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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, pp. 909-912.

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 1 regularizers.

AUTHOR="Kamilov, U. and Bostan, E. and Unser, M.",
TITLE="Generalized Total Variation Denoising via Augmented {L}agrangian
        Cycle Spinning with {H}aar Wavelets",
BOOKTITLE="Proceedings of the Thirty-Seventh {IEEE} International
        Conference on Acoustics, Speech, and Signal Processing
address="Kyoto, Japan",
month="March 25-30,",

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