A Nonlinear Parabolic Model in Processing of Medical Image

Issue		Math. Model. Nat. Phenom. Volume 3, Number 6, 2008 Medical imaging


Page(s)		131 - 145
DOI		10.1051/mmnp:2008084
Published online		24 December 2008

Math. Model. Nat. Phenom. Vol. 3, No. 6, 2008, pp. 131-145
DOI: 10.1051/mmnp:2008084

A Nonlinear Parabolic Model in Processing of Medical Image

R. Aboulaich¹, S. Boujena² and E. El Guarmah¹

¹ ERMA, Mohammadia Engineering School, Mohamed V University, Ibn Sina Str., POB 765 Agdal, Rabat, Morocco
² Mathematics and computing Department, Ain Chock Sciences Faculty, Km8 Route El Jadida, BOP 5366 Maârif, Casablanca

boujena@yahoo.fr
s.boujena@fsac.ac.ma

Published online: 24 December 2008

Abstract
The image's restoration is an essential step in medical imaging. Several Filters are developped to remove noise, the most interesting are filters who permits to denoise the image preserving semantically important structures. One class of recent adaptive denoising methods is the nonlinear Partial Differential Equations who knows currently a significant success. This work deals with mathematical study for a proposed nonlinear evolution partial differential equation for image processing. The existence and the uniqueness of the solution are established. Using a finite differences method we experiment the validity of the proposed model and we illustrate the efficiently of the method using some medical images. The Signal to Noise Ration (SNR) number is used to estimate the quality of the restored images.

Mathematics Subject Classification. 68U10, 94A08

Key words: nonlinear parabolic model -- image processing -- Hilbert space

© EDP Sciences 2008

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