The technique of direct three-dimensional reconstruction from planar projections is analyzed from a linear system viewpoint. It is shown that unfiltered back projection and summation of the one-dimensional planar projections give a point-spread function that behaves like 1/r in three-dimensional space. Thus an analogy between this reconstruction problem and the familiar electrostatic problem is set up. To correct the 1/r blurring, a Laplacian operation on the unfiltered summation is required. Another method for reconstruction is to perform a second derivative operation on the one-dimensional planar projection set before the back projection. The advantages of this reconstruction scheme as compared with reconstruction from line projections are discussed.
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