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An Analysis of the Novikov analytic inversion formula and a new algebraic reconstruction algorithm in SPECT

Elie M. Nasr

Abstract


We present a comparative study between two methods used for image reconstruction in single photon emission tomography (SPECT) with non uniform-attenuation. The first method is a recent algebraic algorithm used for accurate attenuation correction in SPECT. The second of the methods is based on the Novikov explicit inversion formula for the attenuated Radon transform. Our study shows that the algebraic algorithm, in its basic form, is more stable than the explicit inversion formula and produces higher quality reconstructed images. We support our study by a number of convincing numerical results using realistic models of attenuation and several activity distribution models. These numerical simulations cover the case of the full-scan SPECT measurements in both optimal and sub-optimal sampling, as well as the case of the half-scan.

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