Study on sparse image representations and its application to feature domain image processing

本文提出了稀疏信号分解方法及其在彩色图像、混合信号和周期信号中的应用。在彩色图像表示应用中，将基追踪去噪算法扩展到彩色图像去噪中。基跟踪去噪通过在系数上添加L1惩罚项来预测来自噪声观测的信号的系数。L1惩罚产生于假设信号可以被分解成稀疏且统计独立的分量。在本研究中，对L1惩罚进行了改进，对信道不统计独立的多通道信号应用基追踪去噪。实验证明了利用修正惩罚法对彩色图像进行基跟踪去噪。对于语音和噪声的分离，我们假设语音在20-40ms内是平稳的，并且噪声的持续时间短于此时间。在我们的方法中，使用稀疏表示来区分噪声和语音，通过其时间持续特性的差异。对于稀疏表示，采用一对支持不同时间间隔的DFT基对信号进行稀疏表示。较短和较长的DFT基分别代表噪声和语音，并受到稀疏性的惩罚。在回声环境中，噪声的混响出现在分离的语音信号中。为了抑制噪声的混响，我们对分离出来的语音进行频谱减法处理。对于频谱减法，我们提出了噪声混响的功率估计方法。在实验中，我们将提出的方法应用于在回声环境中记录的被噪声突发破坏的有噪声语音信号。结果表明，该方法可使噪声段的信噪比提高约7-10dB。对于作为图像混合基本模型的周期信号混合，稀疏周期分解方法将一个信号分解成少量的周期信号。该分解方法对生成的周期子信号施加惩罚，以提高分解的稀疏性和避免周期的高估。这个惩罚被定义为所得到的周期子信号的$1_2$范数的加权和。这种分解近似为无约束最小化问题。为了解决这一问题，采用了一种松弛算法。在实验中，给出了分解结果，以证明同时检测隐藏在混合信号中的周期和波形。少

In this study, sparse signal decomposition methods and its application to color images, signal mixtures and periodic signals are proposed. In applications to color image representation, the basis pursuit denoising algorithm is extended to the color image denoising. The basis pursuit denoising predicts the coefficients of a signal from a nosy observation by adding an L1 penalty term on the coefficients. The L1 penalty arises from the assumption that the signal can be decomposed into sparse and statistically independent components. In this study, the L1 penalty is modified to apply the basis pursuit denoising for multichannel signals whose channels are not statistically independent. In experiment, the color image denoising by the basis pursuit by using the modified penalty is demonstrated.For speech and noise separation, we assumed that the speech is stationary within 20-40ms and the duration of the noise is shorter than this period. In our approach, a sparse representation is employed t … More o separate the noise and speech by the difference of its time duration properties. For the sparse representation, a pair of DFT bases that support different time interval were employed to the sparse signal representation. The shorter and the longer DFT bases represent the noise and the speech respectively with a penalty of sparseness. In echoic environments the reverberation of the noises appears in the separated speech signals. In order to suppress the reverberation of the noise, we apply a spectrum subtraction to the separated speech. For the spectrum subtraction, we propose a power estimation method for the noise reverberation. In experiment, we apply the proposed method to noisy speech signals that are corrupted by noise bursts recorded in an echoic environment. We demonstrate that the proposed method can improve about 7-10dB in SNR of the noisy segments.For periodic signal mixtures that are fundamental models of the image mixtures, the sparse periodic decomposition methods that decompose a signal into the small number of periodic signals. The proposed decomposition method imposes a penalty on the resultant periodic subsignals in order to improve the sparsity of decomposition and avoid the overestimation of periods. This penalty is defined as the weighted sum of the $1_2$ norms of the resultant periodic subsignals. This decomposition is approximated by an unconstrained minimization problem. In order to solve this problem, a relaxation algorithm is applied. In the experiments, decomposition results are presented to demonstrate the simultaneous detection of periods and waveforms hidden in signal mixtures. Less