Perona‐Malik equation ‐ error estimates for explicit finite volume scheme

Error estimates in the L2 norm for the explicit fully discrete numerical finite volume scheme are derived and proved for Perona‐Malik equation. Numerical example is also presented. First Published Online: 14 Oct 201

A flexible updating framework for preconditioners in PDE-based image restoration algorithms

Abstract We propose the solution of some discretized partial differential equation models for image denoising and deblurring by iterative linear system solvers accelerated by a simple but flexible framework for updating incomplete factorization preconditioners that presents a computational cost linear in the number of the image pixels. Here we performsome tests where the efficiency of the strategy is confirmed

An Efficient Implementation of a 3D CeVeFE DDFV Scheme on Cartesian Grids and an Application in Image Processing

International audienceIn this work we describe the implementation of a 3D Center-Vertex-Face/Edge Discrete Duality Finite Volume (CeVeFE DDFV) scheme using only the degrees of freedom (DOF) disposed on a Cartesian grid. These DOF are organised in a three-mesh structure proper to the CeVeFE DDFV setting. Reposing on a diamond structure, the approach presented here greatly simplifies the implementation, also in the case of grids topologically equivalent to the uniform Cartesian one. The numerical scheme is then applied to a problem in image processing, where uniform Cartesian structure of the DOF is naturally imposed by the pixel/voxel structure. A semi-implicit DDFV scheme is used for solving a nonlinear advection-diffusion equation, the subjective surfaces equation, in order to reconstruct the volume of a tumour from noisy 3D SPECT images with signal intensity on the tumour boundary. The matrix of the linear system has a band structure and the method is fast and able to successfully reconstruct the tumour volume