Determination of weighting functions for energy-weighted acquisition

Energy-weighted acquisition (EWA) is an image filtering technique, with a different spatial filter (weighting function) for each energy. The imaging characteristics of EWA are governed by the weighting functions used during the acquisition of the image. The determination of weighting functions is more complicated than the determination of energy windows in conventional imaging because the number of degrees of freedom is much greater. A methodology by which weighting functions can be produced is described. The weighting function is determined by minimizing a generalized chi-square with variable contributions from coefficients quantifying key image characteristics, e.g., signal-to-noise ratio, spatial resolution, and scatter fraction. Varying the importance of these characteristics gives us a workable function-generation tool, able to address a variety of clinical needs. The resulting weighting functions exhibit good scatter reduction properties at various scatter depths, as demonstrated by measurements of line source response functions in a scattering medium at depths from 5 to 14 cm. Energy weighting can also be used to compensate for collimator penetration from high energy gamma rays. Weighting functions are tested in the laboratory using both planar and SPECT phantoms.