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 connec-tion 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 ef-ficiently solve total-variation (TV) denoising by iteratively shrinking shifted Haar-wavelet transforms. Furthermore, the decoupling naturally lends itself to extensions beyond `1 regularizers. Index Terms — signal denoising, soft-thresholding, cycle spinning, TV denoising 1