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9 papers · 2 filters
An Inner-Outer Iterative Method for Edge Preservation in Image Restoration and Reconstruction
Silvia Gazzola, Misha E. Kilmer, James G. Nagy +2
We present a new inner-outer iterative algorithm for edge enhancement in imaging problems. At each outer iteration, we formulate a Tikhonov-regularized problem where the penalizati…
A deep surrogate approach to efficient Bayesian inversion in PDE and integral equation models
Teo Deveney, Eike Mueller, Tony Shardlow
We investigate a deep learning approach to efficiently perform Bayesian inference in partial differential equation (PDE) and integral equation models over potentially high-dimensio…
Adaptive Regularization Parameter Choice Rules for Large-Scale Problems
Silvia Gazzola, Malena Sabate Landman
This paper derives a new class of adaptive regularization parameter choice strategies that can be effectively and efficiently applied when regularizing large-scale linear inverse p…
Residual estimates for post-processors in elliptic problems
Andreas Dedner, Jan Giesselmann, Tristan Pryer +1
In this work we examine a posteriori error control for post-processed approximations to elliptic boundary value problems. We introduce a class of post-processing operator that `twe…
Guaranteed a posteriori error bounds for low rank tensor approximate solutions
Sergey Dolgov, Tomáš Vejchodský
We propose a guaranteed and fully computable upper bound on the energy norm of the error in low-rank Tensor Train (TT) approximate solutions of (possibly) high dimensional reaction…
Parallel cross interpolation for high-precision calculation of high-dimensional integrals
Sergey Dolgov, Dmitry Savostyanov
We propose a parallel version of the cross interpolation algorithm and apply it to calculate high-dimensional integrals motivated by Ising model in quantum physics. In contrast to…