8 papers · 1 filter
On the Universality of Simple Trust-Region Algorithms
Clemens Sirotenko
We establish universal complexity guarantees for quadratic trust-region methods and identify a common mechanism underlying their universal behavior under convexity, based on a func…
Skip the Hessian, Keep the Rates: Globalized Semismooth Newton with Lazy Hessian Updates
Amal Alphonse, Pavel Dvurechensky, Clemens Sirotenko
Second-order methods are provably faster than first-order methods, and their efficient implementations for large-scale optimization problems have attracted significant attention. Y…
LeAP-SSN: A Semismooth Newton Method with Global Convergence Rates
Amal Alphonse, Pavel Dvurechensky, Ioannis P. A. Papadopoulos +1
We propose LeAP-SSN (Levenberg--Marquardt Adaptive Proximal Semismooth Newton method), a semismooth Newton-type method with a simple, parameter-free globalisation strategy that gua…
Dictionary Learning Based Regularization in Quantitative MRI: A Nested Alternating Optimization Framework
Guozhi Dong, Michael Hintermüller, Clemens Sirotenko
In this article, we propose a novel regularization method for a class of nonlinear inverse problems that is inspired by an application in quantitative magnetic resonance imaging (q…
A neural network approach to learning solutions of a class of elliptic variational inequalities
Amal Alphonse, Michael Hintermüller, Alexander Kister +2
We develop a weak adversarial approach to solving obstacle problems using neural networks. By employing (generalised) regularised gap functions and their properties we rewrite the…
Data-driven methods for quantitative imaging
Guozhi Dong, Moritz Flaschel, Michael Hintermüller +3
In the field of quantitative imaging, the image information at a pixel or voxel in an underlying domain entails crucial information about the imaged matter. This is particularly im…
Unrolled three-operator splitting for parameter-map learning in Low Dose X-ray CT reconstruction
Andreas Kofler, Fabian Altekrüger, Fatima Antarou Ba +6
We propose a method for fast and automatic estimation of spatially dependent regularization maps for total variation-based (TV) tomography reconstruction. The estimation is based o…
Learning Regularization Parameter-Maps for Variational Image Reconstruction using Deep Neural Networks and Algorithm Unrolling
Andreas Kofler, Fabian Altekrüger, Fatima Antarou Ba +6
We introduce a method for fast estimation of data-adapted, spatio-temporally dependent regularization parameter-maps for variational image reconstruction, focusing on total variati…