81 research outputs found
iPiano: Inertial Proximal Algorithm for Non-Convex Optimization
In this paper we study an algorithm for solving a minimization problem
composed of a differentiable (possibly non-convex) and a convex (possibly
non-differentiable) function. The algorithm iPiano combines forward-backward
splitting with an inertial force. It can be seen as a non-smooth split version
of the Heavy-ball method from Polyak. A rigorous analysis of the algorithm for
the proposed class of problems yields global convergence of the function values
and the arguments. This makes the algorithm robust for usage on non-convex
problems. The convergence result is obtained based on the \KL inequality. This
is a very weak restriction, which was used to prove convergence for several
other gradient methods. First, an abstract convergence theorem for a generic
algorithm is proved, and, then iPiano is shown to satisfy the requirements of
this theorem. Furthermore, a convergence rate is established for the general
problem class. We demonstrate iPiano on computer vision problems: image
denoising with learned priors and diffusion based image compression.Comment: 32pages, 7 figures, to appear in SIAM Journal on Imaging Science
A higher-order MRF based variational model for multiplicative noise reduction
The Fields of Experts (FoE) image prior model, a filter-based higher-order
Markov Random Fields (MRF) model, has been shown to be effective for many image
restoration problems. Motivated by the successes of FoE-based approaches, in
this letter, we propose a novel variational model for multiplicative noise
reduction based on the FoE image prior model. The resulted model corresponds to
a non-convex minimization problem, which can be solved by a recently published
non-convex optimization algorithm. Experimental results based on synthetic
speckle noise and real synthetic aperture radar (SAR) images suggest that the
performance of our proposed method is on par with the best published
despeckling algorithm. Besides, our proposed model comes along with an
additional advantage, that the inference is extremely efficient. {Our GPU based
implementation takes less than 1s to produce state-of-the-art despeckling
performance.}Comment: 5 pages, 5 figures, to appear in IEEE Signal Processing Letter
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