IJPAM: Volume 30, No. 1 (2006)


Seongjai Kim
Department of Mathematics and Statistics
Mississippi State University
Mississippi State, MS 39762, USA
e-mail: skim@math.msstate.edu

Abstract.This article studies the method of diffusion modulation, a reformulation of conventional partial differential equation (PDE)-based restoration models. The reformulated models consist of three explicit components: the diffusion operator, the modulator, and the constraint term. Strategies are suggested for their appropriate choices. In particular, the equalized net diffusion (END) and an edge-adaptive constraint term are introduced in order to successfully restore not only fine structures but also slow transitions. The new reformulated models are highly nonlinear; a linearized numerical procedure is suggested and the resulting algorithm is analyzed for stability. The reformulation has proved to outperform conventional PDE-based models in both quality and efficiency.

Received: June 2, 2006

AMS Subject Classification: 35K55, 65M06, 65M12

Key Words and Phrases: diffusion modulation, variational approach, equalized net diffusion, edge-adaptive constraint term, PDE-based image restoration

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2006
Volume: 30
Issue: 1