1,157 research outputs found
On block diagonal and block triangular iterative schemes and preconditioners for stabilized saddle point problems
We review the use of block diagonal and block lower/upper triangular splittings for constructing iterative methods and preconditioners for solving stabilized saddle point problems. We introduce new variants of these splittings and obtain new results on the convergence of the associated stationary iterations and new bounds on the eigenvalues of the corresponding preconditioned matrices. We further consider inexact versions as preconditioners for flexible Krylov subspace methods, and show experimentally that our techniques can be highly effective for solving linear systems of saddle point type arising from stabilized finite element discretizations of two model problems, one from incompressible fluid mechanics and the other from magnetostatics
BM3D Frames and Variational Image Deblurring
A family of the Block Matching 3-D (BM3D) algorithms for various imaging
problems has been recently proposed within the framework of nonlocal patch-wise
image modeling [1], [2]. In this paper we construct analysis and synthesis
frames, formalizing the BM3D image modeling and use these frames to develop
novel iterative deblurring algorithms. We consider two different formulations
of the deblurring problem: one given by minimization of the single objective
function and another based on the Nash equilibrium balance of two objective
functions. The latter results in an algorithm where the denoising and
deblurring operations are decoupled. The convergence of the developed
algorithms is proved. Simulation experiments show that the decoupled algorithm
derived from the Nash equilibrium formulation demonstrates the best numerical
and visual results and shows superiority with respect to the state of the art
in the field, confirming a valuable potential of BM3D-frames as an advanced
image modeling tool.Comment: Submitted to IEEE Transactions on Image Processing on May 18, 2011.
implementation of the proposed algorithm is available as part of the BM3D
package at http://www.cs.tut.fi/~foi/GCF-BM3
- …