arXiv subjects

R I McLachlan

Publications and source records attributed to R I McLachlan.

2 recordsLinked to original sources

arXiv2016

The use of discrete gradient methods for total variation type regularization problems in image processing

Discrete gradient methods are well-known methods of Geometric Numerical Integration, which preserve the dissipation of gradient systems. The preservation of the dissipation of a system is an important feature in numerous image processing tasks. We promote the use of discrete gradient methods in image processing by exhibiting experiments with nonlinear total variation (TV) deblurring, denoising, and inpainting.

math.NA↗

arXiv2014

The multisymplectic diamond scheme

We introduce a class of general purpose linear multisymplectic integrators for Hamiltonian wave equations based on a diamond-shaped mesh. On each diamond, the PDE is discretized by a symplectic Runge--Kutta method. The scheme advances in time by filling in each diamond locally, leading to greater efficiency and parallelization and easier treatment of boundary conditions compared to methods based on rectangular meshes.

math.NA↗