Smooth optimization of orthogonal wavelet basis

J. Frecon, R. Grazzi, S. Salzo, and M. Pontil
Unpublished, 2020


Wavelets have been found to be a powerful tool for signal and image processing tasks. They allow to analyze the noise level separately at multiple scales and to adapt the denoising algorithm accordingly. However, the performance strongly rely on the choice of the wavelet basis. The aim of this work is to learn the wavelet that is adapted to the given class of images at hand, meaning that it yields sparser wavelet coefficients. We tackle this problem by a bilevel approach where the wavelet coefficients are optimized at the lower-level and the wavelet filters are learned at the upper-level. A smooth optimization scheme is then proposed and shown to achieve state-of-the-art performance for denoising and deblurring experiments.