Tomographic feature detection and classification using parallelotope bounded error estimation

We give a novel method for performing statistically significant detection of specified object features which operates directly on X-ray (Gaussian) or radio-isotope (Poisson) tomographic projection data. The method is based on constructing an exact (1-α)100% confidence region on the object derived by backprojecting a projection-domain confidence region into object space. The projection-domain confidence region is a minimal volume hyper-rectangle specified by the projection data and the appropriate quantiles of the standard Gaussian or Poisson distribution. We implement the back-projection step using a very accurate bounded error estimation algorithm which sequentially approximates the feasible set (object-domain confidence region) given the data and its specified error bounds (known Gaussian or Poisson quantiles). By testing whether this object-domain (1-α)100% confidence region contains objects with hypothesized features we obtain a feature detection algorithm which has constant false alarm rate (CFAR) α and is adaptive in the sense that no image reconstruction is required and no unknown nuisance parameters need be estimated