
-
Previous Article
On finding the surface admittance of an obstacle via the time domain enclosure method
- IPI Home
- This Issue
- Next Article
Microlocal analysis of a spindle transform
1. | Halligan Hall, 161 College Ave, Medford MA 02144, USA |
2. | Alan Turing Building, Oxford Road, Manchester, Greater Manchester M13 9PL, UK |
An analysis of the stability of the spindle transform, introduced in [
References:
[1] |
J. R. Driscoll and D. M. Healy,
Computing Fourier transforms and convolutions on the 2-sphere, Advances in Applied Mathematics, 15 (1994), 202-250.
doi: 10.1006/aama.1994.1008. |
[2] |
J. J. Duistermaat, Fourier Integral Operators, volume 130. Springer Science & Business Media, 1996. |
[3] |
R. Felea,
Composition of Fourier integral operators with fold and blowdown singularities, Communications in Partial Differential Equations, 30 (2005), 1717-1740.
doi: 10.1080/03605300500299968. |
[4] |
R. Felea, R. Gaburro and C. J. Nolan,
Microlocal analysis of SAR imaging of a dynamic reflectivity function, SIAM Journal on Mathematical Analysis, 45 (2013), 2767-2789.
doi: 10.1137/120873571. |
[5] |
A. Greenleaf and G. Uhlmann,
Estimates for singular Radon transforms and pseudodifferential operators with singular symbols, Journal of Functional Analysis, 89 (1990), 202-232.
doi: 10.1016/0022-1236(90)90011-9. |
[6] |
V. Guillemin and G. Uhlmann,
Oscillatory integrals with singular symbols, Duke Math. J, 48 (1981), 251-267.
doi: 10.1215/S0012-7094-81-04814-6. |
[7] |
L. Hörmander, The Analysis of Linear Partial Differential Operators IV: Fourier Integral Operators. Corrected reprint of the 1985 original, Springer, 1994. |
[8] |
L. Hörmander, The Analysis of Linear Partial Differential Operators. I. Distribution theory and Fourier analysis. Reprint of the second (1990) edition, Springer, Berlin, 2003.
doi: 10.1007/978-3-642-61497-2. |
[9] |
L. Hörmander, The Analysis of Linear Partial Differential Operators III, Springer, 2007.
doi: 10.1007/978-3-540-49938-1. |
[10] |
F. Marhuenda,
Microlocal analysis of some isospectral deformations, Transactions of the American Mathematical Society, 343 (1994), 245-275.
doi: 10.1090/S0002-9947-1994-1181185-0. |
[11] |
F. Natterer, The Mathematics of Computerized Tomography, SIAM, 2001.
doi: 10.1137/1.9780898719284. |
[12] |
M. K. Nguyen and T. T. Truong, Inversion of a new circular-arc radon transform for Compton scattering tomography, Inverse Problems, 26 (2010), 099802, 1 p.
doi: 10.1088/0266-5611/26/9/099802. |
[13] |
S. J. Norton,
Compton scattering tomography, Journal of Applied Physics, 76 (1994), 2007-2015.
doi: 10.1063/1.357668. |
[14] |
V. P. Palamodov, An analytic reconstruction for the Compton scattering tomography in a plane, Inverse Problems, 27 (2011), 125004, 8pp.
doi: 10.1088/0266-5611/27/12/125004. |
[15] |
R. T. Seeley,
Spherical harmonics, The American Mathematical Monthly, 73 (1966), 115-121.
doi: 10.1080/00029890.1966.11970927. |
[16] |
J. Webber and W. Lionheart, Three dimensional Compton scattering tomography, Inverse Problems, 34 (2018), arXiv: 1704.03378.
doi: 10.1088/1361-6420/aac51e. |
show all references
References:
[1] |
J. R. Driscoll and D. M. Healy,
Computing Fourier transforms and convolutions on the 2-sphere, Advances in Applied Mathematics, 15 (1994), 202-250.
doi: 10.1006/aama.1994.1008. |
[2] |
J. J. Duistermaat, Fourier Integral Operators, volume 130. Springer Science & Business Media, 1996. |
[3] |
R. Felea,
Composition of Fourier integral operators with fold and blowdown singularities, Communications in Partial Differential Equations, 30 (2005), 1717-1740.
doi: 10.1080/03605300500299968. |
[4] |
R. Felea, R. Gaburro and C. J. Nolan,
Microlocal analysis of SAR imaging of a dynamic reflectivity function, SIAM Journal on Mathematical Analysis, 45 (2013), 2767-2789.
doi: 10.1137/120873571. |
[5] |
A. Greenleaf and G. Uhlmann,
Estimates for singular Radon transforms and pseudodifferential operators with singular symbols, Journal of Functional Analysis, 89 (1990), 202-232.
doi: 10.1016/0022-1236(90)90011-9. |
[6] |
V. Guillemin and G. Uhlmann,
Oscillatory integrals with singular symbols, Duke Math. J, 48 (1981), 251-267.
doi: 10.1215/S0012-7094-81-04814-6. |
[7] |
L. Hörmander, The Analysis of Linear Partial Differential Operators IV: Fourier Integral Operators. Corrected reprint of the 1985 original, Springer, 1994. |
[8] |
L. Hörmander, The Analysis of Linear Partial Differential Operators. I. Distribution theory and Fourier analysis. Reprint of the second (1990) edition, Springer, Berlin, 2003.
doi: 10.1007/978-3-642-61497-2. |
[9] |
L. Hörmander, The Analysis of Linear Partial Differential Operators III, Springer, 2007.
doi: 10.1007/978-3-540-49938-1. |
[10] |
F. Marhuenda,
Microlocal analysis of some isospectral deformations, Transactions of the American Mathematical Society, 343 (1994), 245-275.
doi: 10.1090/S0002-9947-1994-1181185-0. |
[11] |
F. Natterer, The Mathematics of Computerized Tomography, SIAM, 2001.
doi: 10.1137/1.9780898719284. |
[12] |
M. K. Nguyen and T. T. Truong, Inversion of a new circular-arc radon transform for Compton scattering tomography, Inverse Problems, 26 (2010), 099802, 1 p.
doi: 10.1088/0266-5611/26/9/099802. |
[13] |
S. J. Norton,
Compton scattering tomography, Journal of Applied Physics, 76 (1994), 2007-2015.
doi: 10.1063/1.357668. |
[14] |
V. P. Palamodov, An analytic reconstruction for the Compton scattering tomography in a plane, Inverse Problems, 27 (2011), 125004, 8pp.
doi: 10.1088/0266-5611/27/12/125004. |
[15] |
R. T. Seeley,
Spherical harmonics, The American Mathematical Monthly, 73 (1966), 115-121.
doi: 10.1080/00029890.1966.11970927. |
[16] |
J. Webber and W. Lionheart, Three dimensional Compton scattering tomography, Inverse Problems, 34 (2018), arXiv: 1704.03378.
doi: 10.1088/1361-6420/aac51e. |













[1] |
Elena Cordero, Fabio Nicola, Luigi Rodino. Time-frequency analysis of fourier integral operators. Communications on Pure and Applied Analysis, 2010, 9 (1) : 1-21. doi: 10.3934/cpaa.2010.9.1 |
[2] |
Lorenz Kuger, Gaël Rigaud. On multiple scattering in Compton scattering tomography and its impact on fan-beam CT. Inverse Problems and Imaging, , () : -. doi: 10.3934/ipi.2022029 |
[3] |
Cécilia Tarpau, Javier Cebeiro, Geneviève Rollet, Maï K. Nguyen, Laurent Dumas. Analytical reconstruction formula with efficient implementation for a modality of Compton scattering tomography with translational geometry. Inverse Problems and Imaging, 2022, 16 (4) : 771-786. doi: 10.3934/ipi.2021075 |
[4] |
Kanghui Guo and Demetrio Labate. Sparse shearlet representation of Fourier integral operators. Electronic Research Announcements, 2007, 14: 7-19. doi: 10.3934/era.2007.14.7 |
[5] |
Raluca Felea, Romina Gaburro, Allan Greenleaf, Clifford Nolan. Microlocal analysis of borehole seismic data. Inverse Problems and Imaging, , () : -. doi: 10.3934/ipi.2022026 |
[6] |
James W. Webber, Eric L. Miller. Bragg scattering tomography. Inverse Problems and Imaging, 2021, 15 (4) : 683-721. doi: 10.3934/ipi.2021010 |
[7] |
Raluca Felea, Romina Gaburro, Allan Greenleaf, Clifford Nolan. Microlocal analysis of Doppler synthetic aperture radar. Inverse Problems and Imaging, 2019, 13 (6) : 1283-1307. doi: 10.3934/ipi.2019056 |
[8] |
Aki Pulkkinen, Ville Kolehmainen, Jari P. Kaipio, Benjamin T. Cox, Simon R. Arridge, Tanja Tarvainen. Approximate marginalization of unknown scattering in quantitative photoacoustic tomography. Inverse Problems and Imaging, 2014, 8 (3) : 811-829. doi: 10.3934/ipi.2014.8.811 |
[9] |
John C. Schotland, Vadim A. Markel. Fourier-Laplace structure of the inverse scattering problem for the radiative transport equation. Inverse Problems and Imaging, 2007, 1 (1) : 181-188. doi: 10.3934/ipi.2007.1.181 |
[10] |
Meghdoot Mozumder, Tanja Tarvainen, Simon Arridge, Jari P. Kaipio, Cosimo D'Andrea, Ville Kolehmainen. Approximate marginalization of absorption and scattering in fluorescence diffuse optical tomography. Inverse Problems and Imaging, 2016, 10 (1) : 227-246. doi: 10.3934/ipi.2016.10.227 |
[11] |
Erfang Ma. Integral formulation of the complete electrode model of electrical impedance tomography. Inverse Problems and Imaging, 2020, 14 (2) : 385-398. doi: 10.3934/ipi.2020017 |
[12] |
Dorota Bors, Andrzej Skowron, Stanisław Walczak. Systems described by Volterra type integral operators. Discrete and Continuous Dynamical Systems - B, 2014, 19 (8) : 2401-2416. doi: 10.3934/dcdsb.2014.19.2401 |
[13] |
Patricio Felmer, Alexander Quaas. Fundamental solutions for a class of Isaacs integral operators. Discrete and Continuous Dynamical Systems, 2011, 30 (2) : 493-508. doi: 10.3934/dcds.2011.30.493 |
[14] |
Hermann Brunner. On Volterra integral operators with highly oscillatory kernels. Discrete and Continuous Dynamical Systems, 2014, 34 (3) : 915-929. doi: 10.3934/dcds.2014.34.915 |
[15] |
Ahmad Al-Salman. Marcinkiewicz integral operators along twisted surfaces. Communications on Pure and Applied Analysis, 2022, 21 (1) : 159-181. doi: 10.3934/cpaa.2021173 |
[16] |
Gary Froyland, Cecilia González-Tokman, Anthony Quas. Detecting isolated spectrum of transfer and Koopman operators with Fourier analytic tools. Journal of Computational Dynamics, 2014, 1 (2) : 249-278. doi: 10.3934/jcd.2014.1.249 |
[17] |
Jorge J. Betancor, Alejandro J. Castro, Marta De León-Contreras. Variation operators for semigroups associated with Fourier-Bessel expansions. Communications on Pure and Applied Analysis, 2022, 21 (1) : 239-273. doi: 10.3934/cpaa.2021176 |
[18] |
Melody Alsaker, Benjamin Bladow, Scott E. Campbell, Emma M. Kar. Automated filtering in the nonlinear Fourier domain of systematic artifacts in 2D electrical impedance tomography. Inverse Problems and Imaging, 2022, 16 (3) : 647-671. doi: 10.3934/ipi.2021066 |
[19] |
Beatrice Bugert, Gunther Schmidt. Analytical investigation of an integral equation method for electromagnetic scattering by biperiodic structures. Discrete and Continuous Dynamical Systems - S, 2015, 8 (3) : 435-473. doi: 10.3934/dcdss.2015.8.435 |
[20] |
Daniela Calvetti, Erkki Somersalo. Microlocal sequential regularization in imaging. Inverse Problems and Imaging, 2007, 1 (1) : 1-11. doi: 10.3934/ipi.2007.1.1 |
2021 Impact Factor: 1.483
Tools
Metrics
Other articles
by authors
[Back to Top]