6533b85afe1ef96bd12b94b6
RESEARCH PRODUCT
Explicit Algorithms for a New Time Dependent Model Based on Level Set Motion for Nonlinear Deblurring and Noise Removal
Antonio MarquinaStanley Oshersubject
Level set (data structures)DeblurringOptimization problemApplied MathematicsConstrained optimizationWhite noiseComputational MathematicsRunge–Kutta methodssymbols.namesakeGaussian noisesymbolsAlgorithmImage restorationMathematicsdescription
In this paper we formulate a time dependent model to approximate the solution to the nonlinear total variation optimization problem for deblurring and noise removal introduced by Rudin and Osher [ Total variation based image restoration with free local constraints, in Proceedings IEEE Internat. Conf. Imag. Proc., IEEE Press, Piscataway, NJ, (1994), pp. 31--35] and Rudin, Osher, and Fatemi [ Phys. D, 60 (1992), pp. 259--268], respectively. Our model is based on level set motion whose steady state is quickly reached by means of an explicit procedure based on Roe's scheme [ J. Comput. Phys., 43 (1981), pp. 357--372], used in fluid dynamics. We show numerical evidence of the speed of resolution and stability of this simple explicit procedure in some representative 1D and 2D numerical examples.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2000-01-01 | SIAM Journal on Scientific Computing |