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A semi-discrete Landweber-Kaczmarz method for cone beam tomography and laminography exploiting geometric prior information

: Vogelgesang, Jonas; Schorr, Christian


Sensing and imaging 17 (2016), Art. 17, 20 pp.
ISSN: 1557-2072
ISSN: 1557-2064
Journal Article
Fraunhofer IZFP ()
Landweber-Kaczmarz iteration; computerized tomography; computed laminography; basis function discretization; a priori information; Algebraic reconstruction techniques

We present a semi-discrete Landweber-Kaczmarz method for solving linear ill-posed problems and its application to Cone Beam tomography and laminography. Using a basis function-type discretization in the image domain, we derive a semi-discrete model of the underlying scanning system. Based on this model, the proposed method provides an approximate solution of the reconstruction problem, i.e. reconstructing the density function of a given object from its projections, in suitable subspaces equipped with basis function-dependent weights. This approach intuitively allows the incorporation of additional information about the inspected object leading to a more accurate model of the X-rays through the object. Also, physical conditions of the scanning geometry, like flat detectors in computerized tomography as used in non-destructive testing applications as well as nonregular scanning curves e.g. appearing in computed laminography (CL) applications ,are directly taken into account during the modeling process. Finally, numerical experiments of a typical CL application in three dimensions are provided to verify the proposed method. The introduction of geometric prior information leads to a significantly increased image quality and superior reconstructions compared to standard iterative methods.