Effect of compensation for scattering angular uncertainty in analytical Compton camera reconstruction

In Compton cameras, the measured scattering angle is associated with anuncertainty which becomes larger as the incident gamma-ray energy decreases.Since this uncertainty degrades the spatial resolution of reconstructed images,Hirasawa and Tomitani (2003 Phys. Med. Biol. 48 1009-26) previouslyrevised their analytical reconstruction algorithm to compensate for it. Asthe new algorithm improved the spatial resolution in effect, they expectedthe enhancement of the statistical noise. In this paper, the effect of thiscompensation has been analysed in view of spatial resolution (the FWHMof the noise-free reconstructed image for a point source distribution), statisticalnoise (the relative standard deviation of reconstructed images for an isotropicsource distribution) and image quality (the roughness of reconstructed imagesfor a phantom). The results describe not only the effect of the compensation,but also the relation between the statistical noise and three parameters, i.e., theincident gamma-ray energy, the spatial resolution and the measured total eventnumbers, in reconstruction with compensation. This relation should be takeninto account for the design of Compton cameras with good quality image, i.e.,useful image, output