Abstract

The limited data problem in tomography refers to two situations: (1) the limited angular view problem where the source and/or detectors are prevented from reaching certain angular displacements and (2) the inability to get a full set of meaningful data because of internal opacities in the object being examined. We address the second situation and show how the size and shape of the convex hull of the opaque object can be estimated from a few measurements. Indeed if only the size and shape of the opacity are required, only O(N) operations (one operation is one addition plus one multiplication) are required as opposed to O(N³) for convolution backprojection reconstruction or O(N² logN) for direct Fourier inversion. Moreover the signal processing operations required to estimate the opacity are much less complicated than those required in image reconstruction.

© 1987 Optical Society of America