Abstract
Image denoising processes often lead to significant loss of fine structures such as edges and textures. This paper studies various innovative mathematical and numerical methods applicable for conventional PDE-based denoising models. The method of diffusion modulation is considered to effectively minimize regions of undesired excessive dissipation. Then we introduce a novel numerical technique for residual-driven constraint parameterization, in order for the resulting algorithm to produce clear images whose corresponding residual is as free of image textures as possible. A linearized Crank-Nicolson alternating direction implicit time-stepping procedure is adopted to simulate the resulting model efficiently. Various examples are presented to show efficiency and reliability of the suggested methods in image denoising.
Highlights
During the last two decades, as the field of image processing requires higher reliability and efficiency, mathematical techniques have become important components of image processing
This paper studies various innovative mathematical and numerical methods applicable for conventional PDE-based denoising models
This paper suggests the method of diffusion modulation and a residual-driven constraint RDC parameterization to obtain clearer images, reduce excessive dissipation effectively, and minimize texture components in the residual
Summary
During the last two decades, as the field of image processing requires higher reliability and efficiency, mathematical techniques have become important components of image processing. Various mathematical frameworks employing powerful tools of partial differential equations PDEs and functional analysis have emerged and successfully applied to various image processing tasks, for image denoising and restoration 1–9 , see 10, 11 Those PDE-based denoising techniques have allowed researchers and practitioners to introduce effective new models and to improve traditional algorithms. In order to reduce the artifact, researchers have studied various mathematical and numerical techniques which either incorporate more effective constraint terms and iterative refinement 5, 12–14 or minimize a functional of second derivatives of the image 15–18 These new mathematical models may preserve fine structures better than conventional ones; more advanced models and appropriate numerical procedures are yet to be developed
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