A compact and accurate set of basis functions for model-based reconstructions

Abstract

Model-based perfusion reconstruction (MBPR) by using a weighting sum of basis functions, is used to describe the dynamic contrast agent distribution by superposition of incorporated prior knowledge. It handles temporal under-sampling in measurements acquired with a slowly rotating X-ray-based imaging system, in our case a C-arm based computed tomography (CT). However, here challenging issue arises that the computing complexity increases proportional to the number of prior knowledge elements. Thus, the aim of this study is to analyze clinical data and elaborate basis functions, that maps various patients with a small orthonormal basis set (ONB). This work is based on five reconstructed clinical perfusion CT data sets. For each patient, regions of interest were manually figured out in order to enhance the content. Therefore, bones and catheters have to be removed out of the data, to prevent a falsification of the curves by them. The principal component analysis (PCA) to compress the relevant information of perfusion and create an ONB was used. In order to achieve an ONB which also optimal maps unknown patients, the cross validation method was used, i.e. the datasets of four patients were utilized for the estimation of the ONB, while the remaining patient was used for evaluation. Finally, the ONB gets evaluated by the mean-absolute-percentage-error (MAPE) of MBPR. A compact ONB with three basis functions that maps all five patients without a significant d eviation o f t he approximated curves and the original ones is obtained. Especially, regions with high blood supply can be reconstructed very accurately and a reduction of noise is qualitatively visible in the image. An optimum ONB for the MBPR requires that the curves can be modeled as exactly as possible with a few basis elements. The use of only a few elements also leads to short computing times. In this work a good approximation of the curves with three basis elements is received. This results in an improved MBPR that in turn can lead to a higher precision of stroke diagnostics and treatments by using C-Arm CT.