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

A common problem associated with X-ray imaging using coded apertures is the reconstruction of low-intensity extended objects. In the decoding of such objects, the overlapping images from the multiple pinholes give rise to noise cross talk and, in many cases, also to signal cross talk. In this paper, an alternate approach is proposed based on the principle used in an earlier (Yin et al., 1980) laboratory device for the real-time viewing of X-ray objects. It is shown that with this approach, the nonoverlapping redundant array, the sidelobes in the point spread function are not eliminated but merely displaced through a suitable choice of geometry. In this manner, the sidelobes no longer contribute to the background in the vicinity of a reconstructed image, and both signal and noise cross talks are completely eliminated. It may now be possible to reconstruct extended X-ray objects in 3-D by simple optical correlation and tomographically by a computer.

The results of two computer simulations demonstrate the feasibility of using the nonoverlapping redundant array (NORA) to form three-dimensional images of objects with X-rays. Pinholes admit the X-rays to nonoverlapping points on a detector. The object is reconstructed in the analog mode by optical correlation and in the digital mode by tomographic computations. Trials were run with a stick-figure pyramid and extended objects with out-of-focus backgrounds. Substitution of spherical optical lenses for the pinholes increased the light transmission sufficiently that objects could be easily viewed in a dark room. Out-of-focus aberrations in tomographic reconstruction could be eliminated using Chang's (1976) algorithm.