Optimal denoising in redundant bases

M Raphan and E P Simoncelli

Published in Proc 14th IEEE Int'l Conf on Image Proc (ICIP), vol.III pp. 113--116, Sep 2007.

Winner, IBM student paper award.

DOI: 10.1109/ICIP.2007.4379259

This paper has been superseded by:
Optimal denoising in redundant representations
M Raphan and E P Simoncelli.
IEEE Trans. Image Processing, vol.17(8), pp. 1342--1352, Aug 2008.


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    • 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 suboptimal application of SURE within individual subbands.
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