Benefits of consistency in image denoising with steerable wavelets

The steerable wavelet transform is a redundant image representation with the remarkable property that its basis functions can be adaptively rotated to a desired orientation. This makes the transform well-suited to the design of wavelet-based algorithms applicable to images with a high amount of directional features. However, arbitrary modification of the wavelet-domain coefficients may violate consistency constraints because a legitimate representation must be redundant. In this paper, by honoring the redundancy of the coefficients, we demonstrate that it is possible to improve the performance of regularized least-squares problems in the steerable wavelet domain. We illustrate that our consistent method significantly improves upon the performance of conventional denoising with steerable wavelets.