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Abstract: In this paper, we propose a sparse overcomplete image approximation method based on the ideas of overcomplete log-Gabor wavelet, mean shift and energy concentration. The proposed approximation method selects the necessary wavelet coefficients with a mean shift based algorithm, and concentrates energy on the selected coefficients. It can sparsely approximate the original image, and converges faster than the existing local competition based method. Then, we propose a new compression scheme based on the above approximation method. The scheme has compression performance similar to JPEG 2000. The images decoded with the proposed compression scheme appear more pleasant to the human eyes than those with JPEG 2000.

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