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Abstract

We derive a number of methods to solve efficiently simple optimization problems subject to a totalvariation
(TV) regularization, under different norms of the TV operator and both for the case of 1-dimensional and
2-dimensional data. In spite of the non-smooth, non-separable nature of the TV terms considered, we show that
a dual formulation with strong structure can be derived. Taking advantage of this structure we develop adaptions
of existing algorithms from the optimization literature, resulting in efficient methods for the problem at hand.
Experimental results show that for 1-dimensional data the proposed methods achieve convergence within good
accuracy levels in practically linear time, both for L1 and L2 norms. For the more challenging 2-dimensional case
a performance of order O(N2 log2 N) for N x N inputs is achieved when using the L2 norm. A final section
suggests possible extensions and lines of further work.