Student or educator? Sign up with your school email and get 6 months of Pro free.
CoChat
Sign Up
Cited by 2,678

The DOI matches its Crossref record.

Signal Recovery by Proximal Forward-Backward Splitting

Combettes, Patrick L., Wajs, Valérie R.·2005·Multiscale Modeling & Simulation
DOI 10.1137/050626090
Open this paper in CoChat — free account

Abstract

We show that various inverse problems in signal recovery can be formulated as the generic problem of minimizing the sum of two convex functions with certain regularity properties. This formulation makes it possible to derive existence, uniqueness, characterization, and stability results in a unified and standardized fashion for a large class of apparently disparate problems. Recent results on monotone operator splitting methods are applied to establish the convergence of a forward-backward algorithm to solve the generic problem. In turn, we recover, extend, and provide a simplified analysis for a variety of existing iterative methods. Applications to geometry/texture image decomposition schemes are also discussed. A novelty of our framework is to use extensively the notion of a proximity operator, which was introduced by Moreau in the 1960s.

Overview

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Integrity signals

Registry

Crossref · 10.1137/050626090

Cites

Statistics

Verification

Claims the paper makes

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

The self-check needs the paper’s full text.

Citations

Cites

No references could be resolved yet.

Research works printed but not linked: 75

  1. 10.5802/afst.541 · DOI
  2. 10.1137/S003614299529230X · DOI · Paper page
  3. Aubin Jean‐Pierre, 1990, Set‐valued analysis
  4. 10.1007/s10851-005-4783-8 · DOI
  5. 10.1007/s11263-005-4948-3 · DOI · Paper page
  6. 10.1007/BF03007664 · DOI
  7. 10.1016/j.na.2004.07.054 · DOI
  8. J. Bect, L. Blanc‐Féraud, G. Aubert, and A. Chambolle, A 𝓁1‐unified variational framework for image restoration , in Proceedings of the Eighth European Conference on Computer Vision (Prague, 2004), Lecture Notes in Comput. Sci. 3024, T. Pajdla and J. Matas, eds., Springer‐Verlag, New York, 2004, pp. 1–13. · DOI
  9. 10.4153/CMB-1992-003-0 · DOI
  10. Butnariu Dan, 2003, J. Convex Anal., 10, 35
  11. 10.1088/0266-5611/18/2/310 · DOI
  12. 10.1109/TASSP.1986.1164990 · DOI
  13. 10.1007/BF02142692 · DOI
  14. Censor Yair, 1997, Parallel optimization
  15. 10.1023/B:JMIV.0000011325.36760.1e · DOI · Paper page
  16. 10.1109/83.661182 · DOI · Paper page
  17. 10.1007/s002110050258 · DOI · Paper page
  18. Cohen Albert, 2003, Numerical analysis of wavelet methods
  19. 10.1109/5.214546 · DOI
  20. 10.1109/78.330356 · DOI
  21. P. L. Combettes, The convex feasibility problem in image recovery , in Advances in Imaging and Electron Physics, Vol. 95, P. Hawkes, ed., Academic Press, New York, 1996, pp. 155–270. · DOI · Paper page
  22. P. L. Combettes, Convexité et signal , in Actes du Congrès de Mathématiques Appliquées et Industrielles SMAI'01, Pompadour, France, 2001, pp. 6–16.
  23. 10.1080/02331930412331327157 · DOI · Paper page
  24. 10.1109/78.782189 · DOI
  25. Combettes Patrick, 2005, J. Nonlinear Convex Anal., 6, 117
  26. 10.1109/34.735804 · DOI
  27. 10.1142/S0219691304000688 · DOI
  28. 10.1002/cpa.20042 · DOI · Paper page
  29. Christine De Mol, Michel Defrise, A note on wavelet‐based inversion algorithms, Contemp. Math., Vol. 313, Amer. Math. Soc., Providence, RI, 2002, 85–962003m:65090 · DOI
  30. 10.1088/0266-5611/12/5/005 · DOI
  31. 10.1093/biomet/81.3.425 · DOI · Paper page
  32. 10.1111/j.2517-6161.1995.tb02032.x · DOI · Paper page
  33. 10.1080/01630569208816489 · DOI
  34. 10.1109/TIP.2003.814255 · DOI · Paper page
  35. 10.1080/713818946 · DOI · Paper page
  36. 10.1109/TCS.1985.1085777 · DOI
  37. Herman Gabor, 1980, Image reconstruction from projections
  38. 10.1137/S0363012997324338 · DOI
  39. 10.1016/j.na.2003.11.004 · DOI
  40. 10.1016/0025-5564(70)90148-3 · DOI
  41. 10.1109/TC.1973.5009169 · DOI · Paper page
  42. 10.1007/978-94-010-9608-9 · DOI
  43. 10.1016/S0096-3003(02)00171-6 · DOI
  44. 10.1080/09500348714550241 · DOI
  45. 10.1016/0041-5553(66)90114-5 · DOI · Paper page
  46. 10.1109/TASSP.1983.1164246 · DOI
  47. Mallat Stéphane, 1998, A wavelet tour of signal processing
  48. 10.1109/23.873021 · DOI
  49. 10.1090/ulect/022 · DOI · Paper page
  50. Moreau Jean‐Jacques, 1962, C. R. Acad. Sci. Paris, 255, 238
  51. Moreau Jean‐Jacques, 1962, C. R. Acad. Sci. Paris, 255, 2897
  52. Moreau Jean‐Jacques, 1963, C. R. Acad. Sci. Paris, 256, 1069
  53. 10.24033/bsmf.1625 · DOI · Paper page
  54. 10.1137/S105262349629856X · DOI
  55. 10.1137/S1540345902413322 · DOI
  56. Papoulis Athanasios, 1962, The Fourier integral and its applications
  57. 10.1109/TCS.1975.1084118 · DOI · Paper page
  58. 10.1109/78.489050 · DOI
  59. 10.1137/0314056 · DOI · Paper page
  60. 10.1016/0167-2789(92)90242-F · DOI · Paper page
  61. 10.1109/78.709518 · DOI
  62. 10.1051/0004-6361:20021571 · DOI · Paper page
  63. 10.1016/S0165-1684(03)00150-6 · DOI
  64. Stark Henry, 1987, Image recovery: theory and application
  65. H. Stark and Y. Yang, Vector Space Projections: A Numerical Approach to Signal and Image Processing, Neural Nets, and Optics , Wiley, New York, 1998.
  66. 10.1088/0266-5611/9/6/011 · DOI
  67. Titterington D., 1985, Astronom. and Astrophys., 144, 381
  68. 10.1016/0016-0032(65)90209-7 · DOI · Paper page
  69. 10.1023/A:1025384832106 · DOI · Paper page
  70. 10.1023/B:JMIV.0000011316.54027.6a · DOI
  71. 10.1109/TCS.1978.1084541 · DOI · Paper page
  72. 10.1109/TMI.1982.4307555 · DOI · Paper page
  73. 10.1016/0022-247X(83)90180-4 · DOI
  74. 10.1142/5021 · DOI · Paper page
  75. 10.1007/978-1-4612-4838-5 · DOI

Cited by

Metadata

Authors
Combettes, P. L., & Wajs, V. R.
Venue
Multiscale Modeling & Simulation
Publisher
Society for Industrial & Applied Mathematics (SIAM)
Published
2005-01
Volume
4
Issue
4
Pages
1168-1200
ISSN
  • 1540-3459 (ISSN-L)
  • 1540-3467
DOI
10.1137/050626090
OpenAlex
W2006262045
Cited by
2,678
References
0
FWCI
24.47
Type
journal article
Language
en
Open access
closed

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review

Data sources

Bibliographic data: Semantic Scholar, OpenAlex, Crossref.

Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).

Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.