A B-spline based and computationally performant projector for iterative reconstruction in tomography Application to dynamic X-ray gated CT

ITERATIVE reconstruction methods for tomography have long proven their potential to enhance reconstruction quality, compared to the filtered backprojection (FBP) [2]. The drawback of iterative methods is their expensive computation time. However ongoing researches on algorithms and recent enhancements in computational power, call for a re-evaluation of the potential of iterative reconstruction in this domain. Such methods require an accurate numerical modelization of the data acquisition process: the so-called projector. The representation of the object of interest (image) is the starting point of the projector. It is assimilated to a continuous function decomposed on a discrete basis of functions. The choice of this basis is essential for an accurate representation of the true function. Standard models such as voxel driven or ray driven [5] are based on raw samples, yielding modelization errors and artifacts on the reconstructed image. More advanced models, such as the recent distance driven [1] projector, define the function at any point considering staircase voxels, and thus make a better modelization. However such a basis of functions provides a coarse representation of the image because of its anisotropic behaviour, causing large modelization errors. Such issues can be dealt with the spherically symmetric volume elements, mostly known as blobs [7] [8] [9] [10] [11], but at the cost of increased complexity. Finally, for implementation purposes, the projection of the staircase voxel, in the distance driven model, is approximated, increasing its modelization errors. We propose the use of B-splines as an alternative to both staircase voxel and blob approaches. B-splines are well known piecewise polynomial functions, and are characterized by the degree of their constituting polynomials. Recent works in sampling theory [18] [19] [15] have shown their efficiency