Inversion of the circular Radon transform on an annulus
نویسندگان
چکیده
The representation of a function by its circular Radon transform (CRT) and various related problems arise in many areas of mathematics, physics and imaging science. There has been a substantial spike of interest towards these problems in the last decade mainly due to the connection between the CRT and mathematical models of several emerging medical imaging modalities. This paper contains some new results about the existence and uniqueness of the representation of a function by its circular Radon transform with partial data. A new inversion formula is presented in the case of the circular acquisition geometry for both interior and exterior problems when the Radon transform is known for only a part of all possible radii. The results are not only interesting as original mathematical discoveries, but can also be useful for applications, e.g. in medical imaging. AMS classification scheme numbers: 44A12, 45D05, 92C55 Submitted to: Inverse Problems Inversion of the circular Radon transform on an annulus 2
منابع مشابه
Circular harmonic decomposition approach for numerical inversion of circular Radon transforms
ABSTRACT Numerical inversions via circular harmonic decomposition for two classes of circular Radon transforms are established. The first class deals with the Radon transform (RT) defined on circular arcs having a chord of fixed length rotating around its middle point (CART) and the second is the RT defined on a set of circles passing through a fixed point of the plane (CRT). These circular Rad...
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