Abstract

If the spatial resolution of an image-acquisition system is limited by the size of its component detector elements, then scanning may be required for the signal to be fully sampled. In such cases interpolation methods are normally applied to reproduce a uniformly sampled signal from the set of observations. Alternatively, however, this step can be treated as a restoration problem, in which case the extra measurements made accessible by detector motion may contain sufficient information to superresolve the signal, i.e., to recover information beyond the limit normally associated with finite detector size. We describe the application of this concept to the problem of constructing the projection matrix from a set of noise-corrupted tomographic measurements made by a moving detector array. In particular we focus on the case encountered in many tomographic applications in which the spatial response functions are approximately stationary with object depth. The method of projections onto convex sets is used in conjunction with an underrelaxation scheme to recover the projection matrix, from which the image is reconstructed by the standard filtered backprojection algorithm. Simulation results demonstrate that this approach applied to data acquired by a wobbling positron emission tomography system can substantially enhance the quality of the reconstructed image, even in the presence of high levels of quantum noise. The projection-matrix recovery step can be performed in a matter of seconds; thus the benefits of signal recovery are gained without a significant sacrifice in computation time.

© 1992 Optical Society of America

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