Sparse Representation and Non-Negative Matrix Factorization for image denoise

Abstract: Recently, the problem of blind image separation has been widely investigated, especially the medical image denoise which is the main step in medical diag-nosis. Removing the noise without affecting relevant features of the image is the main goal. Sparse decomposition over redundant dictionaries become of the most used approaches to solve this problem. NMF codes naturally favor sparse, parts-based representations. In sparse representation, signals represented as a linear combination of a redundant dictionary atoms. In this paper, we propose an algorithm based on sparse representation over the redundant dictionary and Non-Negative Matrix Factorization (N-NMF). The algorithm initializes a dic-tionary based on training samples constructed from noised image, then it searches for the best representation for the source by using the approximate matching pursuit (AMP). The proposed N-NMF gives a better reconstruction of an image from denoised one. We have compared our numerical results with different image denoising techniques and we have found the performance of the proposed technique is promising. Keywords: Image denoising, sparse representation, dictionary learning, matching pursuit, non-negative matrix factorization.