Reconstruction of wavelet coefficients using total variation minimization

Sylvain Durand (1) , Jacques Froment (2)

1 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée
2 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5

We propose a model to reconstruct wavelet coefficients using a total variation minimization algorithm. The approach is motivated by wavelet signal denoising methods, where thresholding small wavelet coefficients leads to pseudo-Gibbs artifacts. By replacing these thresholded coefficients by values minimizing the total variation, our method performs a nearly artifact free signal denoising. In this paper, we detail the algorithm based on a subgradient descent combining a projection on a linear space. The convergence of the algorithm is established and numerical experiments are reported.

Mots clés: wavelets; total variation; denoising

Domaines: Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Sylvain Durand, Jacques Froment. Reconstruction of wavelet coefficients using total variation minimization. SIAM Journal on Scientific Computing, 2003, 24 (5), pp.1754-1767. ⟨hal-00204982⟩