Generalized Total Variation Denoising via Augmented Lagrangian Cycle Spinning with Haar Wavelets
U. Kamilov, E. Bostan, M. Unser
Proceedings of the Thirty-Seventh IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP'12), 京都市 (Kyoto), Japan, March 25-30, 2012, in press.
Please do not bookmark the "In Press" papers as content and presentation may differ from the published version.
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.
| 
