Ahmad Kadri JUNOH, Achmad ABDURRAZZAQ, Zainab YAHYA, Ismail MOHD

A hybrid of tropical-singular value decomposition method for salt and pepper noise removal

The unknown information contained in an image that causes the change of information in the image is callednoise. In this paper, we propose a new method for removing salt and pepper noise by using singular value decompositionand the concept of tropical algebra operations. To determine the performance of the proposed method, 20 test imagesare used as samples. Then three different image quality assessments are used: peak signal-to-noise ratio (PSNR),structural similarity (SSIM), and image enhancement factor (IEF). In addition, six different filtering methods, i.e. MF,DWMF, PSMF, MDBUTM, NAFSM, and BPDF, are used to compare the performance of the proposed method. Theexperimental results show that the proposed method yields better results than the existing methods, in particular theBPDF filtering method.

PDF

___

[1] Carlisle PA. Nomophobia: A Rising Trend in Students (Addiction, Cell Phone Addiction). Scotts Valley, CA, USA: CreateSpace Independent Publishing Platform, 2017.
[2] Parasuraman S, Sam AT, Yee SWK, Chuon BLC, Ren LY. Smartphone usage and increased risk of mobile phone addiction: a concurrent study. International Journal of Pharmaceutical Investigation 2017; 7 (3): 125–131. doi: 10.4103/jphi.JPHI_56_17
[3] Boyat AK, Joshi BK. A review paper: noise models in digital image processing. Signal & Image Processing: An International Journal 2015; 6 (2): 63-75. doi: 10.5121/sipij.2015.6206
[4] Julliand T, Nozick V, Talbot H. Image noise and digital image forensics. In: Digital-Forensics and Watermarking: 14th International Workshop; 7–10 October 2015; Tokyo, Japan. Berlin, Germany: Springer Verlag. pp. 3-17. doi: 10.1007/978-3-319-31960-5_1
[5] Kaur G, Kumar R, Kainth K. A review paper on different noise types and digital image processing. International Journal of Advanced Research in Computer Science and Software Engineering 2016; 6 (6): 562-565.
[6] Dong Y, Xu S. A new directional weighted median filter for removal of random-valued impulse noise. IEEE Signal Processing Letters 2007; 14(3): 193-196. doi: 10.1109/LSP.2006.884014
[7] Wang Z, Zhang D. Progressive switching median filter for the removal of impulse noise from highly corrupted images. IEEE Transaction on Circuits and System II: Analog and Digital Signal Processing 1999; 46 (1): 78-80. doi: 10.1109/82.749102
[8] Toh KKV, Isa NAM. Noise adaptive fuzzy switching median filter for salt-and-pepper noise reduction. IEEE Signal Processing Letters 2010; 17 (3): 281-284. doi: 10.1109/LSP.2009.2038769
[9] Esakkirajan S, Veerakumar T, Subramanyam AN, Prem Chand CH. Removal of high density salt and pepper noise through modified decision based unsymmetric trimmed median filter. IEEE Signal Processing Letters 2011; 18 (5): 287-290. doi: 10.1109/LSP.2011.2122333
[10] Vasanth K, Kumar VJS. Decision-based neighborhood-referred unsymmetrical trimmed variants filter for the removal of high-density salt-and-pepper noise in images and videos. Signal, Image, and Video Processing 2015; 9 (8): 1833-1841. doi: 10.1007/s11760-014-0665-0
[11] Erkan U, Gökrem L. A new method based on pixel density in salt and pepper noise removal. Turkish Journal of Electrical Engineering and Computer Sciences 2018; 26 (1): 162-171. doi: 10.3906/elk-1705-256
[12] Cuninghame-Green R. Lecture Notes in Economics and Mathematical Systems (Vol. 1). Berlin, Germany: SpringerVerlag, 1979.
[13] De Schutter B, Heemels WPMH, Bemporad A. Max-plus-algebraic problems and the extended linear complementarity problem—algorithmic aspects. IFAC Proceedings Volume 2002; 35 (1): 151-156. doi: 10.3182/20020721-6- ES-1901.00513
[14] Bertram A, Easton R. The tropical nullstellensatz for congruences. Advances in Mathematics 2017; 308 (2017): 36–82. doi: 10.1016/j.aim.2016.12.004
[15] Izhakian Z, Rowen L. Congruences and coordinate semirings of tropical varieties. Bulletin des Sciences Mathematiques 2016; 140 (3): 231–259. doi: 10.1016/j.bulsci.2015.12.001
[16] Schmitz K. Generic tropical varieties on subvarieties and in the non-constant coefficient case. Journal of Algebra 2015; 439 (2015): 294–315. doi: 10.1016/j.jalgebra.2015.05.002
[17] Adrovic D, Verschelde J. Tropical algebraic geometry in Maple: a preprocessing algorithm for finding common factors for multivariate polynomials with approximate coefficients. Journal of Symbolic Computation 2011; 46 (7): 755–772. doi: 10.1016/j.jsc.2010.08.011
[18] Grigoriev D, Shpilrain V. Tropical cryptography. Communications in Algebra 2014; 42 (6): 2624–2632. doi: 10.1080/00927872.2013.766827
[19] Anton H, Rorres C. Elementary Linear Algebra with Applications. 9th ed. Hoboken, NJ, USA: John Wiley & Sons, 2005.
[20] Yanai H, Takeuchi K, Takane Y. Projection Matrices, Generalized Inverse Matrices, and Singular Value Decomposition. New York, NY, USA: Springer-Verlag, 2011.
[21] Zhou W, Bovik AC, Sheikh HR, Simoncelli EP. Image quality assessment: from error visibility to structural similarity. IEEE Transactions on Image Processing 2004; 13 (4): 600-612. doi: 10.1109/TIP.2003.819861