Időpont: 2020.06.30., 09:00 – 09:20
Kivonat: The linear relationship between the density of a homogeneous object and the total attenuation of a monochromatic X-ray beam passing through the object can be described by Beer’s law. In real-world applications however, x-ray emitters (such as CT-machines) produce poly-chromatic beams. Lower energy photons are more easily absorbed causing the beam to “harden” as it passes through the object. Therefore in the case of poly-chromatic x-ray beams, the above mentioned linear relationship does not hold. This phenomena is referred to as beam hardening and it causes so-called streak and cupping artifacts  on the reconstructed CT image.
The detection and correction of artifacts caused by beam hardening is an important task for CT applications. Different strategies for reducing the effect of beam hardening have been studied for a long time, and a diverse array of possible approaches has been proposed ranging from hardware filtering to iterative approaches . In this project we propose a model-based  approach for the detection and correction of beam hardening artifacts. The problem in question directly originates from an industrial application which we are about to solve by mathematical modeling and nonlinear optimization. In order to estimate the attenuation coefficients describing the examined object, we utilize the variable projection algorithm . The proposed approach simplifies the nonlinear optimization task solved by previous iterative algorithms, and it is also sensitive to the position of the x-ray emitter, allowing for the detection of position-specific beam-hardening artifacts. In addition to the classical variable projection algorithm, we apply regularization methods  and nonlinear constraints in an attempt to fully make use of the physical meanings of the parameters to be estimated.