Shape estimation in computer tomography from minimal data

Abstract

In computerized tomography, line integrals of the absorptivity are used to reconstruct the object. In some applications only the locations, sizes, and shapes of internal opacities or near-opacities are needed. For these applications it is unnecessary to reconstruct an image by convolution backprojection [O(N3)] or by direct Fourier methods [O(N2log N)]. We propose an algorithm suitable for this problem that requires only O(N) operations (N is of the order of the number of views). We analyze and demonstrate the high performance of the algorithm but show that the performance of the algorithm depends strongly on an appropriate choice of system parameters. These parameters, the number of view N theta, and the detector spacing deltas are shown to be linked, and a choice of deltas strongly constrains the choice of N theta. We show how an optimum N theta can be determined for a fixed deltas, including practical values of deltas. A series of experiments that reinforce the theory is simulated on a computer.