Mathematical Methods of Computerized Tomography, Fall 2008

Office Rm. Blocker 614A

Telephone (979)862-3257

E-mail: kuchment@math.tamu.edu

Home Page: http://www.math.tamu.edu/~kuchment

### Section: 601

### Time: TR 02:20PM-03:35PM

### Room: BLOC 628 or 624

### Textbook: not required. Some notes and Web links will be distributed. The recommended books will be placed on reserve in the library.

### Office hours: T & TR 9:30 - 10:30 am. Additional office hours can be arranged by appointment.

### Mathematics and physics of emerging biomedical imaging. A non-technical survey of various types of tomography (except the recently emerging ones), available online.

### Main resources on mathematics of tomography:

### Frank Natterer, The mathematics of computerized tomography, SIAM, Philadelphia, 2001. The classics of computerized tomography. (will be placed on reserve)

### Frank Natterer and Frank Wübbeling, Mathematical methods in image reconstruction, Philadelphia : Society for Industrial and Applied Mathematics, 2001. An extension to the previous book covering developments occurring since 1986. (will be placed on reserve)

### Frank Natterer's online lectures on algorithms in tomography (also available as the last chapter in [1])

### A more engineering prospective is delivered in

### Avinash C. Kak and Malcolm Slaney, Principles of Computerized Tomographic Imaging (Classics in Applied Mathematics, v. 33), SIAM, Philadelphia, PA 2001. (will be placed on reserve)

### Gabor T. Herman, Image reconstruction from projections : the fundamentals of computerized tomography, New York : Academic Press, 1980. An introductory discussion of practical and mathematical problems of tomography. (will be placed on reserve)

### A rigorous discussion of integral geometry underpinnings of several types of tomography can be found in

### Sigurdur Helgason, The Radon transform, Boston : Birkhauser, 1980. (will be placed on reserve) This is a thorough mathematical study of the properties of Radon transform.

The contents of this book coincides with the first chapter of Sigurdur Helgason's book Groups and geometric analysis : integral geometry, invariant differential operators, and spherical functions. (will be placed on reserve)### Victor Palamodov, Reconstructive integral geometry, Birkhauser 2004. A short and terse mathematical consideration of some tomography problems. More demanding in terms of the math background. (will be placed on reserve)

### I.M. Gelfand, S.G. Gindikin, M.I. Graev, Selected topics in integral geometry, AMS 2003. (will be placed on reserve)

### Andrew Markoe, Analytic Tomography, Cambridge University Press, 2006. (will be placed on reserve)

### Some novel methods are described in

### Habib Ammari, An Introduction to Mathematics of Emerging Biomedical Imaging, Springer 2008.