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Dive into the research topics where Tuomo Valkonen is active.

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Featured researches published by Tuomo Valkonen.


Siam Journal on Imaging Sciences | 2013

Total Generalized Variation in Diffusion Tensor Imaging

Tuomo Valkonen; Kristian Bredies; Florian Knoll

We study the extension of total variation (TV), total deformation (TD), and (second-order) total generalized variation (


Journal of Magnetic Resonance | 2014

Phase reconstruction from velocity-encoded MRI measurements--a survey of sparsity-promoting variational approaches.

Martin Benning; Lynn F. Gladden; Daniel J. Holland; Carola-Bibiane Schönlieb; Tuomo Valkonen

\TGV^2


Inverse Problems | 2014

A primal–dual hybrid gradient method for nonlinear operators with applications to MRI

Tuomo Valkonen

) to symmetric tensor fields. We show that for a suitable choice of finite-dimensional norm, these variational seminorms are rotation-invariant in a sense natural and well suited for application to diffusion tensor imaging (DTI). Combined with a positive definiteness constraint, we employ these novel seminorms as regularizers in Rudin--Osher--Fatemi (ROF) type denoising of medical in vivo brain images. For the numerical realization, we employ the Chambolle--Pock algorithm, for which we develop a novel duality-based stopping criterion which guarantees error bounds with respect to the functional values. Our findings indicate that TD and


Siam Journal on Imaging Sciences | 2014

Imaging with Kantorovich--Rubinstein Discrepancy

Jan Lellmann; Dirk A. Lorenz; Carola-Bibiane Schönlieb; Tuomo Valkonen

\TGV^2


Journal of Mathematical Imaging and Vision | 2017

Bilevel Parameter Learning for Higher-Order Total Variation Regularisation Models

Juan Carlos De Los Reyes; Carola-Bibiane Schönlieb; Tuomo Valkonen

, both of which employ the symmetrized differential, provide improved results compared to other evaluated approaches.


Journal of Mathematical Analysis and Applications | 2016

The structure of optimal parameters for image restoration problems

J.C. De Los Reyes; Carola-Bibiane Schönlieb; Tuomo Valkonen

In recent years there has been significant developments in the reconstruction of magnetic resonance velocity images from sub-sampled k-space data. While showing a strong improvement in reconstruction quality compared to classical approaches, the vast number of different methods, and the challenges in setting them up, often leaves the user with the difficult task of choosing the correct approach, or more importantly, not selecting a poor approach. In this paper, we survey variational approaches for the reconstruction of phase-encoded magnetic resonance velocity images from sub-sampled k-space data. We are particularly interested in regularisers that correctly treat both smooth and geometric features of the image. These features are common to velocity imaging, where the flow field will be smooth but interfaces between the fluid and surrounding material will be sharp, but are challenging to represent sparsely. As an example we demonstrate the variational approaches on velocity imaging of water flowing through a packed bed of solid particles. We evaluate Wavelet regularisation against Total Variation and the relatively recent second order Total Generalised Variation regularisation. We combine these regularisation schemes with a contrast enhancement approach called Bregman iteration. We verify for a variety of sampling patterns that Morozovs discrepancy principle provides a good criterion for stopping the iterations. Therefore, given only the noise level, we present a robust guideline for setting up a variational reconstruction scheme for MR velocity imaging.


Siam Journal on Mathematical Analysis | 2015

The Jump Set under Geometric Regularization. Part 1: Basic Technique and First-Order Denoising

Tuomo Valkonen

We study the solution of minimax problems


Journal of Scientific Computing | 2008

Non-smooth SOR for L1-Fitting: Convergence Study and Discussion of Related Issues

Roland Glowinski; Tommi Kärkkäinen; Tuomo Valkonen; Andriy Ivannikov

\min_x \max_y G(x) + \langle K(x),y\rangle - F^*(y)


international conference on scale space and variational methods in computer vision | 2015

Asymptotic Behaviour of Total Generalised Variation

Konstantinos Papafitsoros; Tuomo Valkonen

in finite-dimensional Hilbert spaces. The functionals


ifip conference on system modeling and optimization | 2015

Preconditioned ADMM with nonlinear operator constraint

Martin Benning; Florian Knoll; Carola-Bibiane Schönlieb; Tuomo Valkonen

G

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Florian Knoll

Graz University of Technology

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Thomas Pock

Graz University of Technology

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Michael Hintermüller

Humboldt University of Berlin

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