(untitled) (Communications in Computational Physics, 2006)
In this work, noise removal in digital images is investigated. The importance of this problem lies in the fact that removal of noise is a necessary pre-processing step for other image processing tasks such as edge detection, image segmentation, image compression, classification problems, image registration etc. A number of different approaches have been proposed in the literature. In this work, a non-linear PDE-based algorithm is developed based on the ideas proposed by Lysaker, Osher and Tai [IEEE Trans. Image Process., 13 (2004), 1345-1357] . This algorithm consists of two steps: flow field smoothing of the normal vectors, followed by image reconstruction. We propose a finite-difference based additive operator-splitting method that allows for much larger time-steps. This results in an efficient method for noise-removal that is shown to have good visual results. The energy is studied as an objective measure of the algorithm performance.