A Complementary Method for Traditional Image Reconstruction Techniques with Application to Spent/Fresh Nuclear Fuel Assemblies

For the imaging of spent nuclear fuel originally a set of parallel projections (a line integral of an object along a line) is taken at multiple angles. In mathematical terms this represents the so-called Radon transform of a two dimensional object f(x,y). The data are then fed into different reconstruction techniques such as, Back Projection, Filtered Back Projection, Maximum Entropy, Neural Networks, Algebraic Reconstruction Techniques etc. to obtain the two dimensional object f(x,y). To sum it up, all these techniques are aimed to answer the following question: “If one is measuring outside an object, is it possible to make conclusions about the inside of the object?”. In most cases it depends on the properties of the object itself (scattering and absorption properties) and the reconstruction technique used. Interesting to notice is that the methods applied to the imaging of the spent fuel assemblies are not different from what is already used in medical field or radio astronomy. However, in the medical field the f(x,y)-function (object) is assumed to be unknown and therefore, can not be represented in a form of a simple analytical expression. In our view this is not the case of spent/fresh nuclear fuel. Therefore, we elaborate on this assumption taking into account the specific nature of the imaging task of the spent/fresh nuclear fuel. In particular, the fact that all fuel assemblies have fixed geometry allows us to describe the function f(x,y) (our object) in a simple analytical form, as a sum of Gaussian functions with specific intensity (b,k) and positions (xi,yi). The Radon transform of this function (data measured around an object at different angles and positions) can be easily calculated. In the case of the gross, partial and bias defects present, the experimental Radon transform (sinogram) will differ from the one that is predicted theoretically. Thus, the presence of defects can be determined. The method can be also used as a complement to the traditional image reconstruction techniques to optimize the number of the measurement angles. This paper describes theoretical and numerical investigations of performance and limitations of the method.