Application of splitting scheme and multigrid method for TV-Stokes denoising

A TV-Stokes Denoising Algorithm

In this paper, we propose a two-step algorithm for denoising digital images with additive noise. Observing that the isophote directions of an image correspond to an incompressible velocity field, we impose the constraint of zero divergence on the tangential field. Combined with an energy minimization problem corresponding to the smoothing of tangential vectors, this constraint gives rise to a n...

Multigrid for Stokes Equations

We discuss a basic iterative method by solving u and p alternatively. Starting from some initial guess u, p, one iteration going from (u, p) to (u, p) is (1) Fix p, solve for u; (2) Fix u, solve for p. When p is fixed, there are two equations for u. We can first solve the momentum equation to get u (the term B p is moved to the right hand side), i.e., Au = f −B p. But unless p is the exact solu...

A Multigrid Method for the Pseudostress Formulation of Stokes Problems

The purpose of this paper is to develop and analyze a multigrid solver for the finite element discretization of the pseudostress system associated with the differential operator A − γ graddiv over 2 × 2 matrix-valued functions. This system is derived from the pseudostressvelocity formulation [11] of two-dimensional Stokes problems through the penalty method or natural time discretization for th...

A Multigrid Method for Total Variation-based Image Denoising

A Nonconforming Multigrid Method for the Stationary Stokes Equations

An optimal-order W-cycle multigrid method for solving the stationary Stokes equations is developed, using PI nonconforming divergence-free finite elements.