LEAST-SQUARES ALGORITHM FOR REGION-OF-INTEREST EVALUATION IN EMISSIONTOMOGRAPHY

In a simulation study, the performances of the least squares algorithm applied to region-of-interest evaluation were studied. The least squa res algorithm is a direct algorithm which does not require any iterati ve computation scheme and also provides estimates of statistical uncer tainties of the region-of-interest values (covariance matrix). A model of physical factors, such as system resolution, attenuation and scatt er, can be specified in the algorithm. In this paper an accurate model of the non-stationary geometrical response to a camera-collimator sys tem was considered. The algorithm was compared with three others which are specialized for region-of-interest evaluation, as well as with th e conventional method of summing the reconstructed quantity over the r egions of interest. For the latter method, two algorithms were used fo r image reconstruction; these included filtered backprojection and con jugate gradient least squares with the model of nonstationary geometri cal response. For noise-free data and for regions of accurate shape le ast squares estimates were unbiased within roundoff errors. For noisy data, estimates were still unbiased but precision worsened for regions smaller than resolution: simulating typical statistics of brain perfu sion studies performed with a collimated camera, the estimated standar d deviation for a 1 cm square region was 10% with an ultra high-resolu tion collimator and 7% with a low energy all purpose collimator. Conve ntional region-of-interest estimates showed comparable precision but w ere heavily biased if filtered backprojection was employed for image r econstruction. Using the conjugate gradient iterative algorithm and th e model of nonstationary geometrical response, bias of estimates decre ased on increasing the number of iterations, but precision worsened th us achieving an estimated standard deviation of more than 25% for the same 1 cm region.