A Polynomial Chaos Stochastic Model for 2D Breast Microwave Scattering

A computational model that quantifies the statistical distributions of the electromagnetic field scattered by a breast with random variations in its complex permittivity profile is presented. It involves the construction of a sparse hyperbolically truncated polynomial chaos expansion for the scattered field at each receiving antenna with the modified cross-validation least-angle regression method and requires significantly less deterministic model evaluations than Monte-Carlo sampling. Tumor detectability, via the Cramér-von Mises criterion, is studied for a simplified and a more realistic two-dimensional breast model. In the latter case, the Karhunen-Loéve transform is applied to reduce the stochastic dimensionality resulting from a large number of correlated permittivity values.