Image reconstruction from the Compton scattering of X-ray fan beams in thick/dense objects

Image reconstruction from Compton scattering measurements results in a nonlinear inverse problem that can produce multiple solutions, particularly in deep/dense objects. In this work, the nonlinearity of the problem is mitigated by a transformation which minimizes the difference of the ratios of measurements with overlapping fields of view. Overlapping eliminates one of the competing factors in the nonlinear problem, and allows solving the inverse problem of image reconstruction beyond the one-mean-free path equivalent depth previously needed to reach a solution in scatter-only imaging. The method also enables the use of wide X-ray fan beam sources, and is numerically applied to exploit the ability of scatter imaging to acquire single-side two-dimensional (2-D) and three-dimensional (3-D) images of relatively dense objects. Examples are presented to demonstrate the method's ability to deal with noisy measurements, at various degrees of overdetermination.