A new restoring algorithm, maximum bounded entropy (MBE), has been investigated. It incorporates prior knowledge of both a lower and upper bound in the unknown object. Its outputs are maximum probable estimates of the object under the following conditions: (a) the photons forming the image behave as classical particles; (b) the object is assumed to be biased toward a flat gray scene in the absence of image data; (c) the object is modeled as consisting of high-gradient foreground details riding on top of a smoothly varying background that is not to be restored but rather must be estimated in a separate step; and (d) the image noise is Poisson. The resulting MBE estimator obeys the sum of maximum entropy for the occupied photon sites in the object and maximum entropy for the unoccupied sites. The result is an estimate of the object that obeys an analytic form that functionally cannot take on values outside the known bounds. The algorithm was applied to the problem of reconstructing rod cross sections due to tomographic viewing. This problem is ideal because the object consists only of upper- and lower-bound values. We found that only four projections are needed to provide a good reconstruction and that twenty projections allow for the resolution of a single pixel wide crack in one of the rods.
B. Roy Frieden and Csaba K. Zoltani, "Maximum bounded entropy: application to tomographic reconstruction," Appl. Opt. 24, 201-207 (1985)