补DUET算法的失真,改善了源信号的信噪比。
第四,在基于超平面法矢量聚类的基础上,我们针对k-SCA条件,提出了稀疏元分析的矩阵估计算法。算法仍然基于超平面法矢量的欠定盲信号分离算法,给出了k元区间的定义和检测方法。该算法的目的是寻找真正满足k-SCA条件的数据点和估计矩阵。
以上四个方面的研究是本论文的主要工作,最后,我们也利用大量的实验仿真证实所提出的理论和算法。
Underdetermined Blind signal separation is the linear mixing problem that the number of the observed signals is less than one of the sources. It is usually resolved using the two-step method based on sparse representation of the signal. The first step is to estimate the marix and the second step is to estimate the sources. Relaxed sparse condition doesn't completely satisfy the sparse condition. It is relaxed sparse and underdetermined blind source separation that is studied in this thesis. Its purpose is to improve the SNR of the estimated sources and to obtain the good sources. There are four contributions in this thesis.
Firstly, the mixing of the speech and Gaussian noise, which is belonged to speech denoising, is considered based on underdetermined blind source separation. The mixtures are not sparse but they are relaxed sparse when the speech is mixed into the noises. We propose a speech denoising based on sparsity according to the relaxed sparse. By the threshold in speech enhancement, the algorithm splits the time frequency domain of the observed signals into two areas that is in Non-Disjoint areas (NON-DA) and disjoints Area (DA). The algorithm adopts the different denoising strategies. In the NON-DA, it throws away the signals. In the DA, it deletes the noise on the "cross" and uses the smooth filter to compensate the distortion.
Secondly, the sparsity is a strick condition and the relaxed sparsity is a relaxed condition which is near to the actual case. Time-frequency mask method is far away the real circumvent as it uses the sparse condition. To obtain a good result, a blind extraction algorithm via time-frequency mask is proposed. The algorithm combines the non-completely sparse blind extraction with the DUET. It can compute the extraction vector of the source and the normal vector of the source direction; it also renews the mixtures and the mixing matrix using a linear transform. Subsequently, the source is recovered using time-frequency mask. Although it has higher computation complexity theoretically, its performance is obviously better than the DUET.
Thirdly, based on the blind extraction via time-frequency mask, we continuly study the relation between the rotatotion transform and the DUET algorithm. An improved DUET algorithm is proposed in this thesis. The algorithm rotates the mixtures and mixing matrix using a rotation matrix, which is formed by any two columns in the mixing matrix, and then do DUET algorithm. Because the results are different in DUET algorithms under different rotations, the algorithm sums the estimated signal to improve the distortion.
Finally, a matrix estimation of sparse component analysis is proposed for k-SCA condition based on the normal vector of hyperplain. The algithm is the extention of the underdetermined BSS based on the normal vector of hyper plain. It gives a definition of k-component interval and the method to identify it. The algorithm is to detect the samples of k-SAC and estimate the matrix.
The above four works are main contributions of this thesis. We also do many experiments to testify our theory and algorithms in this thesis.
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