Image Reconstruction by Linear Programming

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.