The Shannon Total Variation

Discretization schemes commonly used for total variation regularization lead to images that are difficult to interpolate, which is a real issue for applications requiring subpixel accuracy and aliasing control. In the present work, we reconciliate total variation with Shannon interpolation and study...

Full description

Saved in:
Bibliographic Details
Published in:Journal of mathematical imaging and vision 2017-10, Vol.59 (2), p.341-370
Main Authors: Abergel, Rémy, Moisan, Lionel
Format: Article
Language:English
Subjects:
Aliasing
Applications of Mathematics
Computer Science
Engineering Sciences
Formulations
Image Processing
Image Processing and Computer Vision
Isotropy
Mathematical Methods in Physics
Mathematics
Numerical Analysis
Pixels
Regularization
Signal and Image processing
Signal,Image and Speech Processing
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Discretization schemes commonly used for total variation regularization lead to images that are difficult to interpolate, which is a real issue for applications requiring subpixel accuracy and aliasing control. In the present work, we reconciliate total variation with Shannon interpolation and study a Fourier-based estimate that behaves much better in terms of grid invariance, isotropy, artifact removal and subpixel accuracy. We show that this new variant (called Shannon total variation) can be easily handled with classical primal–dual formulations and illustrate its efficiency on several image processing tasks, including deblurring, spectrum extrapolation and a new aliasing reduction algorithm.
ISSN:0924-9907
1573-7683
DOI:10.1007/s10851-017-0733-5