A deconvolution approach for the enhancement of spatial resolution in energy dispersive x-ray diffraction and related imaging methods

摘要

A reconstruction approach is presented, allowing the improvement of spatial resolution of images obtained by sequential pixel scanning techniques. Based on a series of measurements taken under different object positions, the signal contributions from individual voxels of significantly reduced size are calculated. Mathematically, the type of reconstruction used can be regarded as a deconvolution or solving an inverse problem. Due to the specific shape of the convolution kernel in the x-ray diffraction example treated here the problem turns out to be ill-posed, and thus its solution using measured (noisy) data requires the 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. 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 method presented here was developed to overcome resolution limitations in spatially resolved x-ray diffraction measurements on extended objects as used, e.g., for material analysis or the detection of illicit substances in baggage inspection applications. Nevertheless, the technique may easily be utilized for resolution enhancement within other imaging modalities, provided the task can be written as a deconvolution problem and the corresponding convolution kernel is known. According to the features of our experimental setup the developed reconstruction algorithm is explained for energy dispersive x-ray diffraction with pencil beam irradiation as an example application. The spatial resolution enhancement is demonstrated, using simulated and measured data sets corresponding to objects of different material composition.