The Radon Transform on Z *
نویسندگان
چکیده
where S + x denotes the setf-s + x i s e S ) . Thus, the Radon transform can be thought of as a way of replacing/by a "smeared out" version of /. This form of the transform represents a simplified model of the kind of averaging which occurs in certain applied settings, such as various types of tomography and recent statistical averaging techniques. A fundamental question which arises in connection with the Radon transform is whether or not it is possible to invert it, i.e., whether one can recover (in principle) the function/from knowledge of Fs. In this paper we investigate this problem in detail for several special classes of groups, including the group of binary ^-tuples under modulo 2 addition.
منابع مشابه
The Radon Transform on Z
The Radon transform on Zn averages a function over its values on a translate of a fixed subset S in Zn. We discuss invertibility conditions and computer inverse formulas based on the Moore–Penrose inverse and on linear algorithms. We expect the results to be of use in directional and toroidal time series.
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