Department of Mathematics and Systems Analysis

Research groups

Inverse problems

N. Hyvönen, A. Seppänen and S. Staboulis. Optimizing electrode positions in EIT. SIAM Journal on Applied Mathematics 2014, Vol. 74, pp. 1831-1851.

Inverse problems constitute an active and expanding research field of mathematics and its applications. Inverse problems are encountered in several areas of applied sciences such as biomedical engineering and imaging, geosciences, vulcanology, remote sensing, and non-destructive material evaluation. To put it short, a forward problem is to deduce consequences of a cause, while the corresponding inverse problem is to find the causes of a known consequence. Inverse problems are typically encountered  when one has indirect observations of the quantity of interest.

A fundamental feature of inverse problems is that they are ill-posed: Small errors in the measured data can cause arbitrarily large errors in the estimates of the parameters of interest, or can even render the problem unsolvable. It may also occur that an inverse problem does not have a unique solution, i.e., there are several different parameter values that could produce the same observed data. In consequence, to successfully tackle inverse problems, one needs to have comprehensive understanding of the uniqueness and stability of the solution as well as state-of-the-art methods for incorporating prior information into the inverse solver algorithms.

Personnel

Professor Nuutti  Hyvönen
Professor
Nuutti Hyvönen
M307 
Senior University Lecturer Harri  Hakula
Senior University Lecturer
Harri Hakula
M311 
Doctoral Candidate Lauri  Mustonen
Doctoral Candidate
Lauri Mustonen
M329 

Research topics

Diffuse tomography

The objective of diffuse tomography is to deduce information about the internal structure of a body from observations of diffuse fields at its boundary. The two main applications are

Electrical impedance tomography (EIT),
Diffuse optical tomography (DOT).

Wave field phenomena

A commonly used method for making inference of an inaccessible region is to use wave fields for sounding. The employed wave fields may be acoustic, electromagnetic or elastic. The research on wave fields is focused on

Inverse scattering problems,
Remote sensing and imaging.

Inverse source problems

The aim in an inverse source problem is to reconstruct a source based on measurements of the resulting field. Inverse source problems are encountered, e.g., in biomedical applications such as Electroencephalography/cardiography (EEG/ECG) and Magnetoencephalography/cardiography (MEG/MCG). Another area where these problems arise is seismology.

Statistical methods

A very generic and versatile method for investigating inverse problems is to recast them as Bayesian problems of statistical inference. Powerful methods for numerically solving very complicated inverse problems can be developed by using various Monte Carlo sampling algorithms. These methods are also related to dynamical problems that are traditionally referred to as filtering problems.

Research projects

The group has numerous domestic and international research contacts. Domestic collaboration is organized through the Finnish Inverse Problems Society.

Inverse problems links

Publications

2018 | 2017 | 2016 | 2015 | 2014 | 2013 | 2012 | 2011 | 2010 | 2009 | 2008 | 2007 | 2006 | 2005 | 2004 | 2003 | 2002 | 1999 | 1997 | 1996 | 1995 | 1994

2018

Ilmonen, Pauliina, Kaarnioja, Vesa: Generalized eigenvalue problems for meet and join matrices on semilattices, LINEAR ALGEBRA AND ITS APPLICATIONS. 536, 2018, p. 250-273. [BibTeX...]

2017

Hakula, Harri, Neilan, Michael, Ovall, Jeffrey S.: A Posteriori Estimates Using Auxiliary Subspace Techniques, JOURNAL OF SCIENTIFIC COMPUTING. 72(1), 2017, p. 97-127. [BibTeX...]

Shah, Sahas Bikram, Rasilo, Paavo, Hakula, Harri, Arkkio, Antero: Efficient finite element method to estimate eddy current loss due to random interlaminar contacts in electrical sheets, INTERNATIONAL JOURNAL OF NUMERICAL MODELLING: ELECTRONIC NETWORKS DEVICES AND FIELDS., 2017. [BibTeX...]

Hyvönen, N., Majander, H., Staboulis, S.: Compensation for geometric modeling errors by positioning of electrodes in electrical impedance tomography, Inverse Problems. 33(3), 2017. [BibTeX...]

Hyvönen, N., Kaarnioja, V., Mustonen, L., Staboulis, S.: Polynomial collocation for handling an inaccurately known measurement configuration in electrical impedance tomography, SIAM JOURNAL ON APPLIED MATHEMATICS. 77(1), 2017, p. 202-223. [BibTeX...]

2016

Mustonen, Lauri: Numerical study of a parametric parabolic equation and a related inverse boundary value problem, Inverse Problems. 32(10), 2016. [BibTeX...]

Hannukainen, A., Hyvönen, N., Majander, H., Tarvainen, T.: Efficient inclusion of total variation type priors in quantitative photoacoustic tomography, SIAM JOURNAL ON IMAGING SCIENCES. 9(3), 2016, p. 1132-1153. [BibTeX...]

Hannukainen, A., Harhanen, L., Hyvönen, N., Majander, H.: Edge-promoting reconstruction of absorption and diffusivity in optical tomography, Inverse Problems. 32(1), 2016. [BibTeX...]

2015

Hame, Lauri, Hakula, Harri: A Maximum Cluster Algorithm for Checking the Feasibility of Dial-A-Ride Instances, TRANSPORTATION SCIENCE. 49(2), 2015, p. 295-310. [BibTeX...]

Hakula, H., Kaarnioja, V., Laaksonen, M.: Approximate methods for stochastic eigenvalue problems, APPLIED MATHEMATICS AND COMPUTATION.(267), 2015, p. 664-681. [BibTeX...]

Hyvönen, Nuutti, Leinonen, Matti: Stochastic Galerkin finite element method with local conductivity basis for electrical impedance tomography, SIAM/ASA Journal on Uncertainty Quantification. 3(1), 2015, p. 998-1019. [BibTeX...]

Hakula, Harri, Laaksonen, Mikael: Hybrid Stochastic Finite Element Method for Mechanical Vibration Problems, Shock and Vibration.(2015), 2015, p. 812069. [BibTeX...]

Chesnel, Lucas, Hyvönen, Nuutti, Staboulis, Stratos: Construction of invisible conductivity perturbations for the point electrode model in electrical impedance tomography, SIAM JOURNAL ON APPLIED MATHEMATICS. 75(5), 2015, p. 2093-2109. [BibTeX...]

Harhanen, Lauri, Hyvönen, Nuutti, Majander, Helle, Staboulis, Stratos: Edge-enhancing reconstruction algorithm for three-dimensional electrical impedance tomography, SIAM JOURNAL ON SCIENTIFIC COMPUTING. 37(1), 2015, p. B60-B78. [BibTeX...]

2014

Hakula, Harri: hp-boundary layer mesh sequences with applications to shell problems, COMPUTERS AND MATHEMATICS WITH APPLICATIONS. 67(4), 2014, p. 899-917. [BibTeX...]

Hakula, Harri, Tuominen, Tomi: On hp-adaptive solution of thin shells of revolution, IOP CONFERENCE SERIES: MATERIALS SCIENCE AND ENGINEERING. 10(1), 2014. [BibTeX...]

Hyvönen, Nuutti, Seppänen, Aku, Staboulis, Stratos: Optimizing electrode positions in electrical impedance tomography, SIAM JOURNAL ON APPLIED MATHEMATICS. 74(6), 2014, p. 1831-1851. [BibTeX...]

Kettunen, Henrik, Chesnel, Lucas, Hakula, Harri, Wallén, Henrik, Sihvola, Ari: Surface plasmon resonances on cones and wedges, 8th International Congress on Advanced Electromagnetic Materials in Microwaves and Optics (Metamaterials 2014), Copenhagen, Denmark, 24-30 August 2014., p. 163-165. [BibTeX...]

Hakula, Harri, Hyvönen, Nuutti, Leinonen, Matti: Reconstruction algorithm based on stochastic Galerkin finite element method for electrical impedance tomography, Inverse Problems. 30(6), 2014, p. 065006. [BibTeX...]

Leinonen, Matti, Hakula, Harri, Hyvonen, Nuutti: Application of stochastic Galerkin FEM to the complete electrode model of electrical impedance tomography, JOURNAL OF COMPUTATIONAL PHYSICS. 269(1), 2014, p. 181-200. [BibTeX...]

2013

Hakula, Harri, Tuominen, Tomi: Mathematica implementation of the high order finite element method applied to eigenproblems, COMPUTING: ARCHIVES FOR SCIENTIFIC COMPUTING. 95(SUPPL.1), 2013. [BibTeX...]

Häme, Lauri, Hakula, Harri: Dynamic journeying under uncertainty, EUROPEAN JOURNAL OF OPERATIONAL RESEARCH. 225(3), 2013, p. 455-471. [BibTeX...]

Hame, Lauri, Hakula, Harri: Dynamic journeying in scheduled networks, IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS. 14(1), 2013, p. 360-369. [BibTeX...]

Darde, Jeremi, Hannukainen, Antti, Hyvönen, Nuutti: An Hdiv-based mixed quasi-reversibility method for solving elliptic Cauchy problems, SIAM JOURNAL ON NUMERICAL ANALYSIS. 51(4), 2013, p. 2123-2148. [BibTeX...]

Darde, Jeremi, Hyvönen, Nuutti, Seppänen, Aku, Staboulis, Stratos: Simultaneous recovery of admittivity and body shape in electrical impedance tomography: An experimental evaluation, Inverse Problems. 29(8), 2013. [BibTeX...]

Häme, Lauri, Hakula, Harri: Routing by ranking A link analysis method for the constrained dial-A-ride problem, Operations Research Letters. 41(6), 2013, p. 664-669. [BibTeX...]

Hakula, Harri, Rasila, Antti, Vuorinen, Matti: Computation of exterior moduli of quadrilaterals, ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS.(40), 2013, p. 436-451. [BibTeX...]

Hyvönen, Nuutti, Nandakumaran, Akambadath K., Varma, Hari M., Vasu, Ram M.: Generalized eigenvalue decomposition of the field autocorrelation in correlation diffusion of photons in turbid media, MATHEMATICAL METHODS IN THE APPLIED SCIENCES. 36(11), 2013, p. 1447-1458. [BibTeX...]

Griesmaier, Roland, Hyvönen, Nuutti, Seiskari, Otto: A note on analyticity properties of far field patterns, INVERSE PROBLEMS AND IMAGING. 7(2), 2013, p. 491-498. [BibTeX...]

Darde, Jeremi, Hyvönen, Nuutti, Seppänen, Aku, Staboulis, Stratos: Simultaneous reconstruction of outer boundary shape and admittivity distribution in electrical impedance tomography, SIAM JOURNAL ON IMAGING SCIENCES. 6(1), 2013, p. 176-198. [BibTeX...]

2012

Hanke, Martin, Harhanen, Lauri, Hyvönen, Nuutti, Schweickert, Eva: Convex source support in three dimensions, BIT NUMERICAL MATHEMATICS. 52(1), 2012, p. 45-63. [BibTeX...]

Hakula, Harri, Hyvönen, Nuutti, Tuominen, Toni: On the hp-adaptive solution of complete electrode model forward problems of electrical impedance tomography, JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS. 236(236), 2012, p. 4645-4659. [BibTeX...]

Hakula, Harri, Quach, Tri, Rasila, Antti: Conjugate function method for numerical conformal mappings, JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS.(237), 2012, p. 340-353. [BibTeX...]

Hyvönen, Nuutti, Seiskari, Otto: Detection of multiple inclusions from sweep data of electrical impedance tomography, Inverse Problems.(28), 2012. [BibTeX...]

Darde, Jeremi, Hakula, Harri, Hyvönen, Nuutti, Staboulis, Stratos: Fine-tuning electrode information in electrical impedance tomography, INVERSE PROBLEMS AND IMAGING. 6(6), 2012, p. 399-421. [BibTeX...]

Hyvönen, Nuutti, Piiroinen, Petteri, Seiskari, Otto: Point measurements for a Neumann-to-Dirichlet map and the Calderon problem in the plane, SIAM JOURNAL ON MATHEMATICAL ANALYSIS. 44(5), 2012, p. 3526-3536. [BibTeX...]

2011

Hanke, Martin, Hyvönen, Nuutti, Reusswig, Stefanie: Convex backscattering support in electric impedance tomography, Numerische Mathematik. 117(2), 2011, p. 373-396. [BibTeX...]

Hakula, Harri, Rasila, Antti, Vuorinen, Matti: On Moduli of Rings and Quadrilaterals: Algorithms and Experiments, SIAM JOURNAL ON SCIENTIFIC COMPUTING. 33(1), 2011, p. 279-302. [BibTeX...]

Hanke, Martin, Hyvönen, Nuutti, Reusswig, Stefanie: Erratum: An inverse backscatter problem for electric impedance tomography, SIAM JOURNAL ON MATHEMATICAL ANALYSIS. 43(3), 2011, p. 1495-1497. [BibTeX...]

Hanke, Martin, Harrach, Bastian, Hyvönen, Nuutti: Justification of point electrode models in electrical impedance tomography, MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES. 21, 2011, p. 13951413. [BibTeX...]

Häme, Lauri, Hyytiä, Esa, Hakula, Harri: The Traveling Salesman Problem with Differential Neighborhoods, The 27th European Workshop on Computational Geometry (EuroCG) , March 28-30, 2011, Antoniushaus Morschach, Switzerland.., p. 51-54. [BibTeX...]

Havola, Linda, Majander, Helle, Hakula, Harri, Alestalo, Pekka, Rasila, Antti: Aktivoiviin opetusmenetelmiin perustuvat matematiikan opetuskokeilut Aalto-yliopistossa, Tuovi 9: Interaktiivinen tekniikka koulutuksessa 2011 -konferenssin tutkijatapaamisen artikkelit., p. 5-9. [BibTeX...]

Varma, Hari M, Mohanan, Kuriyakkatil P., Hyvönen, Nuutti, Nandakumaran, Akambadath K., Vasu, Ram M.: Ultrasound-modulated optical tomography: recovery of amplitude of vibration in the insonified region from boundary measurement of light correlation, JOURNAL OF THE OPTICAL SOCIETY OF AMERICA A: OPTICS IMAGE SCIENCE AND VISION. 28, 2011, p. 2322-2332. [BibTeX...]

Hakula, Harri, Harhanen, Lauri, Hyvönen, Nuutti: Sweep data of electrical impedance tomography, Inverse Problems. 27(11), 2011, p. 115006. [BibTeX...]

Griesmaier, R, Hyvönen, Nuutti: A regularized Newton method for locating thin tubular conductivity inhomogeneities, Inverse Problems. 27, 2011. [BibTeX...]

2010

Hyvönen, Nuutti, Kalke, M., Lassas, Matti, Setälä, H.: Three-dimensional dental X-ray imaging by combination of panoramic and projection data, INVERSE PROBLEMS AND IMAGING. 4(2), 2010, p. 257-271. [BibTeX...]

Hyvönen, Nuutti, Karhunen, Kimmo, Seppänen, Aku: Frechet derivative with respect to the shape of an internal electrode in electrical impedance tomography, SIAM JOURNAL ON APPLIED MATHEMATICS. 70(6), 2010, p. 1878-1898. [BibTeX...]

Harhanen, Lauri, Hyvönen, Nuutti: Convex source support in half-plane, INVERSE PROBLEMS AND IMAGING. 4(3), 2010, p. 429-448. [BibTeX...]

2009

Hyvönen, Nuutti: An inverse backscatter problem for electric impedance tomography, SIAM JOURNAL ON MATHEMATICAL ANALYSIS. 41, 2009, p. 1948-1966. [BibTeX...]

Calvetti, Daniela, Hakula, Harri, Pursiainen, Sampsa, Somersalo, Erkki: Conditionally Gaussian Hypermodels for Cerebral Source Localization, SIAM JOURNAL ON IMAGING SCIENCES. 2(3), 2009, p. 879-909. [BibTeX...]

Hakula, Harri, Rasila, Antti, Vuorinen, Matti: On moduli of rings and quadrilaterals: algorithms and experiments, 2009. [BibTeX...]

Hyvönen, Nuutti: Comparison of idealized and electrode Dirichlet-to-Neumann maps in electric impedance tomography with an application to boundary determination of conductivity, Inverse Problems. 25, 2009. [BibTeX...]

Artioli, Edoardo, Beirao da Veiga, Lourenco, Hakula, Harri, Lovadina, Carlo: On the asymptotic behaviour of shells of revolution in free vibration, COMPUTATIONAL MECHANICS. 44(1), 2009, p. 45-60. [BibTeX...]

Hyvönen, Nuutti: Approximating idealized boundary data of electric impedance tomography by electrode measurements, MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES. 19, 2009, p. 1185-1202. [BibTeX...]

Hakula, Harri, Hyvönen, Nuutti: On computation of test dipoles for factorization method, BIT. 49, 2009, p. 75-91. [BibTeX...]

2008

Gebauer, Bastian, Hyvonen, Nuutti: Factorization method and inclusions of mixed type in an inverse elliptic boundary value problem, INVERSE PROBLEMS AND IMAGING. 2(3), 2008, p. 355-372. [BibTeX...]

Artioli, Edoardo, de Veiga, Lourenco Beirao, Hakula, Harri, Lovadina, Carlo: Free vibrations for some Koiter shells of revolution, APPLIED MATHEMATICS LETTERS. 21(12), 2008, p. 1245-1248. [BibTeX...]

Hanke, Martin, Hyvonen, Nuutti, Lehn, Manfred, Reusswig, Stefanie: Source supports in electrostatics, BIT NUMERICAL MATHEMATICS. 48(2), 2008, p. 245-264. [BibTeX...]

Lechleiter, A., Hyvönen, Nuutti, Hakula, Harri: The factorization method applied to the complete electrode model of impedance tomography, SIAM JOURNAL ON APPLIED MATHEMATICS. 68(4), 2008, p. 1097-1121. [BibTeX...]

Hanke, M., Hyvönen, Nuutti, Reusswig, R.: Convex source support and its application to electric impedance tomography, SIAM JOURNAL ON IMAGING SCIENCES. 1(4), 2008, p. 364-378. [BibTeX...]

Hakula, Harri, Hyvonen, Nuutti: Two noniterative algorithms for locating inclusions using one electrode measurement of electric impedance tomography, Inverse Problems. 24(5), 2008, p. 055018. [BibTeX...]

Niemi, Antti H., Pitkäranta, Juhani, Hakula, Harri: Point load on a shell, Numerical mathematics and advanced applications., p. 819-826. [BibTeX...]

Calvetti, Daniela, Hakula, Harri, Pursiainen, Sampsa, Somersalo, Erkki: Conditionally Gaussian hypermodels for source localization in brain imaging, arXiv:0811.3185., 2008. [BibTeX...]

2007

Gebauer, B., Hyvönen, Nuutti: Factorization method and irregular inclusions in electrical impedance tomography, Inverse Problems. 23, 2007, p. 2159-2170. [BibTeX...]

Hyvönen, Nuutti, Hakula, Harri, Pursiainen, Sampsa: Numerical implementation of the factorization method within the complete electrode model of electrical impedance tomography, INVERSE PROBLEMS AND IMAGING. 1(2), 2007, p. 299-317. [BibTeX...]

Hyvönen, Nuutti: Frechet derivative with respect to the shape of a strongly convex nonscattering region in optical tomography, Inverse Problems. 23, 2007, p. 2249-2270. [BibTeX...]

Hyvönen, Nuutti: Locating Transparent Regions in Optical Absorption and Scattering Tomography, SIAM JOURNAL ON APPLIED MATHEMATICS. 67, 2007, p. 1101-1123. [BibTeX...]

Hyvönen, Nuutti: Locating transparent cavities in optical absorption and scattering tomography, Workshop: Inverse problems in wave scattering organised by Mathematisches Forschungsinstitut Oberwolfach, March 4-10, 2007.. [BibTeX...]

Niemi, Antti H., Pitkäranta, Juhani, Hakula, Harri: Benchmark computations on point-loaded shallow shells: Fourier vs.FEM, Computer Methods in Applied Mechanics and Engineering. 196(4-6), 2007, p. 894-907. [BibTeX...]

Hyvönen, Nuutti: Application of the factorization method to the characterization of weak inclusions in electrical impedance tomography, ADVANCES IN APPLIED MATHEMATICS. 39(2), 2007, p. 197-221. [BibTeX...]

2006

Pursiainen, Sampsa, Hakula, Harri: A High-order Finite Element Method for Electical Impedance Tomography, PIERS Online. 2(3), 2006, p. 260-264. [BibTeX...]

2005

Niemi, Antti, Pitkäranta, Juhani, Hakula, Harri: A benchmark study: MITC4-S and boundary layer-type deformations, The 18th Nordic Seminar on Computational Mechanics, Silja Serenade, 27.-30.10.2005., p. 71-74. [BibTeX...]

Hyvönen, Nuutti: Application of a weaker formulation of the factorization method to the characterization of absorbing inclusions in optical tomography, Inverse Problems. 21, 2005, p. 1331-1342. [BibTeX...]

2004

Hyvönen, Nuutti: Complete electrode model of electrical impedance tomography: Approximation properties and characterization of inclusions, SIAM JOURNAL ON APPLIED MATHEMATICS. 64, 2004, p. 902-931. [BibTeX...]

Hyvönen, Nuutti: Characterizing inclusions in optical tomography, Inverse Problems. 20, 2004, p. 737-751. [BibTeX...]

Hyvönen, Nuutti: Diffusive tomography methods: special boundary conditions and characterization of inclusions, 2004. [BibTeX...]

Havu, Ville, Hakula, Harri: On sensitive shell under different loadings, 4th European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2004, Jyväskylä, 2004.. [BibTeX...]

2003

Havu, Ville, Hakula, Harri, Tuominen, Tomi: A benchmark study of elliptic and hyperbolic shells of revolution, 2003. [BibTeX...]

Havu, Ville, Hakula, Harri: MITC4-kuorielementin konvergenssiominaisuudet, VIII Suomen mekaniikkapäivät, Espoo 12.-13.6.2003., p. 533-539. [BibTeX...]

2002

Hyvönen, Nuutti: Analysis of optical tomography with non-scattering regions, PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY. 45, 2002, p. 257-276. [BibTeX...]

Pitkäranta, Juhani, Hakula, Harri, Havu, Ville, Malinen, Mika: Convergence of the MITC4 Shell Element, The Fifth World Congress on Computational Mechanics (WCCM V), July 7-12, Vienna, Austria.. [BibTeX...]

1999

Hakula, H.: Controlling 2D Voronoi-Segment Methods, 8th International Mesh Generation Roundtable, October 10-13,South Lake Tahoe, California., p. 221-229. [BibTeX...]

1997

Hakula, H.: High-Order Finite Element Tools for Shell Problems, 1997. [BibTeX...]

1996

Hakula, H., Pitkäranta, J.: Pinched shells of revolution: experiments on high order FEM, ICOSAHOM.95, Houston, Texas, 5-9 June 1995., p. 193-201. [BibTeX...]

Hakula, H., Leino, Y., Pitkäranta, J.: Scale resolution locking, and high-order finite element modelling of shells, Computer Methods in Applied Mechanics and Engineering. 133, 1996, p. 157-182. [BibTeX...]

Hakula, H.: Low-Dispersion Meshes for Scattering Problems, 5th International Conference on Numerical Grid Generation in Computational Field Simulations., p. 639-645. [BibTeX...]

1995

Hakula, H., Leino, Y., Pitkäranta, J.: Scale Resolution, Locking, and High-Order Finite Element Modelling of Shells, 1995. [BibTeX...]

Pitkäranta, J., Leino, Y., Hakula, H., Piila, J.: Shell deformation states and the finite element method: A benchmark study of cylindricalc shells, Computer Methods in Applied Mechanics and Engineering. 128, 1995, p. 81-121. [BibTeX...]

Hakula, H., Pitkäranta, J.: Pinched Shells of Revolution: Experiments on High Order FEM, 1995. [BibTeX...]

1994

Hakula, H.: Generating meshes for scales in shells, Numerical Grid Generation in CFD and Related Fields, Swansea, March 1994., p. 177-186. [BibTeX...]

Hakula, H., Malinen, J., Kallberg, P., Valve, P.: The finite element method applied to the exterior Helmholtz problem on the IBM SP1, Para 94, Kööpenhamina, 20-23 kesäkuu 1994., p. 262-269. [BibTeX...]

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