A new method for reconstruction of cross-sections using Tucker decomposition

Abstract

The full representation of a d-variate function requires exponentially storage size as a function of dimension d and high computational cost. In order to reduce these complexities, function approximation methods (called reconstruction in our context) are proposed, such as: interpolation, approximation, etc. The traditional interpolation model like the multilinear one, has this dimensionality problem. To deal with this problem, we propose a new model based on the Tucker format – a low-rank tensor approximation method, called here the Tucker decomposition. The Tucker decomposition is built as a tensor product of one-dimensional spaces where their one-variate basis functions are constructed by an extension of the Karhunen–Loève decomposition into high-dimensional space. Using this technique, we can acquire, direction by direction, the most important information of the function and convert it into a small number of basis functions. Hence, the approximation for a given function needs less data than that of the multilinear model. Results of a test case on the neutron cross-section reconstruction demonstrate that the Tucker decomposition achieves a better accuracy while using less data than the multilinear interpolation.