Optimal denoising in redundant bases
Recipient, Best Student Paper Award, sponsored by IBM.
Published in:
Proceedings, 14th IEEE Int'l Conference on Image Processing
San Antonio, TX, Sep 2007
Related publications:
• Tech. Report on non-parametric image denoising using implicit-prior methods TR2007-900.
• Learning to be Bayesian without Supervision [generalizes SURE to a variety of noise processes, and to non-parametric estimators] nips-06.
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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