Three-dimensional vascular reconstruction in X-ray imaging

This work concerns the study of algorithms dedicated to 3D vascular reconstruction from a sequence of subtracted angiograms acquired in rotation around a patient. This problem raises difficulties related, on the one hand, to intrinsic instability in the reconstruction process and, on the other hand, to a loss of information during acquisition. In a first approach, Markovian modeling techniques are used to stabilize the reconstruction process. The particular morphology of the vascular network leads to define a model form of two complementary terms: - a smoothing term conditioned by a local direction parameter allowing to regularize the reconstruction while taking into account explicitly the reticular nature of the blood vessels, - a raising term for the density of small vessels based on the use of local curvature information. A second approach addresses the problem of densitometric underestimation of vessels from the use of a limited number of projections. The problem is reformulated using semi-quadratic minimization techniques to bring up a new variable; this variable is interpreted as a 'belonging index' to the reconstruction medium that is gradually estimated from a priori densitometric information. This media membership index allows the reconstruction of a component on the missing data areas in the Fourier space and leads to a better contrast of the vascular structures. Each of these approaches is illustrated by its application on clinical data to show the contribution of the proposed methods