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Proceedings Paper

Variational approach to tomographic reconstruction
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Paper Abstract

We formulate the tomographic reconstruction problem in a variational setting. The object to be reconstructed is considered as a continuous density function, unlike in the pixel-based approaches. The measurements are modeled as linear operators (Radon transform), integrating the density function along the ray path. The criterion that we minimize consists of a data term and a regularization term. The data term represents the inconsistency between applying the measurement model to the density function and the real measurements. The regularization term corresponds to the smoothness of the density function. We show that this leads to a solution lying in a finite dimensional vector space which can be expressed as a linear combination of generating functions. The coefficients of this linear combination are determined from a linear equation set, solvable either directly, or by using an iterative approach. Our experiments show that our new variational method gives results comparable to the classical filtered back-projection for high number of measurements (projection angles and sensor resolution). The new method performs better for medium number of measurements. Furthermore, the variational approach gives usable results even with very few measurements when the filtered back-projection fails. Our method reproduces amplitudes more faithfully and can cope with high noise levels; it can be adapted to various characteristics of the acquisition device.

Paper Details

Date Published: 3 July 2001
PDF: 10 pages
Proc. SPIE 4322, Medical Imaging 2001: Image Processing, (3 July 2001); doi: 10.1117/12.431108
Show Author Affiliations
Jan Kybic, Swiss Federal Institute of Technology/Lausanne (Switzerland)
Thierry Blu, Swiss Federal Institute of Technology/Lausanne (Switzerland)
Michael A. Unser, Swiss Federal Institute of Technology/Lausanne (Switzerland)

Published in SPIE Proceedings Vol. 4322:
Medical Imaging 2001: Image Processing
Milan Sonka; Kenneth M. Hanson, Editor(s)

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