Tomography of objects with a priori known internal geometry

Abstract

We suggest a new method for the reconstruction of density distribution in objects with a priori known structure. We show that, when all contours of constant density in a two-dimensional slice of an object are known, the Radon transform can be reduced to a one-dimensional linear integral equation of the convolution type. Consequently, just one projection may be sufficient for unambiguous determination of the density in that slice. A relevant inversion algorithm is developed and tested using a numerically simulated realistic object, The proposed inversion method may be applicable to some other problems, e.g. deconvolution.