A New Approach to the Emission Computerized Tomography Problem: Simultaneous Calculation of Attenuation and Activity Coefficients

In order to obtain truly quantitative reconstruction of gamma-emitter concentration in Emission Computerized Tomography (ECT) the attenuation within the region of interest has to be accounted for. In this report we propose to calculate simultaneously attenuation and activity concentration coefficients. Starting from the system of non-linear equations which describes the model of single photon gamma-ray emission in a discretized form we show how to reduce it to a mixed convex-concave feasibility problem and apply to it our method of Cyclic Subgradient Projections (CSP). This approach is discussed and some experimental results in its favor are presented.