Image restoration subject to a total variation constraint

• Published in: IEEE transactions on image processing Vol. 13; no. 9; pp. 1213 - 1222
• Main Authors: Combettes, P.L., Pesquet, J.-C.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.09.2004; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Additive noise; Algorithms; Applied sciences; Artificial intelligence; Blocking; Computer Graphics; Computer science; control theory; systems; Computer Simulation; Constraint optimization; Deconvolution; Degradation; Exact sciences and technology; Formulations; Hilbert space; Image denoising; Image Enhancement - methods; Image Interpretation, Computer-Assisted - methods; Image processing; Image restoration; Information filtering; Information Storage and Retrieval - methods; Information, signal and communications theory; Joints; Lagrangian functions; Mathematics; Models, Statistical; Numerical Analysis; Numerical Analysis, Computer-Assisted; Optimization; Pattern Recognition, Automated; Pattern recognition. Digital image processing. Computational geometry; Programming; Reproducibility of Results; Restoration; Sensitivity and Specificity; Signal processing; Signal Processing, Computer-Assisted; Subtraction Technique; Telecommunications and information theory; Deconvolution; Simulation; Image processing; Noise reduction; Image restoration; Convex programming; Optimization
• ISSN: 1057-7149; 1941-0042
• DOI: 10.1109/TIP.2004.832922

Total variation has proven to be a valuable concept in connection with the recovery of images featuring piecewise smooth components. So far, however, it has been used exclusively as an objective to be minimized under constraints. In this paper, we propose an alternative formulation in which total variation is used as a constraint in a general convex programming framework. This approach places no limitation on the incorporation of additional constraints in the restoration process and the resulting optimization problem can be solved efficiently via block-iterative methods. Image denoising and deconvolution applications are demonstrated.