Optimal denoising in redundant bases

Martin Raphan, Eero Simoncelli

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Image denoising methods are often based on estimators chosen to minimize mean squared error (MSE) within the subbands of a multi-scale decomposition. But this does not guarantee optimal MSE performance in the image domain, unless the decomposition is orthonormal. We prove that despite this suboptimality, the expected image-domain MSE resulting from a representation that is made redundant through spatial replication of basis functions (e.g., cycle-spinning) is less than or equal to that resulting from the original non-redundant representation. We also develop an extension of Stein's unbiased risk estimator (SURE) that allows minimization of the image-domain MSE for estimators that operate on subbands of a redundant decomposition. We implement an example, jointly optimizing the parameters of scalar estimators applied to each subband of an overcomplete representation, and demonstrate substantial MSE improvement over the sub-optimal application of SURE within individual subbands.

Original languageEnglish (US)
Title of host publication2007 IEEE International Conference on Image Processing, ICIP 2007 Proceedings
Volume3
DOIs
StatePublished - 2006
Event14th IEEE International Conference on Image Processing, ICIP 2007 - San Antonio, TX, United States
Duration: Sep 16 2007Sep 19 2007

Other

Other14th IEEE International Conference on Image Processing, ICIP 2007
CountryUnited States
CitySan Antonio, TX
Period9/16/079/19/07

Fingerprint

Decomposition
Image denoising

Keywords

  • Bayes least squares
  • Cycle spinning
  • Denoising
  • Over-complete
  • Redundant
  • SURE
  • Translation invariance

ASJC Scopus subject areas

  • Engineering(all)

Cite this

Raphan, M., & Simoncelli, E. (2006). Optimal denoising in redundant bases. In 2007 IEEE International Conference on Image Processing, ICIP 2007 Proceedings (Vol. 3). [4379259] https://doi.org/10.1109/ICIP.2007.4379259

Optimal denoising in redundant bases. / Raphan, Martin; Simoncelli, Eero.

2007 IEEE International Conference on Image Processing, ICIP 2007 Proceedings. Vol. 3 2006. 4379259.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Raphan, M & Simoncelli, E 2006, Optimal denoising in redundant bases. in 2007 IEEE International Conference on Image Processing, ICIP 2007 Proceedings. vol. 3, 4379259, 14th IEEE International Conference on Image Processing, ICIP 2007, San Antonio, TX, United States, 9/16/07. https://doi.org/10.1109/ICIP.2007.4379259
Raphan M, Simoncelli E. Optimal denoising in redundant bases. In 2007 IEEE International Conference on Image Processing, ICIP 2007 Proceedings. Vol. 3. 2006. 4379259 https://doi.org/10.1109/ICIP.2007.4379259
Raphan, Martin ; Simoncelli, Eero. / Optimal denoising in redundant bases. 2007 IEEE International Conference on Image Processing, ICIP 2007 Proceedings. Vol. 3 2006.
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