Image restoration subject to a total variation constraint
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 va...
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| Published in | IEEE transactions on image processing Vol. 13; no. 9; pp. 1213 - 1222 |
|---|---|
| Main Authors | , |
| 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 | |
| Online Access | Get full text |
| ISSN | 1057-7149 1941-0042 |
| DOI | 10.1109/TIP.2004.832922 |
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| Abstract | 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. |
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| AbstractList | 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. 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.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. |
| Author | Combettes, P.L. Pesquet, J.-C. |
| Author_xml | – sequence: 1 givenname: P.L. surname: Combettes fullname: Combettes, P.L. organization: Lab. Jacques-Louis Lions, Univ. Pierre et Marie Curie Paris, France – sequence: 2 givenname: J.-C. surname: Pesquet fullname: Pesquet, J.-C. |
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| Cites_doi | 10.1109/83.661189 10.1109/TIP.2002.804527 10.1109/29.45551 10.1007/978-1-4684-9486-0 10.1109/TC.1973.5009169 10.1109/78.134400 10.1137/S036301299732626X 10.1007/s002110050258 10.1007/978-1-4612-1015-3 10.1137/S0036144593251710 10.1109/TIP.2002.806241 10.1051/m2an:2000104 10.1109/83.563316 10.1109/TMI.1982.4307555 10.1023/B:JMIV.0000011321.19549.88 10.1016/S1076-5670(08)70157-5 10.1016/0167-2789(92)90242-F 10.1109/TMI.2002.806423 10.1109/83.941862 10.1137/S1064827598344169 10.1016/S0096-3003(02)00171-6 10.1137/0727053 10.1109/TASSP.1984.1164297 10.1515/9781400873173 10.1109/MSP.2002.1028350 10.1007/0-387-21810-6_6 10.1109/83.679423 10.1137/S0036139997327794 10.1137/S0363012997324338 10.1109/TSP.2003.812846 10.1109/ICIP.1994.413269 10.1137/S0036141000371150 |
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| Keywords | Deconvolution Simulation Image processing Noise reduction Image restoration Convex programming Optimization |
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| References_xml | – year: 1998 ident: ref39 publication-title: Anisotropic Diffusion in Image Processing – ident: ref34 doi: 10.1109/83.661189 – ident: ref14 doi: 10.1109/TIP.2002.804527 – ident: ref16 doi: 10.1109/29.45551 – year: 0 ident: ref37 publication-title: http //images ee umist ac uk/danny/database html (UMIST Face Database) see also D B Graham and N M Allinson “ Characterizing virtual eigensignatures for general purpose face recognition” in Face Recognition From Theory to Applications NATO ASI Series F Computer and Systems Sciences vol 163 H Wechsler J P Phillips V Bruce F Fogelman-Soulié and T S Huang (Eds ) pp 446– 456 1998 – ident: ref18 doi: 10.1007/978-1-4684-9486-0 – ident: ref21 doi: 10.1109/TC.1973.5009169 – year: 1987 ident: ref33 publication-title: Image Recovery Theory and Application – ident: ref15 doi: 10.1109/78.134400 – ident: ref11 doi: 10.1137/S036301299732626X – year: 1977 ident: ref2 publication-title: Digital Image Restoration – year: 1999 ident: ref17 publication-title: Analyse Convexe et Problè mes Variationnels Paris Dunod 1974 Convex Analysis and Variational Problems – ident: ref7 doi: 10.1007/s002110050258 – year: 1989 ident: ref41 publication-title: Weakly Differentiable Functions doi: 10.1007/978-1-4612-1015-3 – ident: ref4 doi: 10.1137/S0036144593251710 – ident: ref23 doi: 10.1109/TIP.2002.806241 – ident: ref28 doi: 10.1051/m2an:2000104 – ident: ref10 doi: 10.1109/83.563316 – ident: ref40 doi: 10.1109/TMI.1982.4307555 – volume: 1 start-page: 265 year: 1984 ident: ref35 article-title: a priori knowledge in algebraic reconstruction methods publication-title: Advances in Computer Vision and Image Processing – year: 1972 ident: ref3 publication-title: Real Analysis and Probability – ident: ref6 doi: 10.1023/B:JMIV.0000011321.19549.88 – ident: ref9 doi: 10.1016/S1076-5670(08)70157-5 – ident: ref32 doi: 10.1016/0167-2789(92)90242-F – ident: ref5 doi: 10.1109/TMI.2002.806423 – ident: ref1 doi: 10.1109/83.941862 – ident: ref8 doi: 10.1137/S1064827598344169 – ident: ref22 doi: 10.1016/S0096-3003(02)00171-6 – ident: ref26 doi: 10.1137/0727053 – ident: ref36 doi: 10.1109/TASSP.1984.1164297 – year: 1970 ident: ref29 publication-title: Convex Analysis doi: 10.1515/9781400873173 – ident: ref27 doi: 10.1109/MSP.2002.1028350 – ident: ref30 doi: 10.1007/0-387-21810-6_6 – year: 2001 ident: ref24 publication-title: Oscillating Patterns in Image Processing and Nonlinear Evolution Equations— The Fifteenth Dean Jacqueline B Lewis Memorial Lectures – volume: 7 start-page: 813 year: 1998 ident: ref38 article-title: fast, robust total variation-based reconstruction of noisy, blurred images publication-title: IEEE Trans Image Processing doi: 10.1109/83.679423 – ident: ref25 doi: 10.1137/S0036139997327794 – ident: ref20 doi: 10.1137/S0363012997324338 – ident: ref13 doi: 10.1109/TSP.2003.812846 – start-page: 6 year: 2001 ident: ref12 article-title: convexité et signal publication-title: Proc Congrè s de Mathé matiques Appliqué es et Industrielles – ident: ref31 doi: 10.1109/ICIP.1994.413269 – ident: ref19 doi: 10.1137/S0036141000371150 |
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| SubjectTerms | 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 |
| Title | Image restoration subject to a total variation constraint |
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