Explicit nonflat time evolution for PDE-Based image restoration

Authors:
Seongjai Kim;Song-Hwa Kwon
Affiliations:
Department of Mathematics & Statistics, Mississippi State University, Mississippi State, MS;IMA, University of Minnesota, Minneapolis, MN
Venue:
ICVGIP'06 Proceedings of the 5th Indian conference on Computer Vision, Graphics and Image Processing
Year:
2006

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Abstract

This article is concerned with new strategies with which explicit time-stepping procedures of PDE-based restoration models converge with a similar efficiency to implicit algorithms. Conventional explicit algorithms often require hundreds of iterations to converge. In order to overcome the difficulty and to further improve image quality, the article introduces new spatially variable constraint term and timestep size, as a method of nonflat time evolution (MONTE). It has been verified that the explicit time-stepping scheme incorporating MONTE converges in only 4-15 iterations for all restoration examples we have tested. It has proved more effective than the additive operator splitting (AOS) method in both computation time and image quality (measured in PSNR), for most cases. Since the explicit MONTE procedure is efficient in computer memory, requiring only twice the image size, it can be applied particularly for huge data sets with a great efficiency in computer memory as well.