Title :
Minimum square-deviation tomographic reconstruction from few projections
Author :
Dhararnipragada, S. ; Arun, K.S.
Author_Institution :
Dept. of Electr. & Comput. Eng., Illinois Univ., Urbana, IL, USA
Abstract :
The problem of tomographic reconstruction from a few discrete projections is addressed. When the projection data are discrete and few in number, the image formed by the convolution back-projection algorithm may not be consistent with the observed projections and is known to exhibit artifacts. Hence, the problem formulated here is one of finding an image that is closest to a nominal and is consistent with the projection data and other convex constraints such as positivity. The measure of closeness used is a Hilbert space norm, typically a weighted sum/integral of squares, with weights used to reflect expected deviation from the nominal in different regions. In the absence of constraints, this approach leads to a direct, noniterative algorithm (based on a simple matrix-vector computation) for construction of the image. When additional convex constraints such as positivity and upper-bounds need to be enforced on the reconstructed image to improve resolution, a quadratically convergent Newton algorithm is suggested
Keywords :
computerised tomography; least squares approximations; medical image processing; Hilbert space norm; convolution back-projection algorithm; integral of squares; matrix-vector computation; minimum square deviation; noniterative algorithm; positivity; quadratically convergent Newton algorithm; tomographic reconstruction; weighted sum; Contracts; Convolution; Data acquisition; Detectors; Equations; Extraterrestrial measurements; Hilbert space; Image reconstruction; Image resolution; Tomography;
Conference_Titel :
Computer-Based Medical Systems, 1992. Proceedings., Fifth Annual IEEE Symposium on
Conference_Location :
Durham, NC
Print_ISBN :
0-8186-2742-5
DOI :
10.1109/CBMS.1992.244948