Title :
Box Relaxation Schemes in Staggered Discretizations for the Dual Formulation of Total Variation Minimization
Author :
Garamendi, J.F. ; Gaspar, F.J. ; Malpica, Norberto ; Schiavi, E.
Author_Institution :
INRIA, Univ. of Rennes I, Rennes, France
Abstract :
In this paper, we propose some new box relaxation numerical schemes on staggered grids to solve the stationary system of partial differential equations arising from the dual minimization problem associated with the total variation operator. We present in detail the numerical schemes for the scalar case and its generalization to multichannel (vectorial) images. Then, we discuss their implementation in digital image denoising. The results outperform the resolution of the dual equation based on the gradient descent approach and pave the way for more advanced numerical strategies.
Keywords :
image denoising; partial differential equations; box relaxation numerical scheme; digital image denoising; dual equation; dual formulation; dual minimization problem; gradient descent; multichannel image; partial differential equations; staggered discretization; staggered grids; stationary system; total variation minimization; total variation operator; Equations; Image resolution; Mathematical model; Noise reduction; Partial differential equations; TV; Dual formulation; image procing; partial differential equations (PDEs); staggered discretization; total variation (TV); variational methods;
Journal_Title :
Image Processing, IEEE Transactions on
DOI :
10.1109/TIP.2013.2244220
