Journal
IEEE TRANSACTIONS ON IMAGE PROCESSING
Volume 15, Issue 5, Pages 1163-1170Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIP.2005.864184
Keywords
Crank-Nicolson (CN) alternating direction implicit (ADI) method; essentially nondissipative (ENoD) difference method; motion by mean curvature (MMC); total variation minimization (TVM)
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The paper is concerned with PDE-based image restoration. A new model is introduced by hybridizing a non-convex variant of the total variation minimization (TVM) and the motion by mean curvature (MMC) in order to deal with the mixture of the impulse and Gaussian noises reliably. We suggest the essentially nondissipative (ENoD) difference schemes for the MMC component to eliminate the impulse noise with a minimum (ideally no) introduction of dissipation. The MMC-TVM hybrid model and the ENoD schemes are applied for both gray-scale and color images. For color image denoising, we consider the chromaticity-brightness decomposition with the chromaticity formulated in the angle domain. An incomplete Crank-Nicolson alternating direction implicit time-stepping procedure is adopted to solve those differential equations efficiently. Numerical experiments have shown that the new hybrid model and the numerical schemes can remove the mixture of the impulse and Gaussian noises, efficiently and reliably, preserving edges quite satisfactorily.
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