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Image Reconstruction by Linear Programming

MPG-Autoren
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Tsuda,  K
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;
Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Rätsch,  G
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;
Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Zitation

Tsuda, K., & Rätsch, G. (2004). Image Reconstruction by Linear Programming. In S. Thrun, L. Saul, & B. Schölkopf (Eds.), Advances in Neural Information Processing Systems 16: Proceedings of the 2003 Conference (pp. 57-64). Cambridge, MA, USA: MIT Press.


Zitierlink: https://hdl.handle.net/11858/00-001M-0000-0013-D8E7-B
Zusammenfassung
A common way of image denoising is to project a noisy image to the subspace 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 propose
a new method to identify the noisy pixels by 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 appear in contiguous blocks (e.g. sunglasses on faces). The basic idea is to penalize boundary points and interior points of the occluded area differently. 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.