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A Time Dependent Model for Image Denoising
Department of Mathematics Aligarh Muslim University, Aligarh, India
Department of Mathematics Aligarh Muslim University, Aligarh, India
- 1 Department of Mathematics Aligarh Muslim University, Aligarh, India
- 2 Department of Mathematics Aligarh Muslim University, Aligarh, India
Journal of Signal and Information Processing·Volume 06 (2015)·Pages 28–38·Published 21 January 2015·DOI10.4236/jsip.2015.61003
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Abstract
In this paper, we propose a new time dependent model for solving total variation (TV) minimization problem in image denoising. The main idea is to apply a priori smoothness on the solution image. This is a constrained optimization type of numerical algorithm for removing noise from images. The constraints are imposed using Lagrange’s multipliers and the solution is obtained using the gradient projection method. 1D and 2D numerical experimental results by explicit numerical schemes are discussed.
KeywordsTotal VariationImage DenoisingSignal Denoising
- Osher, S. and Rudin, L.I. (1990) Feature Oriented Image Enhancement Using Shock Filters. SIAM Journal on Numerical Analysis, 27, 919-940. http://dx.doi.org/10.1137/0727053
- Rudin, L., Osher, S. and Fatemi, E. (1992) Nonlinear Total Variation Based Noise Removal Algorithm. Physica D, 60, 259-268. http://dx.doi.org/10.1016/0167-2789(92)90242-F
- Rudin, L. and Osher, S. (1994) Total Variation Based Image Restoration with Free Local Constraints. IEEE International Conference on Image Processing, 1, 31-35.
- Chambolle, A. and Lions, P.L. (1997) Image Recovery via Total Variation Minimization and Related Problems. Numerische Mathematik, 76, 167-188. http://dx.doi.org/10.1007/s002110050258
- Hunt, B.R. (1973) The Application of Constrained Least Squares Estimation to Image Restoration by Digital Computer. IEEE Transactions on Computers, 22, 805-812. http://dx.doi.org/10.1109/TC.1973.5009169
- Strang, G. (1964) Accurate Partial Difference Methods II. Non Linear Problems. Numerische Mathematik, 6, 37-46. http://dx.doi.org/10.1007/BF01386051
- Strang, G. (1968) On the Construction and Comparison of Difference Schemes. SIAM Journal on Numerical Analysis, 5, 506-517. http://dx.doi.org/10.1137/0705041
- Phillips, D.L. (1962) A Technique for the Numerical Solution of Certain Integral Equations of the First Kind. Journal of the Association for Computing Machinery (ACM), 9, 84-97. http://dx.doi.org/10.1145/321105.321114
- Twomey, S. (1963) On the Numerical Solution of Fredholm Integral Equations of the First Kind by the Inversion of the Linear System Produced by Quadrature. Journal of the Association for Computing Machinery (ACM), 10, 97-101. http://dx.doi.org/10.1145/321150.321157
- Twomey, S. (1965) The Application of Numerical Filtering to the Solution of Integral Equations Encountered in Indirect Sensing Measurements. Journal of The Franklin Institute, 279, 95-109. http://dx.doi.org/10.1016/0016-0032(65)90209-7
- Chang, Q. and Chern, I.-L. (2003) Acceleration Methods for Total Variation-Based Image Denoising. SIAM Journal on Scientific Computing, 25, 982-994. http://dx.doi.org/10.1137/S106482750241534X
- Witkin, A.P. (1983) Scale-Space Filtering. International Joint Conference on Artificial Intelligence, 2, 1019-1021.
- Marquina, A. (2006) Inverse Scale Space Methods for Blind Deconvolution. UCLA CAM Report, 06-36.