Tomographic feature detection and classification using parallelotope bounded error estimation

We give a novel method for performing statistically signi cant detection of speci ed 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 )100% con dence region on the object derived by backprojecting a projection-domain con dence region into object space. The projection-domain con dence region is a minimal volume hyper-rectangle speci ed by the projection data and the appropriate quantiles of the standard Gaussian or Poisson distribution. We implement the backprojection step using a very accurate bounded error estimation algorithm which sequentially approximates the feasible set (object-domain con dence region) given the data and its specifed error bounds (known Gaussian or Poisson quantiles). By testing whether this object-domain (1 )100% con dence region contains objects with hypothesized features we obtain a feature detection algorithmwhich has constant false alarm rate (CFAR) and is adaptive in the sense that no image reconstruction is required and no unknown nuisance parameters need be estimated.