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**Image reconstruction from projections. The fundamentals of computerized tomography.**
*(English)*
Zbl 0538.92005

Computer Science and Applied Mathematics. New York etc.: Academic Press (A Subsidiary of Harcourt Brace Jovanovich, Publishers). XIV, 316 p. $ 29.50 (1980).

From the preface: The problem of image reconstruction from projections has arisen independently in a large number of scientific fields. An important version of the problem in medicine is that of obtaining the density distribution within the human body from multiple x-ray projections. This process is referred to as computerized tomography; it has revolutionized diagnostic radiology over the past decade.

This book is devoted to the fundamentals of this field. Its topic is the computational and mathematical procedures underlying the data collection, image reconstruction, and image display in the practice of computerized tomography. It is written from the point of view of the practitioner: points of implementation and application are carefully discussed and illustrated. The major emphasis of the book is on reconstruction methods; these are thoroughly surveyed.

Contents: (1) Introduction. (2) An overview of the process of computerized tomography (CT). (3) Physical problems associated with data collection in CT. (4) Computer simulation of data collection in CT. (5) Data collection and reconstruction of the head phantom under various assumptions. (6) Basic concepts of reconstruction algorithms. (7) Backprojection. (8) Convolution method for parallel beams. (9) Other transform methods for parallel beams. (10) Convolution methods for divergent beams. (11) The algebraic reconstruction techniques. (12) Quadratic optimization methods. (13) Noniterative series expansion methods. (14) Truly three-dimensional reconstruction. (15) Three- dimensional display of organs. (16) Mathematical background. References.

This book is devoted to the fundamentals of this field. Its topic is the computational and mathematical procedures underlying the data collection, image reconstruction, and image display in the practice of computerized tomography. It is written from the point of view of the practitioner: points of implementation and application are carefully discussed and illustrated. The major emphasis of the book is on reconstruction methods; these are thoroughly surveyed.

Contents: (1) Introduction. (2) An overview of the process of computerized tomography (CT). (3) Physical problems associated with data collection in CT. (4) Computer simulation of data collection in CT. (5) Data collection and reconstruction of the head phantom under various assumptions. (6) Basic concepts of reconstruction algorithms. (7) Backprojection. (8) Convolution method for parallel beams. (9) Other transform methods for parallel beams. (10) Convolution methods for divergent beams. (11) The algebraic reconstruction techniques. (12) Quadratic optimization methods. (13) Noniterative series expansion methods. (14) Truly three-dimensional reconstruction. (15) Three- dimensional display of organs. (16) Mathematical background. References.

### MSC:

92C50 | Medical applications (general) |

92-02 | Research exposition (monographs, survey articles) pertaining to biology |

68T10 | Pattern recognition, speech recognition |

00A69 | General applied mathematics |

68U99 | Computing methodologies and applications |