3D image reconstruction for a Compton SPECT camera model
Sauve, A.C.; Hero, A.O., III; Rogers, W.L.; Wilderman, S.J.; Clinthorne, N.H.
Nuclear Science, IEEE Transactions on
Volume 46, Issue 6, Dec 1999 Page(s):2075 - 2084
Digital Object Identifier 10.1109/23.819285
Summary:Proposes a 3D image reconstruction algorithm for a 3D Compton
camera being developed at the University of Michigan. The authors
present a mathematical model of the transition matrix of the camera
which exploits symmetries by using an adapted spatial sampling pattern
in the object domain. For each projection angle, the sampling pattern is
uniform over a set of equispaced nested hemispheres. By using this
sampling pattern the system matrix is reduced to a product of a
(approximately) block circulant matrix and a sparse interpolation
matrix. This representation reduces the very high storage and
computation requirement inherent to 3D reconstruction using transition
matrix inversion methods. The authors geometrically optimize their
hemispherical sampling and propose a 3D volumetric interpolation.
Finally, the authors present a 3D image reconstruction method which uses
the Gauss-Seidel algorithm to minimize a penalized least square
objective
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