Journal articles

1. dardé, hyvönen, kuutela and valkonen, Electrodeless electrode model for electrical impedance tomography (2021).

   [ abstract | pdf | arXiv | codes ]

   submitted
2. jauhiainen, pour-ghaz, valkonen and seppänen, Non-planar sensing skins for structural health monitoring based on electrical resistance tomography (2020).

   [ abstract | pdf | arXiv ]

   Computer-Aided Civil and Infrastructure Engineering (2021), doi:10.1111/mice.12689
3. valkonen, Regularisation, optimisation, subregularity (2020).

   [ abstract | pdf | arXiv | codes ]

   Inverse Problems 37 (2021), 045010, doi:10.1088/1361-6420/abe4aa
4. jauhiainen, kuusela, seppänen and valkonen, Relaxed Gauss–Newton methods with applications to electrical impedance tomography (2020).

   [ abstract | pdf | arXiv ]

   SIAM Journal on Imaging Sciences 13 (2020), 1415–1445, doi:10.1137/20M1321711
5. valkonen, Predictive online optimisation with applications to optical flow (2020).

   [ abstract | pdf | arXiv | codes ]

   Journal of Mathematical Imaging and Vision 63 (2021), 329–355, doi:10.1007/s10851-020-01000-4
6. mazurenko, jauhiainen and valkonen, Primal-dual block-proximal splitting for a class of non-convex problems (2019).

   [ abstract | pdf | arXiv | codes ]

   Electronic Transactions on Numerical Analysis 52 (2020), 509–552, doi:10.1553/etna_vol52s509
7. clason, mazurenko and valkonen, Primal-dual proximal splitting and generalized conjugation in nonsmooth nonconvex optimization (2019).

   [ abstract | pdf | arXiv | codes ]

   Applied Mathematics and Optimization (2020), doi:10.1007/s00245-020-09676-1
8. valkonen, Inertial, corrected, primal-dual proximal splitting (2018).

   [ abstract | pdf | arXiv | codes ]

   SIAM Journal on Optimization 30 (2020), 1391–1420, doi:10.1137/18M1182851
9. clason, mazurenko and valkonen, Acceleration and global convergence of a first-order primal-dual method for nonconvex problems (2018).

   [ abstract | pdf | arXiv | codes ]

   SIAM Journal on Optimization 29 (2019), 933–963, doi:10.1137/18M1170194
10. zhu and valkonen, Spherical function regularization for parallel MRI reconstruction (2018).

    [ abstract | pdf | arXiv ]

     
11. valkonen, Preconditioned proximal point methods and notions of partial subregularity (2017).

    [ abstract | pdf | arXiv | link ]

    Journal of Convex Analysis 28 (2021), 251–278
12. valkonen, Interior-proximal primal-dual methods (2017).

    [ abstract | pdf | arXiv | link ]

    Applied Analysis and Optimization 3 (2019), 1–28
13. valkonen, Testing and non-linear preconditioning of the proximal point method (2017).

    [ abstract | pdf | arXiv ]

    Applied Mathematics and Optimization 82 (2020), doi:10.1007/s00245-018-9541-6
14. valkonen, Block-proximal methods with spatially adapted acceleration (2016).

    [ abstract | pdf | arXiv | codes ]

    Electronic Transactions on Numerical Analysis 51 (2019), 15–49, doi:10.1553/etna_vol51s15
15. clason and valkonen, Primal-dual extragradient methods for nonlinear nonsmooth PDE-constrained optimization (2017).

    [ abstract | pdf | arXiv ]

    SIAM Journal on Optimization 27 (2017), 1313–1339, doi:10.1137/16M1080859
16. benning, schönlieb, valkonen and vlačić, Explorations on anisotropic regularisation of dynamic inverse problems by bilevel optimisation (2016).

    [ abstract | pdf | arXiv ]

     
17. valkonen and pock, Acceleration of the PDHGM on partially strongly convex functions (2017).

    [ abstract | pdf | arXiv ]

    Journal of Mathematical Imaging and Vision 59 (2017), 394–414, doi:10.1007/s10851-016-0692-2
18. clason and valkonen, Stability of saddle points via explicit coderivatives of pointwise subdifferentials (2017).

    [ abstract | pdf | arXiv ]

    Set-valued and Variational Analysis 25 (2017), 69–112, doi:10.1007/s11228-016-0366-7
19. gorokh, korolev and valkonen, Diffusion tensor imaging with deterministic error bounds (2016).

    [ abstract | pdf | arXiv ]

    Journal of Mathematical Imaging and Vision 56 (2016), 137–157, doi:10.1007/s10851-016-0639-7
20. de los reyes, schönlieb and valkonen, Bilevel parameter learning for higher-order total variation regularisation models (2017).

    [ abstract | pdf | arXiv ]

    Journal of Mathematical Imaging and Vision 57 (2017), 1–25, doi:10.1007/s10851-016-0662-8
21. de los reyes, schönlieb and valkonen, The structure of optimal parameters for image restoration problems (2016).

    [ abstract | pdf | arXiv ]

    Journal of Mathematical Analysis and Applications 434 (2016), 464–500, doi:10.1016/j.jmaa.2015.09.023
22. hintermüller, valkonen and wu, Limiting aspects of non-convex \mbox{TV}^\varphiTVφ models (2015).

    [ abstract | pdf | arXiv ]

    SIAM Journal on Imaging Sciences 8 (2015), 2581–2621, doi:10.1137/141001457
23. valkonen, The jump set under geometric regularisation. Part 2: Higher-order approaches (2017).

    [ abstract | pdf | arXiv ]

    Journal of Mathematical Analysis and Applications 453 (2017), 1044–1085, doi:10.1016/j.jmaa.2017.04.037
24. valkonen, The jump set under geometric regularisation. Part 1: Basic technique and first-order denoising (2015).

    [ abstract | pdf | arXiv ]

    SIAM Journal on Mathematical Analysis 47 (2015), 2587–2629, doi:10.1137/140976248
25. lellmann, lorenz, schönlieb and valkonen, Imaging with Kantorovich-Rubinstein discrepancy (2014).

    [ abstract | pdf | arXiv ]

    SIAM Journal on Imaging Sciences 7 (2014), 2833–2859, doi:10.1137/140975528
26. valkonen, A primal-dual hybrid gradient method for non-linear operators with applications to MRI (2014).

    [ abstract | pdf | arXiv ]

    Inverse Problems 30 (2014), 055012, doi:10.1088/0266-5611/30/5/055012
27. benning, gladden, holland, schönlieb and valkonen, Phase reconstruction from velocity-encoded MRI measurements – A survey of sparsity-promoting variational approaches (2014).

    [ abstract | pdf ]

    Journal of Magnetic Resonance 238 (2014), 26–43, doi:10.1016/j.jmr.2013.10.003
28. valkonen, A method for weighted projections to the positive definite cone (2015).

    [ abstract | pdf ]

    Optimization 64 (2015), 2253–2275, doi:10.1080/02331934.2014.929680
29. valkonen, bredies and knoll, Total generalised variation in diffusion tensor imaging (2013).

    [ abstract | pdf | codes ]

    SIAM Journal on Imaging Sciences 6 (2013), 487–525, doi:10.1137/120867172
30. bredies, kunisch and valkonen, Properties of L^1\mbox{-TGV}^2L1-TGV2 : The one-dimensional case (2013).

    [ abstract | pdf ]

    Journal of Mathematical Analysis and Applications 398 (2013), 438–454, doi:10.1016/j.jmaa.2012.08.053
31. valkonen, Strong polyhedral approximation of simple jump sets (2012).

    [ abstract | pdf ]

    Nonlinear Analysis: Theory, Methods, & Applications 75 (2012), 3641–3671, doi:10.1016/j.na.2012.01.022
32. valkonen, Transport equation and image interpolation with SBD velocity fields (2011).

    [ abstract | pdf ]

    Journal de mathématiques pures et appliquées 95 (2011), 459–494, doi:10.1016/j.matpur.2010.10.010
33. valkonen, Optimal transportation networks and stations (2009).

    [ abstract | pdf ]

    Interfaces and Free Boundaries 11 (2009), 569–597, doi:10.4171/IFB/223
34. valkonen, Refined optimality conditions for differences of convex functions (2010).

    [ abstract | pdf ]

    Journal of Global Optimization 48 (2010), 311–321, doi:10.1007/s10898-009-9495-y
35. valkonen, Extension of primal-dual interior point methods to diff-convex problems on symmetric cones (2013).

    [ abstract | pdf ]

    Optimization 62 (2013), doi:10.1080/02331934.2011.585465
36. glowinski, kärkkäinen, valkonen and ivannikov, Nonsmooth SOR for L^1L1 -fitting: Convergence study and Discussion of Related Issues (2008).

    [ abstract | pdf ]

    Journal of Scientific Computing 37 (2008), 103–138, doi:10.1007/s10915-008-9229-1
37. valkonen and kärkkäinen, Continuous reformulations and heuristics for the Euclidean travelling salesperson problem (2009).

    [ abstract | pdf ]

    ESAIM: Control, Optimization and Calculus of Variations 15 (2009), doi:10.1051/cocv:2008056
38. valkonen and kärkkäinen, Clustering and the perturbed spatial median (2010).

    [ abstract | pdf ]

    Mathematical and Computer Modelling 52 (2010), 87–106, doi:10.1016/j.mcm.2010.01.018
39. valkonen, Convergence of a SOR-Weiszfeld type algorithm for incomplete data sets (2006).

    [ abstract ]

    Numerical Functional Analysis and Optimization 27 (2006), 931–952, doi:10.1080/01630560600791213, (Errata in vol. 29, no 9–10, 2008)

Book chapters

40. valkonen, First-order primal-dual methods for nonsmooth nonconvex optimisation (2019).

    [ abstract | pdf | arXiv ]

    Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging, editors: chen, schönlieb, tai and younes, Springer (2020), in press
41. valkonen, Optimising Big Images (2016).

    [ abstract ]

    Big Data Optimization: Recent Developments and Challenges, editors: emrouznejad. Studies in Big Data, Springer-Verlag (2016), 97–131, doi:10.1007/978-3-319-30265-2_5

Conference proceedings

42. benning, knoll, schönlieb and valkonen, Preconditioned ADMM with nonlinear operator constraint (2016).

    [ abstract | pdf | arXiv ]

    System Modeling and Optimization: 27th IFIP TC 7 Conference, CSMO 2015, Sophia Antipolis, France, June 29–July 3, 2015, Revised Selected Papers, editors: bociu, désidéri and habbal, Springer, doi:10.1007/978-3-319-55795-3_10 (2016), 117–126
43. calatroni, cao, de los reyes, schönlieb and valkonen, Bilevel approaches for learning of variational imaging models (2016).

    [ abstract | pdf | arXiv ]

    Variational Methods in Imaging and Geometric Control, editors: bergounioux, peyré, schnörr, caillau and haberkorn. Radon Series on Computational and Applied Mathematics 18 (2016), 252–290, doi:10.1515/9783110430394-008
44. papafitsoros and valkonen, Asymptotic behaviour of total generalised variation (2015).

    [ abstract | pdf | arXiv ]

    International Conference on Scale Space and Variational Methods in Computer Vision (SSVM2015). Lecture Notes in Computer Science 9087 (2015), 702–714, doi:10.1007/978-3-319-18461-6_56
45. knoll, valkonen, bredies and stollberger, Higher order variational denoising for diffusion tensor imaging (2013).

    [ abstract | link ]

    Proceedings of the International Society for Magnetic Resonance in Medicine, (ISMRM 2013 Magna Cum Laude Award) (2013)
46. valkonen and liebmann, GPU-accelerated regularisation of large diffusion tensor volumes (2013).

    [ abstract | pdf | codes ]

    Computing 95 (2013), 771–784, doi:10.1007/s00607-012-0277-x, Special issue for ESCO 2012, Pilsen, Czech Republic
47. valkonen, knoll and bredies, TGV for diffusion tensors: A comparison of fidelity functions (2013).

    [ abstract | pdf | codes ]

    Journal of Inverse and Ill-Posed Problems 21 (2013), 355–377, doi:10.1515/jip-2013-0005, Special issue for IP:M&S 2012, Antalya, Turkey
48. bredies and valkonen, Inverse problems with second-order total generalized variation constraints (2011).

    [ abstract | pdf | arXiv ]

    Proceedings of the 9th International Conference on Sampling Theory and Applications (SampTA) 2011, Singapore (2011)

Thesis

49. valkonen, Diff-convex combinations of Euclidean distances: a search for optima (2008).

    [ abstract | pdf | link ]

    Jyväskylä Studies in Computing 99, University of Jyväskylä (2008), Ph.D Thesis

Teaching material

50. clason and valkonen, Introduction to Nonsmooth Analysis and Optimization (2020).

    [ abstract | pdf | arXiv ]

    Work in progress
51. valkonen, Optimisation for computer vision and data science (2017).

    [ abstract | pdf ] 

    Lecture Notes, Partially same material as “Set-valued analysis and optimisation”
52. valkonen, Set-valued analysis and optimisation (2015).

    [ abstract | pdf ] 

    Lecture Notes
53. valkonen, Measure and Image (2013).

    [ abstract | pdf ] 

    Lecture Notes

Scientific software

54. valkonen, Codes for “Regularisation, optimisation, subregularity” (2021).
    [ link ]
    Software on Zenodo, doi:10.5281/zenodo.4432967
55. valkonen, Julia codes for “Predictive online optimisation with applications to optical flow” (2020).
    [ link ]
    Software on Zenodo, doi:10.5281/zenodo.3659180
56. clason, mazurenko and valkonen, Julia codes for “Primal-dual proximal splitting and generalized conjugation in non-smooth non-convex optimization” (2020).
     
    Software on Zenodo, doi:10.5281/zenodo.3647614
57. mazurenko, jauhiainen and valkonen, Diffusion tensor imaging codes from “Primal-dual block-proximal splitting for a class of non-convex problems” (2019).
    [ link ]
    Software on Zenodo, doi:10.5281/zenodo.3528137
58. valkonen, Source codes for “Inertial, corrected, primal-dual proximal splitting” (2019).
    [ link ]
    Software on Zenodo, doi:10.5281/zenodo.3531934
59. clason and valkonen, Codes supporting: Primal-dual extragradient methods for nonlinear nonsmooth PDE-constrained optimization [nlpdegm] (2017).
    [ link ]
    Software on Zenodo, doi:10.5281/zenodo.398822
60. valkonen, Codes supporting “Block-proximal methods with spatially adapted acceleration” (2017).
    [ link ]
    Software on Zenodo, doi:10.5281/zenodo.1042419
61. valkonen, An efficient C code for diffusion tensor denoising with total generalised variation (2012).
    [ link ]
    Software on Zenodo, doi:10.5281/zenodo.3667665