Multiple point spread function modeling for deconvolution of 3D X-ray diffraction data

Abstract

X-ray diffraction imaging is an important analytical tool in a variety of biological and medical imaging applications. However, the images obtained are often degraded by the point spread function (PSF) of the imaging system. An accurate knowledge of the system PSF is essential for a successful deconvolution of the degraded images. In this paper, we present a novel modeling procedure to determine the PSF of an X-ray diffraction (XRD) system based on experimental data. Different regions of an XRD pattern have different orientations due to the diffuse light distortion (DLD). A new multiple PSF model is introduced and used to restore XRD data. Raw PSFs are collected using isolated spots from XRD data in high resolution regions. An adaptive ridge regression (ARR) technique is first used to remove noise and baseline from the raw PSF data. A target Gaussian function is used to model the raw PSFs. A gradient descent algorithm is used to find optimum parameters of the Gaussian function. A set of XRD data are restored by a nonlinear iterative deconvolution algorithm using the modeled PSFs. Experimental results using a single and multiple PSFs are presented and discussed. We show that by using a multiple PSF model in the deconvolution algorithm, improved restored XRD data are obtained and as a result the symmetry estimator and integration error are enhanced.