Carlos A. Berenstein

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Professor, Mathematics and the Institute for Systems Research

Carlos Berenstein received his Licenciado en Matematicas in 1966 from the University of Buenos Aires. In 1969 and 1970 he was awarded his M.S. and Ph.D. degrees from New York University.

Carlos Berenstein was an Instructor at the University of Buenos Aires 1964 to 1965, and a Research Fellow at CNICT (Buenos Aires) in 1966. He worked as an Assistant Professor at Harvard University from 1970 to 1973, and a Research Fellow from 1975 to 1976. He served as Assistant Professor at the University of Maryland from 1973 to 1975, and later as an Associate Professor from 1976 to 1980. He became full Professor at the University of Maryland in 1980 and in 1985 joined the Systems Research Center as a research faculty appointment.

He has held Visiting Professor positions at Scuola Normale Superiore (Pisa), Brandeis University, IMPA (Rio de Janeiro), University of Kiel, Université P. et M. Curie (Paris), Université de Paris (Orsay and Paris IV), Ecole Polytechnique, Univ. de Bordeaux, and Bar Ilan University. Dr. Berenstein was the Director of the Center for Applications of Mathematics at George Mason University from 1990 to 1991.

Dr. Berenstein received a Sloan Foundation Graduate Fellowship, from 1967 to 1970 and the Founder's Day Award of New York University in 1971. He received a grant from the U.S. Army Research Office in Durham and has received continuous support from the NSF since 1973 He is currently supported by NSA. The Argonne Universities Association also awarded Dr. Berenstein a "Special Year" grant. In 1989, Dr. Berenstein received the National Academy of Science Travel Award to Soviet Union, and in 1990, he received the Hironaka Fellowship and was a Visiting Professor at the Research Institute of Mathematical Sciences in Kyoto, Japan from June to July in 1990.

Information on courses taught during Fall 2005

Math 464

Research Interests

Professor Berenstein's research interests lie in the theory and applications of complex variables, convolution equations, complexity, and linear systems.


C.A. Berenstein and A. Yger, "Effective Bezout Identities on Q[z1, ...,zn]," Acta Mathematica, 66 1991, pp. 69-120.

C.A. Berenstein and E.V. Patrick, "Exact Deconvolution or Multiple Operators--An Overview Plus Performance Characterizations for Imaging Sensors," IEEE Proc. in Multidimensional Signal Processing, April 1990, pp. 723-734.

C.A. Berenstein and M. Coplan, et al.,"Computerized Tomographic Imaging for Space Plasma Physics," J. Applied Physics, 68 1990, pp. 5883-5889.

C.A. Berenstein, J. Baras, and N. Sidiropoulos, "Optimal Filtering of Digital Binary Images Corrupted by Union or Intersection Noise," to appear in IEEE Trans. on Image Processing.

C.A. Berenstein and E. Casadio Tarabusi, "Inversion Formulas for the k-dimensional Radon Transform in Real Hyperbolic Spaces," Duke Math. J., 62, 1991, pp. 613-632.

C.A. Berenstein and A. Yger, "Analytic Bezout Identities," Advances in Applied Math., 10 ,1989, pp. 51-74.

C.A. Berenstein and R. Gay, "Le Probleme de Pompeiu Local," J. Analyse Math., 52, 1989, pp. 133-166.

C.A. Berenstein and P.C. Yang, "An Inverse Neumann Problem," J. Reine Angew, Math. 382 , 1987, pp. 1-21.

C.A. Berenstein and D. Walnut, "Local Inversion of the Radon Transform in Even Dimensions Using Wavelets," to appear in the proc. of the Vienna conference 75 Years of Radon Transform.

C.A. Berenstein and, R. Gay, A. Vidras, and A. Yger, "Residue currents and Bezout Identities," Progress in Mathematics Science, Birkhäuser, 1993.

Technical Reports can be accessed here from the ISR Technical Reports Archive

Wavelet-based localized tomography: A new tool for medical radiology
An ISR accomplishment



| Accomplishment | Impact | Research team | For more information |

Click on any small picture to see a larger version.


Contrary to conventional wisdom, there is an algorithm (wavelet-based) that allows to build (retrofit) CAT scanners that produce accurate images of a region of interest by radiating only that region.

CAT scans are one of the major diagnostic tools in medical radiology. The new approach allows to obtain images of the same quality subjecting the patient to less radiation exposure or, correspondingly, significantly enhanced quality at the current radiation levels. One possible application, being pursued with D. Walnut (GMU), is a procedure to obtain high quality images of the lungs and thus contributing to early detection of lung cancer.



In medicine: earlier detection of cancerous growth, especially in the lung, could lead to early successful surgical intervention. Currently, by the time lung cancer is detected, it is usually fatal.

In material science: Allowing the use of CT scan to detect more easily cracks and defects in large objects.


Carlos Alberto Berenstein (ISR)
K.J. Ray Liu (ISR)
David Francis Walnut
Farrokh Rashid-Farrokhi (ISR)

Additional information

View this patent at the | Patent Trademark Office | IBM Intellectual Property Network |
Related ISR technical report: 95-73

C. A. Berenstein & D. Walnut, 75 years of Radon Transform, S. Gindikin and P. Michor, eds., International Press, p. 28-58, 1994.

F. Rashid-Farrokhi, K. J. R. Liu, C. A. Berenstein and D. Walnut, IEEE Trans. Image Proc. 6 (1997), 1412-1997.

C. A. Berenstein, Integral geometry, Radon transforms and complex analysis, Springer-Verlag LN Math. 1684, p. 1-33, 1998.

Finalist for Invention of the Year 1995, University of Maryland

Invited talk at AMS-SIAM Symposium on Tomography, Summer 2000 (opening lecturer).