Tuomo Valkonen
University of Cambridge
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Publication
Featured researches published by Tuomo Valkonen.
Siam Journal on Imaging Sciences | 2013
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
Martin Benning; Lynn F. Gladden; Daniel J. Holland; Carola-Bibiane Schönlieb; Tuomo Valkonen
\TGV^2
Inverse Problems | 2014
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
Jan Lellmann; Dirk A. Lorenz; Carola-Bibiane Schönlieb; Tuomo Valkonen
\TGV^2
Journal of Mathematical Imaging and Vision | 2017
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
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
Tuomo Valkonen
We study the solution of minimax problems
Journal of Scientific Computing | 2008
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
Konstantinos Papafitsoros; Tuomo Valkonen
in finite-dimensional Hilbert spaces. The functionals
ifip conference on system modeling and optimization | 2015
Martin Benning; Florian Knoll; Carola-Bibiane Schönlieb; Tuomo Valkonen
G