Optimal Denoising in Redundant Representations

Abstract--Image denoising methods are often designed to minimize mean-squared error (MSE) within the subbands of a multiscale decomposition. However, most high-quality denoising results have been obtained with overcomplete representations, for which minimization of MSE in the subband domain does not guarantee optimal MSE performance in the image domain. We prove that, despite this suboptimality, the expected image-domain MSE resulting from applying estimators to subbands that are made redundant through spatial replication of basis functions (e.g., cycle spinning) is always less than or equal to that resulting from applying the same estimators to the original nonredundant representation. In addition, we show that it is possible to further exploit overcompleteness by jointly optimizing the subband estimators for image-domain MSE. We develop an extended version of Stein's unbiased risk estimate (SURE) that allows us to perform this optimization adaptively, for each observed noisy ima...

• Type: Journal
• Year: 2008
• Where: TIP
• Authors: Martin Raphan, Eero P. Simoncelli
• Keywords: Estimators, Image-domain Mse, Optimal Mse Performance, TIP 2008