Sparse Representation and Non-Negative Matrix Factorization for image denoise

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.

[1]  K. Thangavel,et al.  Computed radiography skull image enhancement using Wiener filter , 2012, International Conference on Pattern Recognition, Informatics and Medical Engineering (PRIME-2012).

[2]  R. M. Farouk,et al.  Medical Image Denoising based on Log-Gabor Wavelet Dictionary and K-SVD Algorithm , 2016 .

[3]  Emmanuel J. Candès,et al.  The curvelet transform for image denoising , 2001, Proceedings 2001 International Conference on Image Processing (Cat. No.01CH37205).

[4]  H. Sebastian Seung,et al.  Learning the parts of objects by non-negative matrix factorization , 1999, Nature.

[5]  Jérôme Idier,et al.  Algorithms for Nonnegative Matrix Factorization with the β-Divergence , 2010, Neural Computation.

[6]  M. Elad,et al.  $rm K$-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation , 2006, IEEE Transactions on Signal Processing.

[7]  R. M. Farouk,et al.  Image Denoising based on Sparse Representation and Non-Negative Matrix Factorization , 2012 .

[8]  Zhe Liu,et al.  Image Denoising with Nonsubsampled Wavelet-Based Contourlet Transform , 2008, 2008 Fifth International Conference on Fuzzy Systems and Knowledge Discovery.

[9]  Karen O. Egiazarian,et al.  Pointwise Shape-Adaptive DCT for High-Quality Denoising and Deblocking of Grayscale and Color Images , 2007, IEEE Transactions on Image Processing.

[10]  David Zhang,et al.  Two-stage image denoising by principal component analysis with local pixel grouping , 2010, Pattern Recognit..

[11]  A. Bruckstein,et al.  K-SVD : An Algorithm for Designing of Overcomplete Dictionaries for Sparse Representation , 2005 .

[12]  Michael Elad,et al.  Image Denoising Via Sparse and Redundant Representations Over Learned Dictionaries , 2006, IEEE Transactions on Image Processing.

[13]  Avideh Zakhor,et al.  Matching pursuit video coding at very low bit rates , 1995, Proceedings DCC '95 Data Compression Conference.

[14]  I. El-Henawy,et al.  On wavelets applications in medical image denoising , 2003 .