Noise power spectrum for filtered backprojection using discrete representations

Jeanpierre V. Guedon; Robert M. Gagne; Kyle J. Myers; Robert F. Wagner

doi:10.1117/12.130895

9 December 1992 Noise power spectrum for filtered backprojection using discrete representations

Jeanpierre V. Guedon, Robert M. Gagne, Kyle J. Myers, Robert F. Wagner

Author Affiliations +

Proceedings Volume 1768, Mathematical Methods in Medical Imaging; (1992) https://doi.org/10.1117/12.130895
Event: San Diego '92, 1992, San Diego, CA, United States

Abstract

Previous formulations for the noise power spectrum (NPS) of tomographic images have usually been obtained using a radially bandlimited discrete representation of the continuous 2- D function under reconstruction. Also, the same sampling distance is used to represent discrete versions of the function and its projection. In this paper, the expression for the NPS is generalized to spline and bandlimited subspaces of square-integrable functions and to unequal sampling distances for the image and the projection data. The theory was used to predict the NPS obtained using several different sets of basis functions: radially bandlimited (Shepp- Logan) and angular dependent splines, i.e., B-splines of degree 0 (Haar system), degree 1, degree 3, and separable bandlimited. Measurement of the NPS of simulated images was used to confirm the predictions of the theory. The NPS shows different radial and angular dependent characteristics for each set of basis functions, and for oversampling of the projection data. The magnitude of the aliasing in the reconstructed image depends on the choice of basis functions. Thus the basis functions used and the type of object imaged must be considered in any evaluation of the imaging system.

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Jeanpierre V. Guedon, Robert M. Gagne, Kyle J. Myers, and Robert F. Wagner "Noise power spectrum for filtered backprojection using discrete representations", Proc. SPIE 1768, Mathematical Methods in Medical Imaging, (9 December 1992); doi: 10.1117/12.130895; https://doi.org/10.1117/12.130895

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