The Radon transform on a family of curves in the plane. II

Author:
A. M. Cormack

Journal:
Proc. Amer. Math. Soc. **86** (1982), 293-298

MSC:
Primary 44A15; Secondary 44A20, 53C65, 92A07

DOI:
https://doi.org/10.1090/S0002-9939-1982-0667292-4

MathSciNet review:
667292

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A further discussion of Radon's problem for curves in the plane given, for fixed , by . real, . Functions yielding null transforms, and zeros of the Fourier components of the transforms are given for general . and several orthogonal expansions are given for .

**[1]**A. M. Cormack, J. of Appl. Phys.**34**(1963), 2722.**[2]**-, J. of Appl. Phys.**35**(1964), 2908.**[3]**A. M. Cormack and E. T. Quinto,*A Radon transform on spheres through the origin in**and applications to the Darboux equation*, Trans. Amer. Math. Soc.**260**(1980), 575-581. MR**574800 (81i:44001)****[4]**A. M. Cormack,*The Radon transform on a family of curves in the plane*, Proc. Amer. Math. Soc.**83**(1981), 325-330. MR**624923 (83b:44001)****[5]**S. Helgason,*The Radon transform*, Birkhauser, Boston, Mass., 1980. MR**573446 (83f:43012)****[6]**F. John,*Plane waves and spherical means*, Interscience, New York, 1955. MR**0075429 (17:746d)****[7]**A. K. Louis, Medical Image Processing Report T52, SUNY, Buffalo, 1981.**[8]**W. Magnus, F. Oberhettinger and R. P. Soni,*Formulas and theorems for the special functions of mathematical physics*, Springer-Verlag, New York, 1966. MR**0232968 (38:1291)****[9]**R. B. Marr,*On the reconstruction of a function on a circular domain from a sampling of its line integrals*, J. Math. Anal. Appl.**45**(1974), 357-374. MR**0336156 (49:932)****[10]**R. M. Perry,*On reconstructing a function on the exterior of a disk from its Radon transform*, J. Math. Anal. Appl.**59**( 1977), 324-341. MR**0445175 (56:3519)****[11]**E. T. Quinto, J. Math. Anal. Appl. (to appear).

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
44A15,
44A20,
53C65,
92A07

Retrieve articles in all journals with MSC: 44A15, 44A20, 53C65, 92A07

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1982-0667292-4

Keywords:
Radon transform

Article copyright:
© Copyright 1982
American Mathematical Society