频域卷积混合盲分离研究
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摘要
卷积混合盲分离是信号处理的研究热点之一,在数据传输、无线通信、图像恢复、语音增强、生物医学信号检测等领域中都得到了广泛的应用。卷积混合的分离既能在时域执行也能在频域执行,其中频域方法利用短时傅立叶变换将卷积混合转换为多个频率片上的瞬时混合,显著的降低了分离的难度,吸引了研究者们越来越多的关注。
目前,频域方法仍存在大量问题有待深入研究,分离性能需要进一步提高。首先,“循环—部分卷积误差”导致短时傅立叶变换系数和源信号频谱瞬时混合间存在差异,影响了各频率片分离矩阵的估计精度和分离性能。其次,各频率片上瞬时盲分离中顺序不确定性的差异形成了“扰动不确定性”,使所合成的分离滤波器阵列不再为真实混合滤波器阵列的逆系统,严重损害了卷积混合的分离性能。最后,现有的代价函数设计方法完全忽视了“跨频率片独立性”,这导致其对分离矩阵的特征描述不够全面,影响了迭代的收敛速度和分离性能。为此,本文对抑制“循环—部分卷积误差”、消除“扰动不确定性”和“跨频率片独立性”的应用这三方面开展研究以提高频域方法的分离性能。
论文的主要贡献和创新点包括以下几个方面:
1)提出了两种抑制“循环—部分卷积误差”的预处理手段:时域滤波器和加权修正离散傅立叶变换。时域滤波器将短时傅立叶变换系数视为“带噪瞬时混合”,采用“非连续多帧平滑”的滤波形式来抑制“循环—部分卷积误差”带来的“噪声”,能提高后续频域方法对各频率片上混合矩阵的估计精度并提高分离性能。加权修正离散傅立叶变换则是一种基于幅度谱分布特征的最优变换,其变换系数在加权最小均方误差意义下最接近所希望提取的源信号频谱的瞬时混合,等效完成了“循环—部分卷积误差”抑制,可代替短时傅立叶变换中的离散傅立叶变换从而提高现有频域方法的分离性能。
2)依据不同频率片上不同维频域源信号间“跨频率片独立性”,我们提出了一种基于跨频率片去相关的“跨频频域方法”,利用相邻多个频率片的信息估计每个频率片上分离矩阵。该方法利用了现有频域方法所忽视的“跨频率片独立性”,使其代价函数对各频率片上分离矩阵所具有特征的描述更为全面,从而能获得更快的迭代收敛速度和更高的分离性能。
3)依据所提出的基于单频点稠密短时谱的信号重构方法,我们提出了一种单频点频域方法,仅利用一个频率片的信息来完成卷积混合盲分离。由于从根本上消除了扰动不确定性发生的可能,单频点频域方法能获得更高的分离性能。
4)提出了“频域独立准则的时域优化”的通用公式,可将任何频域算法在各频率片上分离矩阵的迭代公式合成时域分离滤波器迭代梯度,直接获得时域分离滤波器的最优解。该方法被用于所提出的“跨频频域方法”,消除了扰动不确定性发生的可能。
本论文对频域卷积混合盲分离的理论进行了深入的研究,所提出的算法具有一定的创新性,对于卷积混合盲分离的应用研究具有一定的参考价值。
Blind source separation of convolutive mixtures (CMBSS) is a hotspot of modern signal processing. It has been widely used in many fields, such as tele-communications, audio signal separation, biomedical signal processing and image processing. Convolutive blind separation could be implemented in either temporal domain (TDCMBSS) or frequency domain (FDCMBSS). Since convolutive mixture can be simplified into instantaneous mixture in frequency domain by Short Time Fourier Transform (STFT), more and more attention is paid for FDCMBSS and a lot of algorithms are proposed in the past few years.
Despite extensive efforts so far, there are still many open issues that deteriorate the separation performance and need further investigation. How to remove the Permutation indeterminacy, how to suppress the difference between circular and partial convolution and how to introduce the across frequency independence are three key issues. The research of this thesis will focus on these three aspects to improve the separation performance.
The main contributions of this thesis are as following:
1) To suppress the difference between circular and partial convolution, we propose two preprocessing approach for the existed FDCMBSS method, i.e. Temporal Filter and Weighted Modified Discrete Fourier Transform (WMDFT). Temporal Filter treats the STFT coefficients as a noisy-instantaneous mixture, and employs multi-inconsecutive-frames moving average to suppress the noise introduced by the difference between circular and partial convolution. WMDFT is an optimal transform whose coefficients approximates to the noise-free instantaneous mixture of source spectrum in a weighted least square sense, which is equivalent to suppress the difference between circular and partial convolution. The experiments results show that the proposed two preprocessing techniques are effective.
2) Based on the independence between sources on different frequency bins, a cross-frequency-based approach is proposed for the convolutive blind source separation. The information on the adjacent frequency bins is used to estimate the separating matrix on each frequency bin. By incorporating the cross frequency independence in its cost function, the cross-frequency-based approach specifies the property of separating matrix more precisely than the existed FDCMBSS methods, and possesses a higher separation performance with faster convergence speed. The validity of this proposed method is confirmed by the simulation results.
3) Based on the derived signal reconstruction algorithm with dense spectrum on one frequency bin, a single-bin-based approach is proposed for convolutive blind separation in the frequency domain. Since it can implement convolutive separation with only one frequency bin, there's no permutation indetermincy in single-bin-based approach, which improves the performance of proposed single-bin-based approach. The simulation results show the correctness and effectiveness of this method.
4) To remove the permutation indetermincy, a general formulation for thetime-domain optimization of frequency-domain Independence Criterion is proposed. It's able to convert the existed learning rule of frequency domain separating matrix into learning rule of time domain separating filters. The permutation problem of the proposed cross-frequency-based approach is removed by this general formulation.
The principle and algorithms of FDCMBSS are studied in this thesis. Theproposed methods expand the application of FDCMBSS with practical and theoreticalsignificance.
目前,频域方法仍存在大量问题有待深入研究,分离性能需要进一步提高。首先,“循环—部分卷积误差”导致短时傅立叶变换系数和源信号频谱瞬时混合间存在差异,影响了各频率片分离矩阵的估计精度和分离性能。其次,各频率片上瞬时盲分离中顺序不确定性的差异形成了“扰动不确定性”,使所合成的分离滤波器阵列不再为真实混合滤波器阵列的逆系统,严重损害了卷积混合的分离性能。最后,现有的代价函数设计方法完全忽视了“跨频率片独立性”,这导致其对分离矩阵的特征描述不够全面,影响了迭代的收敛速度和分离性能。为此,本文对抑制“循环—部分卷积误差”、消除“扰动不确定性”和“跨频率片独立性”的应用这三方面开展研究以提高频域方法的分离性能。
论文的主要贡献和创新点包括以下几个方面:
1)提出了两种抑制“循环—部分卷积误差”的预处理手段:时域滤波器和加权修正离散傅立叶变换。时域滤波器将短时傅立叶变换系数视为“带噪瞬时混合”,采用“非连续多帧平滑”的滤波形式来抑制“循环—部分卷积误差”带来的“噪声”,能提高后续频域方法对各频率片上混合矩阵的估计精度并提高分离性能。加权修正离散傅立叶变换则是一种基于幅度谱分布特征的最优变换,其变换系数在加权最小均方误差意义下最接近所希望提取的源信号频谱的瞬时混合,等效完成了“循环—部分卷积误差”抑制,可代替短时傅立叶变换中的离散傅立叶变换从而提高现有频域方法的分离性能。
2)依据不同频率片上不同维频域源信号间“跨频率片独立性”,我们提出了一种基于跨频率片去相关的“跨频频域方法”,利用相邻多个频率片的信息估计每个频率片上分离矩阵。该方法利用了现有频域方法所忽视的“跨频率片独立性”,使其代价函数对各频率片上分离矩阵所具有特征的描述更为全面,从而能获得更快的迭代收敛速度和更高的分离性能。
3)依据所提出的基于单频点稠密短时谱的信号重构方法,我们提出了一种单频点频域方法,仅利用一个频率片的信息来完成卷积混合盲分离。由于从根本上消除了扰动不确定性发生的可能,单频点频域方法能获得更高的分离性能。
4)提出了“频域独立准则的时域优化”的通用公式,可将任何频域算法在各频率片上分离矩阵的迭代公式合成时域分离滤波器迭代梯度,直接获得时域分离滤波器的最优解。该方法被用于所提出的“跨频频域方法”,消除了扰动不确定性发生的可能。
本论文对频域卷积混合盲分离的理论进行了深入的研究,所提出的算法具有一定的创新性,对于卷积混合盲分离的应用研究具有一定的参考价值。
Blind source separation of convolutive mixtures (CMBSS) is a hotspot of modern signal processing. It has been widely used in many fields, such as tele-communications, audio signal separation, biomedical signal processing and image processing. Convolutive blind separation could be implemented in either temporal domain (TDCMBSS) or frequency domain (FDCMBSS). Since convolutive mixture can be simplified into instantaneous mixture in frequency domain by Short Time Fourier Transform (STFT), more and more attention is paid for FDCMBSS and a lot of algorithms are proposed in the past few years.
Despite extensive efforts so far, there are still many open issues that deteriorate the separation performance and need further investigation. How to remove the Permutation indeterminacy, how to suppress the difference between circular and partial convolution and how to introduce the across frequency independence are three key issues. The research of this thesis will focus on these three aspects to improve the separation performance.
The main contributions of this thesis are as following:
1) To suppress the difference between circular and partial convolution, we propose two preprocessing approach for the existed FDCMBSS method, i.e. Temporal Filter and Weighted Modified Discrete Fourier Transform (WMDFT). Temporal Filter treats the STFT coefficients as a noisy-instantaneous mixture, and employs multi-inconsecutive-frames moving average to suppress the noise introduced by the difference between circular and partial convolution. WMDFT is an optimal transform whose coefficients approximates to the noise-free instantaneous mixture of source spectrum in a weighted least square sense, which is equivalent to suppress the difference between circular and partial convolution. The experiments results show that the proposed two preprocessing techniques are effective.
2) Based on the independence between sources on different frequency bins, a cross-frequency-based approach is proposed for the convolutive blind source separation. The information on the adjacent frequency bins is used to estimate the separating matrix on each frequency bin. By incorporating the cross frequency independence in its cost function, the cross-frequency-based approach specifies the property of separating matrix more precisely than the existed FDCMBSS methods, and possesses a higher separation performance with faster convergence speed. The validity of this proposed method is confirmed by the simulation results.
3) Based on the derived signal reconstruction algorithm with dense spectrum on one frequency bin, a single-bin-based approach is proposed for convolutive blind separation in the frequency domain. Since it can implement convolutive separation with only one frequency bin, there's no permutation indetermincy in single-bin-based approach, which improves the performance of proposed single-bin-based approach. The simulation results show the correctness and effectiveness of this method.
4) To remove the permutation indetermincy, a general formulation for thetime-domain optimization of frequency-domain Independence Criterion is proposed. It's able to convert the existed learning rule of frequency domain separating matrix into learning rule of time domain separating filters. The permutation problem of the proposed cross-frequency-based approach is removed by this general formulation.
The principle and algorithms of FDCMBSS are studied in this thesis. Theproposed methods expand the application of FDCMBSS with practical and theoreticalsignificance.
引文
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