Algorithms for two-dimensional reconstruction

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Abstract
The 2-dimensional reconstruction problem which occurs in radiography, radioastronomy, EM and many other fields is as follows. A 2-dimensional object which can be characterized by a variable density is scanned by some means in such a way as to provide a series of measurements of the line integrals of the density along say N straight lines which intersect the object. The problem is to calculate the density at points in the object from the measurements of the line integrals. A number of algorithms is now available for performing this calculation. When these algorithms are used in practice most seem to use all of the N measures of the line integrals to calculate the density at each point in the object. In algorithms of this kind the use of all N points for each density calculation is unnecessary. Use of the unnecessary data points, while it may contribute to noise reduction, generates a noise-like error in the reconstruction at all but a few points at which reconstruction of the density is made.