Optimal denoising in redundant bases

Martin Raphan, Eero P. 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
PagesIII113-III116
DOIs
StatePublished - 2006
Event14th IEEE International Conference on Image Processing, ICIP 2007 - San Antonio, TX, United States
Duration: Sep 16 2007Sep 19 2007

Publication series

NameProceedings - International Conference on Image Processing, ICIP
Volume3
ISSN (Print)1522-4880

Other

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

Keywords

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

ASJC Scopus subject areas

  • Engineering(all)

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  • Cite this

    Raphan, M., & Simoncelli, E. P. (2006). Optimal denoising in redundant bases. In 2007 IEEE International Conference on Image Processing, ICIP 2007 Proceedings (pp. III113-III116). [4379259] (Proceedings - International Conference on Image Processing, ICIP; Vol. 3). https://doi.org/10.1109/ICIP.2007.4379259