1 code implementation • 3 May 2024 • Neil Dizon, Jyrki Jauhiainen, Tuomo Valkonen
Online optimisation facilitates the solution of dynamic inverse problems, such as image stabilisation, fluid flow monitoring, and dynamic medical imaging.
1 code implementation • 6 Dec 2022 • Tuomo Valkonen
Point source localisation is generally modelled as a Lasso-type problem on measures.
no code implementations • 8 Dec 2020 • Jyrki Jauhiainen, Mohammad Pour-Ghaz, Tuomo Valkonen, Aku Seppänen
Electrical resistance tomography (ERT) -based distributed surface sensing systems, or sensing skins, offer alternative sensing techniques for structural health monitoring, providing capabilities for distributed sensing of, for example, damage, strain and temperature.
Image Reconstruction Computational Physics Numerical Analysis Differential Geometry Numerical Analysis
no code implementations • 19 May 2020 • Kristian Bredies, Tuomo Valkonen
Total Generalized Variation (TGV) has recently been introduced as penalty functional for modelling images with edges as well as smooth variations.
1 code implementation • 8 Feb 2020 • Tuomo Valkonen
To prove convergence we need a predictor for the dual variable based on (proximal) gradient flow.
1 code implementation • 9 Jan 2019 • Christian Clason, Stanislav Mazurenko, Tuomo Valkonen
We demonstrate that difficult non-convex non-smooth optimization problems, such as Nash equilibrium problems and anisotropic as well as isotropic Potts segmentation model, can be written in terms of generalized conjugates of convex functionals.
Optimization and Control
no code implementations • 9 Feb 2018 • Christian Clason, Stanislav Mazurenko, Tuomo Valkonen
The primal--dual hybrid gradient method (PDHGM, also known as the Chambolle--Pock method) has proved very successful for convex optimization problems involving linear operators arising in image processing and inverse problems.
Optimization and Control
1 code implementation • 20 Jun 2016 • Christian Clason, Tuomo Valkonen
We study the extension of the Chambolle--Pock primal-dual algorithm to nonsmooth optimization problems involving nonlinear operators between function spaces.
Optimization and Control
no code implementations • 20 Nov 2015 • Tuomo Valkonen, Thomas Pock
We propose several variants of the primal-dual method due to Chambolle and Pock.
no code implementations • 7 Sep 2015 • Artur Gorokh, Yury Korolev, Tuomo Valkonen
Errors in the data and the forward operator of an inverse problem can be handily modelled using partial order in Banach lattices.
no code implementations • 8 May 2015 • Juan Carlos De Los Reyes, Carola-Bibiane Schönlieb, Tuomo Valkonen
The analysis is done on the original -- in image restoration typically non-smooth variational problem -- as well as on a smoothed approximation set in Hilbert space which is the one considered in numerical computations.
1 code implementation • 8 May 2015 • Luca Calatroni, Cao Chung, Juan Carlos De Los Reyes, Carola-Bibiane Schönlieb, Tuomo Valkonen
We review some recent learning approaches in variational imaging, based on bilevel optimisation, and emphasize the importance of their treatment in function space.
no code implementations • 9 Jul 2014 • Tuomo Valkonen
In Part 1, we developed a new technique based on Lipschitz pushforwards for proving the jump set containment property $\mathcal{H}^{m-1}(J_u \setminus J_f)=0$ of solutions $u$ to total variation denoising.
no code implementations • 6 Jul 2014 • Tuomo Valkonen
Their proof unfortunately depends heavily on the co-area formula, as do many results in this area, and as such is not directly extensible to higher-order, curvature-based, and other advanced geometric regularisers, such as total generalised variation (TGV) and Euler's elastica.
no code implementations • 1 Jul 2014 • Jan Lellmann, Dirk A. Lorenz, Carola Schönlieb, Tuomo Valkonen
We propose the use of the Kantorovich-Rubinstein norm from optimal transport in imaging problems.