An ECAT Reconstruction Method Which Corrects for Attenuation and Detector Response

Measured projection values of activity distributions in tissue are degraded by the detector aperture function and the exponential attenuation along the path to the object boundary. The aperture function varies with the distance to the detector and turns the integration path into a "weighted cone" shape. Fortunately, summation of opposite views shows a nearly uniform response. Adding opposite projections reduces the problem to a deconvolution problem. Division of the projection values by the total attenuation along the path from the object boundary to the rotated axis yields an integral equation which is independent of the boundary. An additional assumption of constant attenuation in a circular activity region followed by Fourier series expansion of period 2π gives a set of solvable Volterra equations.