A new interpretation of translation invariant denoising

Translation invariant (TI) image denoising outperforms orthogonal wavelet thresholding by averaging a collection of denoised estimates from different orthogonal bases. The paper proposes a new perspective of TI processing as an average of a collection of cyclic-basis frame reconstructions, each a stationary signal estimate, contrasting with the nonstationary estimates of orthogonal wavelet thresholding. This viewpoint clarifies that certain characteristics of TI (i.e. reduced edge contour artifacts) are inherited from each cyclic-basis reconstruction, rather than from the process of averaging. We relate performance advantages of TI in smooth areas of images to statistical relationships of the cyclic-basis reconstructions. In edge regions, the quality of cyclic-basis reconstructions varies significantly with pixel position relative to the edge contour. These differences couple with convexity arguments to explain the large performance gains of TI in edge regions. They also suggest an improved approach to frame reconstruction, based on estimating relative location information, and identifying the best cyclic-basis reconstruction for the estimated pixel location.