Total Variation Projection With First Order Schemes

This article proposes a new algorithm to compute the projection on the set of images whose total variation is bounded by a constant. The projection is computed through a dual formulation that is solved by first order non-smooth optimization methods. This yields an iterative algorithm that applies it...

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Veröffentlicht in:IEEE transactions on image processing Jg. 20; H. 3; S. 657 - 669
Hauptverfasser: Fadili, Jalal M, Peyré, Gabriel
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York, NY IEEE 01.03.2011
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:
Algorithms
Applied sciences
Computer Science
Convergence
Convex functions
Detection, estimation, filtering, equalization, prediction
Duality
Engineering Sciences
Exact sciences and technology
forward-backward splitting
Image processing
Image Processing, Computer-Assisted - methods
Information, signal and communications theory
Inverse problems
Mathematical models
Miscellaneous
Models, Theoretical
Nesterov scheme
Noise reduction
Optimization
Pattern recognition
Phantoms, Imaging
Projection
Projection algorithms
proximal operator
Signal and communications theory
Signal and Image Processing
Signal processing
Signal, noise
Studies
Surface layer
Synthesis
Telecommunications and information theory
Television
Texture
Tomography
total variation
State of the art
Threshold detection
Noise reduction
forward-backward splitting
Iterative method
Duality
Algorithm
Optimization
Inverse problem
Projection method
Deconvolution
Television
First order
proximal operator
inverse problems
Convergence rate
Tomography
Signal processing
Numerical simulation
projection
total variation
Nesterov scheme
Vector field
Pattern synthesis
Total variation
duality
ISSN:1057-7149, 1941-0042, 1941-0042
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Beschreibung
Zusammenfassung:This article proposes a new algorithm to compute the projection on the set of images whose total variation is bounded by a constant. The projection is computed through a dual formulation that is solved by first order non-smooth optimization methods. This yields an iterative algorithm that applies iterative soft thresholding to the dual vector field, and for which we establish convergence rate on the primal iterates. This projection algorithm can then be used as a building block in a variety of applications such as solving inverse problems under a total variation constraint, or for texture synthesis. Numerical results are reported to illustrate the usefulness and potential applicability of our TV projection algorithm on various examples including denoising, texture synthesis, inpainting, deconvolution and tomography problems. We also show that our projection algorithm competes favorably with state-of-the-art TV projection methods in terms of convergence speed.
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ISSN:1057-7149
1941-0042
1941-0042
DOI:10.1109/TIP.2010.2072512