Application of Kernel-Based Methods to Medical Image Reconstruction

The problem of reconstructing a CT image could be thought as that of finding an Approximation of a function from discrete Radon data. This problem arises often in the context of medical imaging when we want to reconstruct the internal structure of a sample starting from its X-ray tomography.

Classical reconstruction methods are based on the so-called back projection formula. Our reconstruction relies on generalized Hermite-Birkoff interpolation by positive definite kernels.

This leads to a very flexible method, which works for arbitrary distributions of Radon lines. The method can be categorized as an Algebraic Reconstruction Technique (ART).

We discuss a fast implementation of the ART when the geometry of the data give raise to matrices with a circulant block structure.