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

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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