An analytical approach to single photon emission computed tomography with the attenuation effect

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Abstract
The problem of transverse plane reconstruction from an ensemble of projections is considered in its general formulation and an analytically exact solution to the attenuated tomographic operator is proposed. Such a technique, called the regularizing iterative method (RIM), allows the introduction of a priori knowledge on the size and shape of the activity distribution and in principle on the exact attenuation distribution. The relaxation factor used is so named because it provides noise filtering for a small number of iterations. The effectiveness of RIM was studied in the single photon emission computed tomography (SPECT) problem with the aim of correcting for attenuation before quantitative study. Its application involves the use of a rotating scintillation camera connected to a mini-computer system. Various mathematical and physical phantoms were studied, and a satisfactory attenuation correction was always obtained in the final image with an improvement in the contrast and signal-to-noise ratio. Preliminary clinical studies on liver transverse sections seems to indicate an improvement in deep lesion detectability, compared with images obtained by the filtered (Ramp) back projection technique.