Noncoherent image denoising
Orchard, Michael T.
Master of Science
The techniques of Translation Invariant (TI) denoising and statistical modeling are widely used in image denoising. This thesis studies how these techniques exploit location information in images and identifies a class of noncoherent image denoising algorithms. We analyze the performance of TI denoising from the perspective of cyclic-basis reconstruction. It shows that TI denoising achieves an average performance without direct estimation of location information. Motivated by this perspective, we propose a Redundant Quaternion Wavelet Transform (RQWT) which both avoids aliasing and separates local signal energy and location information into quaternion magnitude and phases respectively. RQWT is a natural framework for studying the statistical models in noncoherent image denoisers, because they all ignore quaternion phases. Straightforward signal estimation in the RQWT framework closely matches the state-of-the-art noncoherent image denoisers and provides a natural bound on their performance, thereby showing the importance of exploring location information in quaternion phases.
Electronics; Electrical engineering