Optimal denoising in redundant bases

Martin Raphan, Eero P. Simoncelli

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


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
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
ISSN (Print)1522-4880


Other14th IEEE International Conference on Image Processing, ICIP 2007
Country/TerritoryUnited States
CitySan Antonio, TX


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

ASJC Scopus subject areas

  • General Engineering


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