Journal article
Higher Degree Total Variation (HDTV) Regularization for Image Recovery
IEEE transactions on image processing, Vol.21(5), pp.2559-2571
2012
DOI: 10.1109/TIP.2012.2183143
PMID: 22249711
Abstract
We introduce novel image regularization penalties to overcome the practical problems associated with the classical total variation (TV) scheme. Motivated by novel reinterpretations of the classical TV regularizer, we derive two families of functionals involving higher degree partial image derivatives; we term these families as isotropic and anisotropic higher degree TV (HDTV) penalties, respectively. The isotropic penalty is the mixed norm of the directional image derivatives, while the anisotropic penalty is the separable norm of directional derivatives. These functionals inherit the desirable properties of standard TV schemes such as invariance to rotations and translations, preservation of discontinuities, and convexity. The use of mixed norms in isotropic penalties encourages the joint sparsity of the directional derivatives at each pixel, thus encouraging isotropic smoothing. In contrast, the fully separable norm in the anisotropic penalty ensures the preservation of discontinuities, while continuing to smooth along the line like features; this scheme thus enhances the linenlike image characteristics analogous to standard TV. We also introduce efficient majorize-minimize algorithms to solve the resulting optimization problems. The numerical comparison of the proposed scheme with classical TV penalty, current second-degree methods, and wavelet algorithms clearly demonstrate the performance improvement. Specifically, the proposed algorithms minimize the staircase and ringing artifacts that are common with TV and wavelet schemes, while better preserving the singularities. We also observe that anisotropic HDTV penalty provides consistently improved reconstructions compared with the isotropic HDTV penalty.
Details
- Title: Subtitle
- Higher Degree Total Variation (HDTV) Regularization for Image Recovery
- Creators
- Yue Hu - Department of Electrical and Computer Engineering, University of Rochester, Rochester, NY 14627, United StatesMathews JACOB - Department of Electrical and Computer Engineering, University of Iowa, Iowa City, IA 52242, United States
- Resource Type
- Journal article
- Publication Details
- IEEE transactions on image processing, Vol.21(5), pp.2559-2571
- Publisher
- Institute of Electrical and Electronics Engineers; New York, NY
- DOI
- 10.1109/TIP.2012.2183143
- PMID
- 22249711
- ISSN
- 1057-7149
- eISSN
- 1941-0042
- Language
- English
- Date published
- 2012
- Academic Unit
- Roy J. Carver Department of Biomedical Engineering; Radiology; Electrical and Computer Engineering; Iowa Neuroscience Institute; Radiation Oncology
- Record Identifier
- 9984070639802771
Metrics
15 Record Views