Publications

Journal articles

[1] T.V., Testing and non-linear preconditioning of the proximal point method (2017). Submitted. [ arXiv |  .pdf ]
[2] T.V., Block-proximal methods with spatially adapted acceleration (2016). Submitted. [ arXiv |  director's cut  |  .pdf ]
[3] C. Clason and T.V., Primal-dual extragradient methods for nonlinear nonsmooth PDE-constrained optimization, SIAM Journal on Optimization (2017). To appear. [ arXiv |  .pdf ]
[4] M. Benning, C.-B. Schönlieb, T.V. and V. Vlačić, Explorations on anisotropic regularisation of dynamic inverse problems by bilevel optimisation (2016). Submitted. [ arXiv |  .pdf ]
[5] T.V. and T. Pock, Acceleration of the PDHGM on partially strongly convex functions, Journal of Mathematical Imaging and Vision (2016). To appear. [ DOI |  arXiv |  .pdf ]
[6] C. Clason and T.V., Stability of saddle points via explicit coderivatives of pointwise subdifferentials, Set-valued and Variational Analysis 25 (2017), 69–112. [ DOI |  arXiv |  .pdf ]
[7] A. Gorokh, Y. Korolev and T.V., Diffusion tensor imaging with deterministic error bounds, Journal of Mathematical Imaging and Vision 56 (2016), 137–157. [ DOI |  arXiv |  .pdf ]
[8] J. C. de Los Reyes, C.-B. Schönlieb and T.V., Bilevel parameter learning for higher-order total variation regularisation models, Journal of Mathematical Imaging and Vision 57 (2017), 1–25. [ DOI |  arXiv |  .pdf ]
[9] J. C. de Los Reyes, C.-B. Schönlieb and T.V., The structure of optimal parameters for image restoration problems, Journal of Mathematical Analysis and Applications 434 (2016), 464–500. [ DOI |  arXiv |  .pdf ]
[10] M. Hintermüller, T.V. and T. Wu, Limiting aspects of non-convex TVφ models, SIAM Journal on Imaging Sciences 8 (2015), 2581–2621. [ DOI |  arXiv |  .pdf ]
[11] T.V., The jump set under geometric regularisation. Part 2: Higher-order approaches, Journal of Mathematical Analysis and Applications (2017). To appear. [ arXiv |  .pdf ]
[12] T.V., The jump set under geometric regularisation. Part 1: Basic technique and first-order denoising, SIAM Journal on Mathematical Analysis 47 (2015), 2587–2629. [ DOI |  arXiv |  .pdf ]
[13] J. Lellmann, D. Lorenz, C.-B. Schönlieb and T.V., Imaging with Kantorovich-Rubinstein discrepancy, SIAM Journal on Imaging Sciences 7 (2014), 2833–2859. [ DOI |  arXiv |  .pdf ]
[14] T.V., A primal-dual hybrid gradient method for non-linear operators with applications to MRI, Inverse Problems 30 (2014), 055012. [ DOI |  arXiv |  .pdf ]
[15] M. Benning, L. Gladden, D. Holland, C.-B. Schönlieb and T.V., Phase reconstruction from velocity-encoded MRI measurements -- A survey of sparsity-promoting variational approaches, Journal of Magnetic Resonance 238 (2014), 26–43. [ DOI |  .pdf ]
[16] T.V., A method for weighted projections to the positive definite cone, Optimization 64 (2015), 2253–2275. [ DOI |  .pdf ]
[17] T.V., K. Bredies and F. Knoll, Total generalised variation in diffusion tensor imaging, SIAM Journal on Imaging Sciences 6 (2013), 487–525. [ DOI |  .pdf ]
[18] K. Bredies, K. Kunisch and T.V., Properties of L1-TGV2: The one-dimensional case, Journal of Mathematical Analysis and Applications 398 (2013), 438–454. [ DOI |  .pdf ]
[19] T.V., Strong polyhedral approximation of simple jump sets, Nonlinear Analysis: Theory, Methods, & Applications 75 (2012), 3641–3671. [ DOI |  .pdf ]
[20] T.V., Transport equation and image interpolation with SBD velocity fields, Journal de mathématiques pures et appliquées 95 (2011), 459–494. [ DOI |  .pdf ]
[21] T.V., Optimal transportation networks and stations, Interfaces and Free Boundaries 11 (2009), 569–597. [ DOI |  .pdf ]
[22] T.V., Refined optimality conditions for differences of convex functions, Journal of Global Optimization 48 (2010), 311–321. [ DOI |  .pdf ]
[23] T.V., Extension of primal-dual interior point methods to diff-convex problems on symmetric cones, Optimization 62 (2013). [ DOI |  .pdf ]
[24] R. Glowinski, T. Kärkkäinen, T.V. and A. Ivannikov, Nonsmooth SOR for L1-fitting: Convergence study and discussion of related issues, Journal of Scientific Computing 37 (2008), 103–138. [ DOI |  .pdf ]
[25] T.V. and T. Kärkkäinen, Continuous reformulations and heuristics for the Euclidean travelling salesperson problem, ESAIM: Control, Optimization and Calculus of Variations 15 (2009). [ DOI |  .pdf ]
[26] T.V. and T. Kärkkäinen, Clustering and the perturbed spatial median, Mathematical and Computer Modelling 52 (2010), 87–106. [ DOI |  .pdf ]
[27] T.V., Convergence of a SOR-Weiszfeld type algorithm for incomplete data sets, Numerical Functional Analysis and Optimization 27 (2006), 931–952. (Errata in vol. 29, no 9–10, 2008). [ DOI ]

Book chapters

[28] T.V., Optimising big images, in: Big Data Optimization: Recent Developments and Challenges, Edited by A. Emrouznejad, Studies in Big Data, Springer-Verlag, 2016, 97–131. [ DOI ]

Conference proceedings

[29] M. Benning, F. Knoll, C.-B. Schönlieb and T.V., Preconditioned ADMM with nonlinear operator constraint, in: System Modeling and Optimization: 27th IFIP TC 7 Conference, CSMO 2015, Sophia Antipolis, France, June 29--July 3, 2015, Revised Selected Papers, Edited by L. Bociu, J.-A. Désidéri and A. Habbal, Springer International Publishing, 2016, 117–126. [ DOI |  arXiv |  .pdf ]
[30] L. Calatroni, C. Cao, J. C. de Los Reyes, C.-B. Schönlieb and T.V., Bilevel approaches for learning of variational imaging models (2015). Submitted. [ arXiv |  .pdf ]
[31] K. Papafitsoros and T.V., Asymptotic behaviour of total generalised variation, in: Scale Space and Variational Methods in Computer Vision (SSVM 2015), Lecture Notes in Computer Science, volume 9087, 2015, 702–714. [ DOI |  arXiv |  .pdf ]
[32] F. Knoll, T.V., K. Bredies and R. Stollberger, Higher order variational denoising for diffusion tensor imaging, in: Proceedings of the International Society for Magnetic Resonance in Medicine, 21:2078, 2013. (ISMRM 2013 Magna Cum Laude Award).
[33] T.V. and M. Liebmann, GPU-accelerated regularisation of large diffusion tensor volumes, Computing 95 (2013), 771–784. Special issue for ESCO 2012, Pilsen, Czech Republic. [ DOI |  .pdf ]
[34] T.V., F. Knoll and K. Bredies, TGV for diffusion tensors: A comparison of fidelity functions, Journal of Inverse and Ill-Posed Problems 21 (2013), 355–377. Special issue for IP:M&S 2012, Antalya, Turkey. [ DOI |  .pdf ]
[35] K. Bredies and T.V., Inverse problems with second-order total generalized variation constraints, in: Proceedings of the 9th International Conference on Sampling Theory and Applications (SampTA) 2011, Singapore, 2011. [ .pdf ]

Thesis

[36] T.V., Diff-convex combinations of Euclidean distances: a search for optima, number 99 in Jyväskylä Studies in Computing, University of Jyväskylä, 2008. Ph.D Thesis. [ .pdf ]

Teaching material

[37] T.V., Set-valued analysis and optimisation, Lecture Notes (2015). [ .pdf ]
[38] T.V., Measure and image, Lecture Notes (2013). [ .pdf ]