TY - CHAP

T1 - Looking Ahead

AU - Hansen, Per Christian

AU - Jørgensen, Jakob Sauer

AU - Lionheart, William R.B.

PY - 2021

Y1 - 2021

N2 - Tomographic imaging is enjoying an explosion of growth as new measurement technology opens up novel tomographic modalities, with higher resolution in space and time, as well as adding extra dimensions with spectral, polarization, phase contrast, and diffraction measurement techniques. Energy-resolved detectors for X-rays, e.g., open up new methods that make use of scattered radiation, with some Compton tomography modalities resulting from integrals of volume images over surfaces instead of straight lines [174]. Problems in multistatic radar and seismic imaging result in weighted integrals over ellipses and ellipsoids [124]. While analytical methods are available for some generalizations of the Radon transform, practical problems typically have limited and noisy data. Once a discretization of the forward problem has been implemented generalizing the ideas in Chapter 9, regularized solutions can be obtained using the methods of Chapters 12 and 13.

AB - Tomographic imaging is enjoying an explosion of growth as new measurement technology opens up novel tomographic modalities, with higher resolution in space and time, as well as adding extra dimensions with spectral, polarization, phase contrast, and diffraction measurement techniques. Energy-resolved detectors for X-rays, e.g., open up new methods that make use of scattered radiation, with some Compton tomography modalities resulting from integrals of volume images over surfaces instead of straight lines [174]. Problems in multistatic radar and seismic imaging result in weighted integrals over ellipses and ellipsoids [124]. While analytical methods are available for some generalizations of the Radon transform, practical problems typically have limited and noisy data. Once a discretization of the forward problem has been implemented generalizing the ideas in Chapter 9, regularized solutions can be obtained using the methods of Chapters 12 and 13.

U2 - 10.1137/1.9781611976670.ch14

DO - 10.1137/1.9781611976670.ch14

M3 - Book chapter

SN - 978-1-61197-666-3

T3 - Fundamentals of Algorithms

SP - 317

EP - 318

BT - Computed Tomography: Algorithms, Insight, and Just Enough Theory

A2 - Hansen, Per Christian

A2 - Jørgensen, Jakob Sauer

A2 - Lionheart, William R. B.

PB - Society for Industrial and Applied Mathematics

ER -