Infoscience

Journal article

# Generalized Total Variation Denoising via Augmented Lagrangian Cycle Spinning with Haar Wavelets

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 $ℓ _{ 1 }$ regularizers.

#### Reference

• EPFL-ARTICLE-211477

Record created on 2015-09-18, modified on 2017-05-10