X-ray radiographs reconstruction based on nonlinear least squares with deconvolution

Abstract

Abstract High energy X-ray radiographs reconstruction is a typical nonlinear process. However, most of the current reconstruction methods are based on a linear approximation model, which uses optical depth images for reconstruction. As radiographs are convolved by the system blur, images reconstructions with these algorithms are blurred, especially at edges. In this paper, a nonlinear least squares reconstruction model for transmittance images is established and optimized by the Levenberg–Marquardt algorithm assuming that the system blur is known. The numerical experiments show that the reconstruction error of this approach is greatly reduced and the edges sharpness is significantly improved, compared with the traditional constrained conjugate gradient method and the trust region reflective method. For images contaminated by blur and low noise, the reconstruction is still improved and acceptable even when an inaccurate system blur is used. Furthermore, we propose an idea of rectifying the system blur measured by experiments. Our reconstruction method is practical in deconvolution and shows a promising prospect in high energy X-ray radiographs reconstruction.