Method and arrangement for medical x-ray imaging and reconstruction from sparse data

摘要

The invention relates to a medical X-ray device 5 arrangement for producing three-dimensional information of an object 4 in a medical X-ray imaging medical X-ray device arrangement comprising an X-ray source 2 for X-radiating the object from different directions and a detector 6 for detecting the X-radiation to form projection data of the object 4. The medical X-ray device 5 arrangement comprises: means 15 for modelling the object 4 mathematically independently of X-ray imaging and means 15 for utilizing said projection data and said mathematical modelling of the object in Bayesian inversion based on Bayes' formula $p\text{(}xm)=\frac{p_{\mathrm{pr}}\left(x\right)p(mx)}{p\left(m\right)}$ to produce three-dimensional information of the object, the prior distribution p_pr(x) representing mathematical modelling of the object, the object image vector x, which comprise values of the X-ray attenuation coefficient inside the object, m representing projection data, the likelihood distribution p(m|x) representing the X-radiation attenuation model between the object image vector x and projection data m, p(m) being a normalization constant and the posteriori distribution p(x|m) representing the three-dimensional information of the object 4.