A fixed-point augmented Lagrangian method for total variation minimization problems

Authors:
Yuping Duan;Weimin Huang
Affiliations:
-;-
Venue:
Journal of Visual Communication and Image Representation
Year:
2013

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Abstract

In this paper, we propose a fixed-point augmented Lagrangian method (FPALM) for general convex problems arising in image processing. We can easily obtain the alternating minimization algorithm (AMA) referred to [1] from the proposed FPALM. The proof for the convergence of the FPALM is provided under some mild assumptions. We present two kinds of first-order augmented Lagrangian schemes and show their connections to first-order primal-dual algorithms [2]. Furthermore, we apply an acceleration rule to both the FPALM and AMA to achieve better convergence rates. Numerical examples on different image denosing models including the ROF model, the vectorial TVmodel, high order models and the TV-L^1 model are provided to demonstrate the efficiency of the proposed algorithms.