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 L. Busch, M. Lassas and L. Oksanen) On exponential instability of an inverse problem for the wave equation. pdf
   

2. (with H. Shahgholian) A free boundary approach to non-scattering obstacles with vanishing contrast. pdf
   

3. (with D. Johansson and J. Nurminen) Inverse problems for semilinear elliptic equations with low regularity. pdf
   

4. (with L. Oksanen and Rakesh) Rigidity in the Lorentzian Calderón problem with formally determined data. pdf
   

5. (with L. Oksanen and Rakesh) Fixed angle inverse scattering for Riemannian metrics. pdf
   

6. (with D. Johansson and J. Nurminen) Inverse problems for semilinear elliptic PDE with a general nonlinearity a(x,u). pdf
   

7. (with M. Mazzucchelli and L. Tzou) A general support theorem for analytic double fibration transforms. pdf
   

8. The Calderón problem and normal forms. pdf
   

Monographs

9. (with J. Feldman and G. Uhlmann) The Calderón problem - an introduction.
   Graduate Studies in Mathematics (to appear), AMS.
   

10. (with G. Paternain and G. Uhlmann) Geometric inverse problems, with emphasis on two dimensions.
    Monograph published by Cambridge University Press in 2023. This version is free to view and download for personal use only. pdf
    

Articles in refereed scientific journals

11. (with G. Covi and M. de Hoop) Geometrical optics for the fractional Helmholtz equation and applications to inverse problems.
    Math. Models Methods Appl. Sci. (to appear). pdf
    

12. (with M. Lassas, L. Oksanen, S. Sahoo and A. Tetlow) Coefficient determination for non-linear Schrödinger equations on manifolds.
    SIAM J. Math. Anal. (to appear). pdf
    

13. (with K. Krupchyk, S. Ma, S. Sahoo and S. St-Amant) Inverse problems for semilinear Schrödinger equations at large frequency via polynomial resolvent estimates on manifolds.
    Pure Appl. Anal. 7 (2025), no. 1, 65-100. pdf
    

14. (with P.-Z. Kow and S. Zou) Increasing resolution and instability for linear inverse scattering problems.
    J. Funct. Anal. 289 (2025), no. 1, 110923. pdf
    

15. (with S. Ma and S. Sahoo) The anisotropic Calderón problem at large fixed frequency on manifolds with invertible ray transform.
    J. London Math. Soc. 110 (2024), no. 4, e13006. pdf
    

16. (with T. Liimatainen) Applications of the Stone-Weierstrass theorem in the Calderón problem.
    Ann. Fenn. Math. 49 (2024), no. 2, 583-600. pdf
    

17. (with P.-Z. Kow and H. Shahgholian) On scattering behavior of corner domains with anisotropic inhomogeneities.
    SIAM J. Math. Anal. 56 (2024), no. 4, 4834-4853. pdf
    

18. (with G. Paternain) The non-Abelian X-ray transform on surfaces.
    J. Diff. Geom. 126 (2024), no. 3, 1185-1205. pdf
    

19. (with P.-Z. Kow and H. Shahgholian) A minimization problem with free boundary and its application to inverse scattering problems.
    Interfaces Free Bound. 26 (2024), no. 3, 415-471. pdf
    

20. (with L. Oksanen, P. Stefanov and G. Uhlmann) Inverse problems for real principal type operators.
    Amer. J. Math. 146 (2024), no. 1, 161-240. pdf
    

21. (with P.-Z. Kow, S. Larson and H. Shahgholian) Quadrature domains for the Helmholtz equation with applications to non-scattering phenomena.
    Potential Anal. 60 (2024), 387-424. pdf
    

22. (with G. Paternain) Carleman estimates for geodesic X-ray transforms.
    Ann. Sci. Éc. Norm. Supér. 56 (2023), no. 5, 1339-1380. pdf
    

23. (with G. Covi and M. de Hoop) Uniqueness in an inverse problem of fractional elasticity.
    Proc. Royal Soc. A 479 (2023), no. 2278, 20230474. pdf
    

24. (with P.-Z. Kow and H. Shahgholian) On positivity sets of Helmholtz solutions.
    Vietnam J. Math. 51 (2023), no. 4, special issue dedicated to Carlos Kenig, 985-994. pdf
    

25. (with S. Ma and L. Potenciano) Fixed angle inverse scattering for sound speeds close to constant.
    SIAM J. Math. Anal. 55 (2023), no. 4, 3420-3456. pdf
    

26. (with S. Sahoo) The linearized Calderón problem for polyharmonic operators.
    J. Diff. Eq. 360 (2023), 407-451. pdf
    

27. (with H. Schlüter) Jacobian of solutions to the conductivity equation in limited view.
    Inverse Problems 39 (2023), no. 2, 025001. pdf
    

28. (with L. Tzou) Inverse problems for semilinear elliptic PDE with measurements at a single point.
    Proc. AMS 151 (2023), 2023-2030. pdf
    

29. (with M. Lassas and T. Liimatainen) The Calderón problem for the conformal Laplacian.
    Comm. Anal. Geom. 30 (2022), no. 5, 1121-1184. pdf
    

30. (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
    

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

32. (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
    

33. (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
    

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

35. (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
    

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

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

38. (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
    

39. (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
    

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

41. (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
    

42. (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
    

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

44. (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
    

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

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

47. (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
    

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

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

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

51. (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
    

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

53. (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
    

54. (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
    

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

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

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

58. (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
    

59. (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
    

60. (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
    

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

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

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

64. (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
    

65. (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
    

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

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

68. (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
    

69. (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
    

70. (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
    

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

72. (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
    

73. (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
    

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

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

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

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

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

79. (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
    

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

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

82. (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
    

83. (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
    

84. (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
    

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

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

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

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

89. (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
    

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

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

92. (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
    

93. (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
    

94. (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
    

95. (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
    

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

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

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

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

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

101. (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
     

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

103. (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
     

104. 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

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

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

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

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

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

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

Chapters in books and other compilations

111. On geometric inverse problems and microlocal analysis.
     Chapter in Microlocal analysis and inverse problems in tomography and geometry (edited by E. Quinto, P. Stefanov and G. Uhlmann), Radon Series on Computational and Applied Mathematics 30, de Gruyter, 2024. pdf
     

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

113. 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
     

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

115. (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

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

117. (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
     

118. (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
     

119. 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
     

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

121. (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
     

122. (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
     

123. (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
     

124. (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
     

125. (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
     

126. (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
     

127. (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
     

128. (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