Image Reconstruction by Linear Programming

Part of Advances in Neural Information Processing Systems 16 (NIPS 2003)

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Koji Tsuda, Gunnar Rätsch


A common way of image denoising is to project a noisy image to the sub- space of admissible images made for instance by PCA. However, a major drawback of this method is that all pixels are updated by the projection, even when only a few pixels are corrupted by noise or occlusion. We pro- pose a new method to identify the noisy pixels by (cid:1) 1-norm penalization and update the identified pixels only. The identification and updating of noisy pixels are formulated as one linear program which can be solved efficiently. Especially, one can apply the ν-trick to directly specify the fraction of pixels to be reconstructed. Moreover, we extend the linear program to be able to exploit prior knowledge that occlusions often ap- pear in contiguous blocks (e.g. sunglasses on faces). The basic idea is to penalize boundary points and interior points of the occluded area dif- ferently. We are able to show the ν-property also for this extended LP leading a method which is easy to use. Experimental results impressively demonstrate the power of our approach.