Enhanced spatial resolution for EDXRD inspection methods by reconstruction from multiple measurements

Energy Dispersive X-Ray Diffraction (EDXRD) in transmission geometry enables spatially localized measurements on extended objects and is favorably used in airport baggage inspection systems. Here, a method is presented to improve their comparably low spatial resolution in the direction of the incident beam by performing a one-dimensional object scan instead of a single data acquisition. The series of measurements taken under different object positions allows reconstruction of the signal contributions from individual voxels at a significantly enhanced resolution. The type of reconstruction used can be regarded as a two-dimensional deconvolution or solving an inverse problem. Due to the specific shape of the convolution kernel the problem turns out to be ill-posed, and thus its solution using measured (noisy) data requires application of a suitable regularization method. Detailed studies on this issue led to the development of a novel iterative algorithm combining several deconvolution runs with preceding and intermediate image processing steps. The Tikhonov method was used for regularization. However, depending on the object under investigation the original Euclidean norm (least squares fit) was advantageously replaced by the 1-norm (least absolute deviation, LAD problem). The algorithm was tested using simulated and measured data sets of different material compositions under pencil beam irradiation. The results demonstrate the significant increase in spatial resolution achieved by means of the method.