Attenuation map reconstruction in uncollimated cone beam geometry using coupled PDEs

SPECT images suffer, among other physical causes of degradation, from photonic attenuation. The most accurate method for correcting photonic attenuation is to incorporate a model of the linear attenuation phenomenon into the emission reconstruction process. This technique requires computation of the nonuniform attenuation distribution (the attenuation map), which is achieved by reconstructing from transmission data. The presence of noise in these data makes it necessary to use a regularized algorithm. The algebraic reconstruction method presented here involves a second order regularization, which theoretically produces a higher quality attenuation map. Through the use of a conjugate gradient technique, the algorithm alternately solves two coupled PDE´s associated respectively with the attenuation map and the image of its edges (the boundaries map). This method was applied to attenuation map reconstructions in cone beam geometry. The acquisitions were performed without use of a collimator since the direction of photon incidence is radial. The evaluation was performed on a numerical thorax simulation and on a very simple phantom composed of materials which have linear attenuation coefficients similar to those encountered in the thoracic region. As a result, the attenuation coefficients of the phantom are slightly underestimated. We attribute this discrepancy to scatter and partial volume effect. However, the results from these studies are encouraging since the geometry of the objects is accurately recovered