A First Order Primal-Dual Algorithm for Nonconvex TV^q Regularization

Thomas Mollenhoff, Evgeny Strekalovskiy, Daniel Cremers
Technische Universitat Munchen, Institut fur Informatik
TU Munich, Technical report TUM-I149, 2014


   title={A First Order Primal-Dual Algorithm for Nonconvex TV^q Regularization},

   author={M{"o}llenhoff, Thomas and Strekalovskiy, Evgeny and Cremers, Daniel},



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We propose an efficient first order primal-dual method for solving variational problems with nonconvex regularization such as TV^q. It is based on the recent idea in [1] to reformulate an existing primal-dual algorithm for convex optimization using Moreau’s identity. A systematic comparison to recent state of the art algorithms for nonconvex optimization (iteratively reweighted l1 optimization, quadratic splitting and convex relaxation methods) shows that the proposed algorithm has several advantages. Compared to iterative reweighting it does not require Lipschitz continuity or concavity of the regularizer and thus is also applicable to the case q = 0. Unlike the quadratic splitting approach it requires no additional hyperparameters. In contrast to convex relaxation methods it does not require a discretization of the color values and is orders of magnitudes faster and memory efficient. Numerous experiments indicate that TV^q is a well suited prior for piecewise constant images and allows to better preserve discontinuities than classical TV regularization.
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