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2013 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (2013)
Portland, OR, USA
June 23, 2013 to June 28, 2013
ISSN: 1063-6919
ISBN: 978-0-7695-4989-7
pp: 1759-1766
Natural image statistics indicate that we should use non-convex norms for most regularization tasks in image processing and computer vision. Still, they are rarely used in practice due to the challenge to optimize them. Recently, iteratively reweighed 1 minimization has been proposed as a way to tackle a class of non-convex functions by solving a sequence of convex 2 - 1 problems. Here we extend the problem class to linearly constrained optimization of a Lipschitz continuous function, which is the sum of a convex function and a function being concave and increasing on the non-negative orthant (possibly non-convex and non-concave on the whole space). This allows to apply the algorithm to many computer vision tasks. We show the effect of non-convex regularizers on image denoising, deconvolution, optical flow, and depth map fusion. Non-convexity is particularly interesting in combination with total generalized variation and learned image priors. Efficient optimization is made possible by some important properties that are shown to hold.
non-smooth non-convex optimization, optimization

P. Ochs, A. Dosovitskiy, T. Brox and T. Pock, "An Iterated L1 Algorithm for Non-smooth Non-convex Optimization in Computer Vision," 2013 IEEE Conference on Computer Vision and Pattern Recognition(CVPR), Portland, OR, USA USA, 2013, pp. 1759-1766.
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