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Efficient projection and backprojection scheme for spherically symmetric basis functions in divergent beam geometry
Author(s) -
Ziegler Andy,
Köhler Thomas,
Nielsen Tim,
Proksa Roland
Publication year - 2006
Publication title -
medical physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.473
H-Index - 180
eISSN - 2473-4209
pISSN - 0094-2405
DOI - 10.1118/1.2388570
Subject(s) - aliasing , iterative reconstruction , projection (relational algebra) , sampling (signal processing) , algorithm , basis (linear algebra) , iterative method , beam (structure) , reconstruction algorithm , image resolution , image quality , mathematics , computer science , optics , computer vision , geometry , physics , filter (signal processing) , image (mathematics)
In cone‐beam transmission tomography the measurements are performed with a divergent beam of x‐rays. The reconstruction with iterative methods is an approach that offers the possibility to reconstruct the corresponding images directly from these measurements. Another approach based on spherically symmetric basis functions (blobs) has been reported with results demonstrating a better image quality for iterative reconstruction algorithms. When combining the two approaches (i.e., using blobs in iterative cone‐beam reconstruction of divergent rays) the problem of blob sampling without introducing aliasing must be addressed. One solution to this problem is to select a blob size large enough to ensure a sufficient sampling, but this prevents a high resolution reconstruction, which is not desired. Another solution is a heuristic low‐pass filtering, which removes this aliasing, but neglects the different contributions of blobs to the absorption depending on the spatial position in the volume and, therefore, cannot achieve the best image quality. This article presents a model of sampling the blobs which is motivated by the beam geometry. It can be used for high resolution reconstruction and can be implemented efficiently.