Smooth optimization of orthogonal wavelet basis

J. Frecon, R. Grazzi, S. Salzo and M. Pontil
Submitted to Conférence sur l'Apprentissage Automatique (CAp), 2021

Abstract

Wavelets are 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 basis that is adapted to both the denoising task and the class of images at hand. We tackle this problem by a smooth bilevel approach where the wavelet coefficients are optimized at the lower-level and the wavelet filters are learned at the upper-level. Numerical experiments support the added benefits over classical wavelets.

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