4,071 research outputs found
Accelerated graph-based nonlinear denoising filters
Denoising filters, such as bilateral, guided, and total variation filters,
applied to images on general graphs may require repeated application if noise
is not small enough. We formulate two acceleration techniques of the resulted
iterations: conjugate gradient method and Nesterov's acceleration. We
numerically show efficiency of the accelerated nonlinear filters for image
denoising and demonstrate 2-12 times speed-up, i.e., the acceleration
techniques reduce the number of iterations required to reach a given peak
signal-to-noise ratio (PSNR) by the above indicated factor of 2-12.Comment: 10 pages, 6 figures, to appear in Procedia Computer Science, vol.80,
2016, International Conference on Computational Science, San Diego, CA, USA,
June 6-8, 201
Acceleration of the PDHGM on strongly convex subspaces
We propose several variants of the primal-dual method due to Chambolle and
Pock. Without requiring full strong convexity of the objective functions, our
methods are accelerated on subspaces with strong convexity. This yields mixed
rates, with respect to initialisation and with respect to
the dual sequence, and the residual part of the primal sequence. We demonstrate
the efficacy of the proposed methods on image processing problems lacking
strong convexity, such as total generalised variation denoising and total
variation deblurring
Variational image regularization with Euler's elastica using a discrete gradient scheme
This paper concerns an optimization algorithm for unconstrained non-convex
problems where the objective function has sparse connections between the
unknowns. The algorithm is based on applying a dissipation preserving numerical
integrator, the Itoh--Abe discrete gradient scheme, to the gradient flow of an
objective function, guaranteeing energy decrease regardless of step size. We
introduce the algorithm, prove a convergence rate estimate for non-convex
problems with Lipschitz continuous gradients, and show an improved convergence
rate if the objective function has sparse connections between unknowns. The
algorithm is presented in serial and parallel versions. Numerical tests show
its use in Euler's elastica regularized imaging problems and its convergence
rate and compare the execution time of the method to that of the iPiano
algorithm and the gradient descent and Heavy-ball algorithms
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