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Abstract

A common way of image denoising is to project a noisy image to the subspace ofadmissible images made for instance by PCA. However, a major drawback of thismethod is that all pixels are updated by the projection, even when only a few pixels arecorrupted by noise or occlusion. We propose a new method to identify the noisy pixelsby`1-norm penalization and update the identified pixels only. The identification andupdating of noisy pixels are formulated as a single linear program. The application ofthe well-knownν-trick is particularly useful in this context as it allows the specificationof the fraction of pixels to be updated. Moreover, we extend the linear program to beable to exploit prior knowledge that occlusions often appear in contiguous blocks (e.g.sunglasses on faces). The basic idea is to penalize boundary points and interior pointsof the occluded area differently. We are able to show theν-property also for thisextended LP leading a method which is easy to use. Experimental results impressivelydemonstrate the power of our approach.