A tomographic reconstruction algorithm is developed for the nonoverlap
ping redundant array x-ray imaging system whereby the background contr
ibutions from out-of-focus planes can be eliminated. The algorithm mak
es use of two constraints derived from the physical characteristics of
the nonoverlapping redundant array system in tandem with the correlat
ion decoding process. It is simple, direct, and noniterative. Tomograp
hic images of computer-generated planar and three-dimensional objects
are provided to illustrate the effectiveness of the algorithm.