Generalized Total Variation Denoising via Augmented Lagrangian Cycle Spinning with Haar Wavelets
Ulugbek Kamilov, EPFL STI LIB

Seminar • 12 March 2012

Abstract
We consider the denoising of signals and images using regularized least-squares method. In particular, we propose a simple minimization algorithm for regularizers that are functions of the discrete gradient. By exploiting the connection of the discrete gradient with the Haar-wavelet transform, the n-dimensional vector minimization can be decoupled into n scalar minimizations. The proposed method can efficiently solve total-variation (TV) denoising by iteratively shrinking shifted Haar-wavelet transforms. Furthermore, the decoupling naturally lends itself to extensions beyond l1 regularizers.