Sparse Representation and Non-Negative Matrix Factorization for image denoise

Aamir Mohammed Adam


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 repre-sented 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 dictionary based on training samples constructed from noised im-age, 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 numer-ical results with different image denoising techniques and we have found the performance of the proposed technique is promising.


El-Henawy, I., El-Areef, T., and Karawia A.(2003). “On wavelets applications in med-ical image denoising”, Machine Graphics & Vision International Journal, vol. 12, no. 3, pp. 393-404.

Janaki Sivakumar, K. Thangavel, P. Sara-vanan 2012. "Computed radiography skull image enhancement using Wiener fil-ter", Pattern Recognition Informatics and Medical Engineering (PRIME), Internation-al Conference on, 307-311

R. M. Farouk and H. A. Khalil. “Image De-noising based on Sparse Representation and Non-Negative Matrix Factorization” Life Science Journal,9(2), 2012.

R.M. Farouk, M. E. Abd El-aziz, M Aly, “Medical Image Denoising based on Log-Gabor Wavelet Dictionary and K-SVD Al-gorithm” International Journal of Computer Applications (0975 – 8887): 141, 2016.

Jean-Luc, S., E. J. Candes, et al. (2002). "The curvelet transform for image de-noising." IEEE Transactions on Image Pro-cessing 11: 670-684.

Liu, Z. and H. Xu (2008). “Image De-noising with Nonsubsampled Wavelet-Based Contourlet Transform”, Fifth Interna-

tional Conference on Fuzzy Systems and Knowledge Discovery: 301-305.

M.Aharon, M.Elad, et al. (2006). "The K-SVD: an algorithm for designing of over-complete dictionaries for sparse representa-tion.", IEEE Transaction on Signal Pro-cessing 54(11): 4311–4322.

M.Elad and M.Aharon (2006). "Image de-noising via sparse and redundant representa-tions over learned dictionaries.", IEEE Transaction on Image Processing 15: 3736–3745.

A.Foi, V.Katkovnik, et al. (2007). "Pointwise shape-adaptive DCT for high quality denoising”, Life Science Journal, 2012;9(x) editor@ 341 Life Science and deblocking of grayscale and color images." IEEE Transac-tion on Image Processing 16(5).

Zhang, L., W. Dong, et al. (2010). "Two-stage image denoising by principal compo-

nent analysis with local pixel grouping.", Pattern Recognition 43: 1531-1549.

Lee, D. D. and H. S. Seung (1999). "Learn-ing of the parts of objects by non-negative matrix factorization.", Nature 401: 788–791.

Lee, D. D. and H. S. Seung (2001). "Algo-rithms for Nonnegative Matrix Factoriza-tion.", Advances in Neural Information Pro-cessing Systems 13: 556-562.

Neff, R. and A. Zakhor (1995). “Matching Pursuit Video Coding at Very Low Bit Rates Data Compression”, Snowbird, UT, USA.

Naperville Imaging Center, accessed on March 2015.


  • There are currently no refbacks.