University of Jyväskylä   Department of Mathematics and Statistics
Faculty of Mathematics and Science

 

Mikko Salo

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Accepted manuscript or preprint versions of the articles may be found below in pdf form. The final versions appear in the indicated journals.

Submitted articles

  1. (with S. Sahoo) The linearized Calderón problem for polyharmonic operators. pdf

  2. (with H. Schlüter) Jacobian of solutions to the conductivity equation in limited view. pdf

  3. (with S. Ma and S. Sahoo) The anisotropic Calderón problem at large fixed frequency on manifolds with invertible ray transform. pdf

  4. (with P.-Z. Kow, S. Larson and H. Shahgholian) Quadrature domains for the Helmholtz equation with applications to non-scattering phenomena. pdf

  5. (with M. Lassas, L. Oksanen and A. Tetlow) Inverse problems for non-linear Schrödinger equations with time-dependent coefficients. pdf

  6. (with S. Ma and L. Potenciano) Fixed angle inverse scattering for sound speeds close to constant. pdf

  7. The Calderón problem and normal forms. pdf

Monographs

  1. (with G. Paternain and G. Uhlmann) Geometric inverse problems, with emphasis on two dimensions.
    Monograph to be published by Cambridge University Press. This version is free to view and download for personal use only. pdf

Articles in refereed scientific journals

  1. (with L. Oksanen, P. Stefanov and G. Uhlmann) Inverse problems for real principal type operators.
    Amer. J. Math. (to appear). pdf

  2. (with G. Paternain) The non-Abelian X-ray transform on surfaces.
    J. Diff. Geom. (to appear). pdf

  3. (with G. Paternain) Carleman estimates for geodesic X-ray transforms.
    Ann. Sci. Éc. Norm. Supér. (to appear). pdf

  4. (with L. Tzou) Inverse problems for semilinear elliptic PDE with measurements at a single point.
    Proc. AMS (to appear). pdf

  5. (with M. Lassas and T. Liimatainen) The Calderón problem for the conformal Laplacian.
    Comm. Anal. Geom. (to appear). pdf

  6. (with S. Lu and B. Xu) Increasing stability in the linearized inverse Schrödinger potential problem with power type nonlinearities.
    Inverse Problems 38 (2022), no. 6, 065009. pdf

  7. (with K. Krupchyk and T. Liimatainen) Linearized Calderón problem and exponentially accurate quasimodes for analytic manifolds.
    Adv. Math. 403 (2022), 108362. pdf

  8. (with S. Ma) Fixed angle inverse scattering in the presence of a Riemannian metric.
    J. Inverse Ill-posed Probl. 30 (2022), no, 4, 495-520. pdf

  9. (with T. Liimatainen, Y.-H. Lin and T. Tyni) Inverse problems for elliptic equations with fractional power type nonlinearities.
    J. Diff. Eq. 306 (2022), 189-219. pdf

  10. (with H. Koch and A. Rüland) On instability mechanisms for inverse problems.
    Ars Inveniendi Analytica (2021), no. 7, 93 pp. pdf

  11. (with H. Shahgholian) Free boundary methods and non-scattering phenomena.
    Res. Math. Sci. 8 (2021), special issue "Transmission eigenvalues and related spectral problems in scattering theory", 58. pdf

  12. (with C. Meroño and L. Potenciano) The fixed angle scattering problem with a first order perturbation.
    Ann. Henri Poincaré 22 (2021), 3699-3746. pdf

  13. (with G. Paternain) A sharp stability estimate for tensor tomography in non-positive curvature.
    Math. Z. 298 (2021), 1323-1344. pdf

  14. (with M. Lassas, T. Liimatainen and Y.-H. Lin) Partial data inverse problems and simultaneous recovery of boundary and coefficients for semilinear elliptic equations.
    Rev. Mat. Iberoamericana 37 (2021), no. 4, 1553-1580. pdf

  15. (with M. Lassas, T. Liimatainen and Y.-H. Lin) Inverse problems for elliptic equations with power type nonlinearities.
    J. Math. Pures Appl. 145 (2021), 44-82. pdf

  16. (with Rakesh) Fixed angle inverse scattering for almost symmetric or controlled perturbations.
    SIAM J. Math. Anal. 52 (2020), no. 6, 5467-5499. pdf

  17. (with D. Dos Santos Ferreira, Y. Kurylev, M. Lassas and T. Liimatainen) The linearized Calderón problem in transversally anisotropic geometries.
    Int. Math. Res. Not. (2020), no. 22, 8729-8765. pdf

  18. (with P. Angulo, D. Faraco and L. Guijarro) Limiting Carleman weights and conformally transversally anisotropic manifolds.
    Trans. Amer. Math. Soc. 373 (2020), 5171-5197. pdf

  19. Applications of microlocal analysis in inverse problems.
    Mathematics 8 (2020), no. 7, 1184. pdf

  20. (with T. Ghosh, A. Rüland and G. Uhlmann) Uniqueness and reconstruction for the fractional Calderón problem with a single measurement.
    J. Funct. Anal. 279 (2020), no. 1, 108505. pdf

  21. (with Rakesh) The fixed angle scattering problem and wave equation inverse problems with two measurements.
    Inverse Problems 36 (2020), 035005. pdf

  22. (with T. Ghosh and G. Uhlmann) The Calderón problem for the fractional Schrödinger equation.
    Analysis & PDE 13 (2020), no. 2, 455-475. pdf

  23. (with C. Meroño and L. Potenciano) Resolvent estimates for the magnetic Schrödinger operator in dimension n ≥ 2.
    Rev. Math. Complutense 33 (2020), 619-641. pdf

  24. (with M. Lassas and T. Liimatainen) The Poisson embedding approach to the Calderón problem.
    Math. Annalen 377 (2020), 19-67. pdf

  25. (with A. Rüland) The fractional Calderón problem: low regularity and stability.
    Nonlinear Analysis 193 (2020), special issue "Nonlocal and Fractional Phenomena", 111529. pdf

  26. (with A. Rüland) Quantitative approximation properties for the fractional heat equation.
    Math. Control Relat. Fields 10 (2020), no. 1, 1-26. pdf

  27. (with J. Ilmavirta and J. Lehtonen) Geodesic X-ray tomography for piecewise constant functions on nontrapping manifolds.
    Math. Proc. Cambridge Philos. Soc. 168 (2020), no. 1, 29-41. pdf

  28. (with G. Paternain, G. Uhlmann and H. Zhou) The geodesic X-ray transform with matrix weights.
    Amer. J. Math. 141 (2019), 1707-1750. pdf

  29. (with B. Harrach and V. Pohjola) Dimension bounds in monotonicity methods for the Helmholtz equation.
    SIAM J. Math. Anal. 51 (2019), no. 4, 2995-3019. pdf

  30. (with C. Guillarmou and L. Tzou) The linearized Calderón problem on complex manifolds.
    Acta Math. Sinica 35 (2019), special issue in honor of Carlos Kenig, no. 6, 1043-1056. pdf

  31. (with A. Rüland) Quantitative Runge approximation and inverse problems.
    Int. Math. Res. Not. (2019), no. 20, 6216-6234. pdf

  32. (with B. Harrach and V. Pohjola) Monotonicity and local uniqueness for the Helmholtz equation.
    Analysis & PDE 12 (2019), no. 7, 1741-1771. pdf

  33. (with A. Rüland) Exponential instability in the fractional Calderón problem.
    Inverse Problems 34 (2018), no. 4, 045003. pdf

  34. (with T. Brander, B. Harrach and M. Kar) Monotonicity and enclosure methods for the p-Laplace equation.
    SIAM J. Appl. Math. 78 (2018), no. 2, 742-758. pdf

  35. (with J. Lehtonen and J. Railo) Tensor tomography on Cartan-Hadamard manifolds.
    Inverse Problems 34 (2018), special issue: 100 years of the Radon transform, no. 4, 044004. pdf

  36. (with F. Chung, P. Ola and L. Tzou) Partial data inverse problems for Maxwell equations via Carleman estimates.
    Ann. Inst. H. Poincaré Anal. Non Linéaire 35 (2018), no. 3, 605-624. pdf

  37. (with L. Päivärinta and E. Vesalainen) Strictly convex corners scatter.
    Rev. Mat. Iberoamericana 33 (2017), no. 4, 1369-1396. pdf

  38. (with V. Julin and T. Liimatainen) p-harmonic coordinates for Hölder metrics and applications.
    Comm. Anal. Geom. 25 (2017), no. 2, 395-430. pdf

  39. (with F. Chung and L. Tzou) Partial data inverse problems for the Hodge Laplacian.
    Analysis & PDE 10 (2017), no. 1, 43-93. pdf

  40. (with C. Guo and M. Kar) Inverse problems for p-Laplace type equations under monotonicity assumptions.
    RIMUT 48 (2016), special issue in honor of Giovanni Alessandrini, 79-99. pdf

  41. (with D. Dos Santos Ferreira, Y. Kurylev and M. Lassas) The Calderón problem in transversally anisotropic geometries.
    J. Eur. Math. Soc. 18 (2016), no. 11, 2579-2626. pdf

  42. (with T. Liimatainen) Local gauge conditions for ellipticity in conformal geometry.
    Int. Math. Res. Not. (2016), no. 13, 4058-4077. pdf

  43. (with J. Ilmavirta) Broken ray transform on a Riemann surface with a convex obstacle.
    Comm. Anal. Geom. 24 (2016), no. 2, 379-408. pdf

  44. (with C. Guillarmou, G. Paternain and G. Uhlmann) The X-ray transform for connections in negative curvature.
    Comm. Math. Phys. 343 (2016), no. 1, 83-127. pdf

  45. (with G. Hu and E. Vesalainen) Shape identification in inverse medium scattering problems with a single far-field pattern.
    SIAM J. Math. Anal. 48 (2016), no. 1, 152-165. pdf

  46. (with G. Paternain and G. Uhlmann) Invariant distributions, Beurling transforms and tensor tomography in higher dimensions.
    Math. Ann. 363 (2015), no. 1, 305-362. pdf

  47. (with T. Brander and M. Kar) Enclosure method for the p-Laplace equation.
    Inverse Problems 31 (2015), 045001. pdf

  48. (with M. Lassas and L. Tzou) Inverse problems and invisibility cloaking for FEM models and resistor networks.
    Math. Models Methods Appl. Sci. 25 (2015), no. 2, 309-342. pdf

  49. (with G. Paternain and G. Uhlmann) On the range of the attenuated ray transform for unitary connections.
    Int. Math. Res. Not. (2015), no. 4, 873-897. pdf

  50. (with P. Caro) Stability of the Calderón problem in admissible geometries.
    Inverse Probl. Imaging 8 (2014), no. 4, 939-957. pdf

  51. (with T. Liimatainen) n-harmonic coordinates and the regularity of conformal mappings.
    Math. Res. Lett. 21 (2014), no. 2, 341-361. pdf

  52. (with G. Paternain and G. Uhlmann) Spectral rigidity and invariant distributions on Anosov surfaces.
    J. Diff. Geom. 98 (2014), no. 1, 147-181. pdf

  53. (with C. Kenig) Recent progress in the Calderón problem with partial data.
    Contemp. Math. 615 (2014), 193-222. pdf

  54. (with G. Paternain and G. Uhlmann) Tensor tomography: progress and challenges.
    Chinese Ann. Math. Ser. B 35 (2014), no. 3, 399-428. pdf

  55. (with D. Dos Santos Ferreira and C. Kenig) On L^p resolvent estimates for Laplace-Beltrami operators on compact manifolds.
    Forum Math. 26 (2014), no. 3, 815-849. pdf

  56. (with C. Kenig) The Calderón problem with partial data on manifolds and applications.
    Analysis & PDE 6 (2013), no. 8, 2003-2048. pdf

  57. (with G. Paternain and G. Uhlmann) Tensor tomography on surfaces.
    Invent. Math. 193 (2013), no. 1, 229-247. pdf

  58. (with D. Dos Santos Ferreira and C. Kenig) Determining an unbounded potential from Cauchy data in admissible geometries.
    Comm. PDE 38 (2013), no. 1, 50-68. pdf

  59. (with J. Chen, G. Zhao, E. Rahtu and M. Pietikäinen) Automatic dynamic texture segmentation using local descriptors and optical flow.
    IEEE Trans. Image Processing 22 (2013), no. 1, 326-339. pdf

  60. (with G. Paternain and G. Uhlmann) The attenuated ray transform for connections and Higgs fields.
    Geom. Funct. Anal. 22 (2012), no. 5, 1460-1489. pdf

  61. (with T. Liimatainen) Nowhere conformally homogeneous manifolds and limiting Carleman weights.
    Inverse Probl. Imaging 6 (2012), no. 3, 523-530. pdf

  62. (with X. Zhong) An inverse problem for the p-Laplacian: boundary determination.
    SIAM J. Math. Anal. 44 (2012), no. 4, 2474-2495. pdf

  63. (with C. Kenig and G. Uhlmann) Reconstructions from boundary measurements on admissible manifolds.
    Inverse Probl. Imaging 5 (2011), no. 4, 859-877. pdf

  64. (with G. Uhlmann) The attenuated ray transform on simple surfaces.
    J. Diff. Geom. 88 (2011), no. 1, 161-187. pdf

  65. (with C. Guillarmou and L. Tzou) Inverse scattering at fixed energy on surfaces with Euclidean ends.
    Comm. Math. Phys. 303 (2011), no. 3, 761-784. pdf

  66. (with C. Kenig and G. Uhlmann) Inverse problems for the anisotropic Maxwell equations.
    Duke Math. J. 157 (2011), no. 2, 369-419. pdf

  67. (with L. Päivärinta and G. Uhlmann) Inverse scattering for the magnetic Schrödinger operator.
    J. Funct. Anal. 259 (2010), no. 7, 1771-1798. pdf

  68. (with V. Brytik and M. de Hoop) Sensitivity analysis of wave-equation tomography: a multi-scale approach.
    J. Fourier Anal. Appl. 16 (2010), no. 4, 544-589. pdf

  69. (with L. Tzou) Inverse problems with partial data for a Dirac system: a Carleman estimate approach.
    Adv. Math. 225 (2010), no. 1, p. 487-513. pdf

  70. (with P. Caro and P. Ola) Inverse boundary value problem for Maxwell equations with local data.
    Comm. PDE 34 (2009), no. 11, p. 1425-1464. pdf

  71. (with D. Dos Santos Ferreira, C. Kenig, and G. Uhlmann) Limiting Carleman weights and anisotropic inverse problems.
    Invent. Math. 178 (2009), no. 1, p. 119-171. pdf

  72. (with L. Tzou) Carleman estimates and inverse problems for Dirac operators.
    Math. Ann. 344 (2009), no. 1, p. 161-184. pdf

  73. Stability for solutions of wave equations with C^{1,1} coefficients.
    Inverse Probl. Imaging 1 (2007), no. 3, p. 537-556. pdf

  74. (with K. Knudsen) Determining nonsmooth first order terms from partial boundary measurements.
    Inverse Probl. Imaging 1 (2007), no. 2, p. 349-369. pdf

  75. Semiclassical pseudodifferential calculus and the reconstruction of a magnetic field.
    Comm. PDE 31 (2006), no. 11, p. 1639-1666. pdf

  76. (with J.-N. Wang) Complex spherical waves and inverse problems in unbounded domains.
    Inverse Problems 22 (2006), no. 6, p. 2299-2309. pdf

  77. (with E. Rahtu and J. Heikkilä) A new convexity measure based on a probabilistic interpretation of images.
    IEEE Trans. Pattern Analysis and Machine Intelligence 28 (2006), no. 9, p. 1501-1512. pdf

  78. (with R. Brown) Identifiability at the boundary for first-order terms.
    Appl. Anal. 85 (2006), no. 6-7, p. 735-749. pdf

  79. (with E. Rahtu and J. Heikkilä) Affine invariant pattern recognition using Multiscale Autoconvolution.
    IEEE Trans. Pattern Analysis and Machine Intelligence 27 (2005), no. 6, p. 908-918. pdf

  80. Inverse problems for nonsmooth first order perturbations of the Laplacian.
    Ann. Acad. Sci. Fenn. Math. Diss. 139 (2004), 67 pp. pdf

Articles in other scientific journals

  1. Rungen lause ja sovelluksia inversio-ongelmiin. (in Finnish)
    Arkhimedes 3 (2018). pdf

  2. On the work of Joonas Ilmavirta. (translated in Polish)
    Wiadomosci Matematyczne, to appear. pdf

  3. Konformigeometrian mittaehtoja. (in Finnish)
    Suomalaisen Tiedeakatemian vuosikirja (2015). pdf

  4. Matka maapallon keskipisteeseen - sädemuunnosten matematiikkaa. (in Finnish)
    Arkhimedes 1-2 (2014), p. 12-18. pdf

  5. Ihmisen uudet silmät - käänteisten ongelmien matematiikkaa. (in Finnish)
    Solmu 3 (2011), p. 28-30. pdf

  6. Inversio-ongelmat - matematiikkaa ja sen sovelluksia. (in Finnish)
    Arkhimedes 5 (2006), p. 20-25. pdf

Chapters in books and other compilations

  1. Distributions and Fourier transform.
    Chapter in Encyclopedia of Applied and Computational Mathematics (edited by B. Engquist), Springer-Verlag, 2015. pdf

  2. The Calderón problem on Riemannian manifolds.
    Chapter in Inverse Problems and Applications: Inside Out II (edited by G. Uhlmann), MSRI Publications, Cambridge University Press, 2012. pdf

  3. Töissä tiedeyhteisössä. (in Finnish)
    Chapter in Letters to a young researcher (edited by M. Paso), Finnish Academy of Science and Letters, 2011. pdf

  4. (with M. Lassas and G. Uhlmann) Wave imaging.
    Chapter in Handbook of Mathematical Methods in Imaging (edited by O. Scherzer), Springer-Verlag, 2011. pdf

Articles in refereed conference proceedings

  1. The fractional Calderón problem.
    Journées équations aux dérivées partielles (2017), Exp. No. 7, 8 p. pdf

  2. (with E. Rahtu, J. Kannala, and J. Heikkilä) Segmenting salient objects from images and videos.
    Proc. European Conference on Computer Vision, ECCV 2010, Lecture Notes in Computer Science 6315, p. 366-379. pdf

  3. (with E. Rahtu and J. Heikkilä) Compressing sparse feature vectors using random ortho-projections.
    Proc. International Conference on Pattern Recognition, ICPR 2010, p. 1397-1400. pdf

  4. Inverse boundary value problems for the magnetic Schrödinger equation.
    Proc. Inverse Problems in Applied Sciences - Towards Breakthrough (Sapporo 2006), J. Phys Conf. Series 73 (2007) 012020. pdf

  5. (with E. Rahtu and J. Heikkilä) Affine registration using multiscale approach.
    Proc. Finnish Signal Processing Symposium, FINSIG 2007. pdf

  6. (with E. Rahtu and J. Heikkilä) Nonlinear functionals in the construction of multiscale affine invariants.
    Proc. Scandinavian Conference on Image Analysis, SCIA 2007, p. 482-491. pdf

  7. (with E. Rahtu and J. Heikkilä) Multiscale autoconvolution histograms for affine invariant pattern recognition.
    Proc. British Machine Vision Conference, BMVC 2006, vol. 3, p. 1059-1068. pdf

  8. (with E. Rahtu and J. Heikkilä) A new affine invariant image transform based on ridgelets.
    Proc. British Machine Vision Conference, BMVC 2006, vol. 3, p. 1039-1048. pdf

  9. (with J. Kannala and J. Heikkilä) Algorithms for computing a planar homography from conics in correspondence.
    Proc. British Machine Vision Conference, BMVC 2006, vol. 1, p. 77-86. pdf

  10. (with E. Rahtu, J. Heikkilä, and J. Flusser) Generalized affine moment invariants for object recognition.
    Proc. International Conference on Pattern Recognition, ICPR 2006, vol. 2, p. 634-637. pdf

  11. (with E. Rahtu and J. Heikkilä) A new efficient method for producing global affine invariants.
    Proc. International Conference on Image Analysis and Processing, ICIAP 2005, p. 407-414. pdf

  12. (with J. Kannala, E. Rahtu, and J. Heikkilä) A new method for affine registration of images and point sets.
    Proc. Scandinavian Conference on Image Analysis, SCIA 2005, p. 224-234. pdf

  13. (with E. Rahtu and J. Heikkilä) Convexity recognition using Multi-Scale Autoconvolution.
    Proc. International Conference on Pattern Recognition, ICPR 2004, vol. 1, p. 692-695. pdf