Inversion of some projection matrices

Chapters in this book

1. Frontmatter I
2. CONTENTS V
3. Preface VIII
4. Acknowledgement IX
5. Image Reconstruction of Celestial Objects from a Few Strip-Integrated Projections by Lunar Occultations 1
6. Numerical study of a non-linear sound radiating inverse problem of underwater acoustics 7
7. Optical tomography of natural and artificial optical disturbances in the near terrestrial space 12
8. Some numerical experiments in tomography of scattering medium 25
9. Integral geometry 31
10. Inversion formulae for one class of multidimensional integral Volterra equations of the first kind 49
11. The Cauchy problem for /1-harmonic functions 54
12. Simultaneous determination of sounding signal and wave propagation velocity in a vertically-inhomogeneous medium 70
13. Vector tomography of plasmas using Faraday rotation 78
14. A variational approach to non-linear backprojection 82
15. Three-Dimensional Restoration of Single Photon Emission Computed Tomography Images Using the Kalman-Metz Filter 98
16. An extended Kaczmarz's method for ʅ_p minimum norm solutions 106
17. On explicit formula« for inverting the X-ray transform 117
18. Algebraic reconstructions from efficient sampling schemes in tomography 124
19. An approach to 2-D ray tracing intended for non-linear seismic tomography 138
20. Asymptotic expansions of continuous solutions of system of Volterra integral equations of the first kind 155
21. On new methods for determining static time corrections from phase velocities of surface waves 158
22. Soft A'-ray tomography on Tokamaks using flux coordinates 165
23. Ray reflection tomography: review and comments 169
24. Tomographic methods for information processing in seismology. Nonlinear version 188
25. Penalty method with internal prox-regularization for an inverse source problem 194
26. Inverse problems in single photon emission computed tomography 201
27. Application of GCV-aided Phillips-Tikhonov regularization to direction finding of magnetospheric VLF/ELF radio waves 218
28. A problem of emission tomography for a domain of small diameter 229
29. Direct and inverse problems of thermoelasticity 232
30. GCV-Aided regularizations in sparse-data computed tomography with an application to plasma imaging 235
31. Frames on the range of the Radon transform 240
32. On the stability estimation of finite-difference and differential-difference analogues of a two-dimensional integral geometry problem 246
33. Hyperfunctions and Radon transform 259
34. Inversion of some projection matrices 264
35. Interference tomography of the ocean bottom 270
36. Determination of sea bottom characteristics using acoustic field spatial dependence 274
37. An algorithm for solving a problem in elasto-electrodynamics 283
38. Three-dimensional structure of lateral heterogeneities in p-velocities in the upper mantle of the southern margin of Siberia from teleseismic data 288
39. Simultaneous determination of elastic and electromagnetic medium parameters 302
40. A modification of ART method for cone-beam tomography of high space resolution 309
41. A new approach to the problem of 3D interpolation from an arbitrary set of points 318
42. A space-time tomography algorithm for t h e five-camera soft X-ray diagnostic at the RTP Tokamak 324
43. Direct and inverse problems for system of electromagneto-elasticity equations 332
44. A Method of the numerical ray tracing for a 3D-inhomogeneous isotropic medium 336
45. Sampling and resolution in CT 343
46. Some problems of computerized tomography in the static potentials fields 355
47. Luminescent tomography of semiconductor materials 360
48. On a reconstruction formula for ray transform after discrete incomplete data given on a line 363
49. Constraction of a velocity model from seismological data 373
50. Solution of convolution integral equations of the first kind on a segment 377
51. Image reconstruction for fan beam X-ray tomography using a new integral transform pair 384