The Radon transform and local tomography.

*(English)*Zbl 0863.44001
Boca Raton, FL: CRC Press. xviii, 485 p. (1996).

The authors start by introductory chapters where they explain the contents of the book, give several physical motivations to the problems of tomography, and call again the basic definitions and properties about the Radon transform and related transforms. The main aim of the book is the theory developed by the authors which deal with the study of singularities of the Radon transform and its applications to imaging in tomography.

They give methods for finding discontinuities of functions and the sizes of the jumps of these functions across the discontinuities from local tomographic data. The methods proposed are generalized local tomography, pseudolocal tomography and geometrical tomography. They study also incomplete tomographic data and the inversion of the cone-beam data. Moreover, they discuss a multidimensional algorithm for finding discontinuities of signals from noisy discrete data, and a general test of randomness and its applications.

In this book, the authors present and discuss numerical examples which show that the algorithms for tomographic imaging proposed are of practical values.

They give methods for finding discontinuities of functions and the sizes of the jumps of these functions across the discontinuities from local tomographic data. The methods proposed are generalized local tomography, pseudolocal tomography and geometrical tomography. They study also incomplete tomographic data and the inversion of the cone-beam data. Moreover, they discuss a multidimensional algorithm for finding discontinuities of signals from noisy discrete data, and a general test of randomness and its applications.

In this book, the authors present and discuss numerical examples which show that the algorithms for tomographic imaging proposed are of practical values.

Reviewer: K.Trimeche (Tunis)

##### MSC:

44A12 | Radon transform |

92C55 | Biomedical imaging and signal processing |

65R10 | Numerical methods for integral transforms |

65R30 | Numerical methods for ill-posed problems for integral equations |

44-02 | Research exposition (monographs, survey articles) pertaining to integral transforms |