## 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.

Published in:
Proceedings of the Thirty-Seventh IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP'12), 京都市 (Kyoto), Japan, 909–912
Year:
2012
Publisher:
IEEE
Laboratories: