Optimal unbiased reduction of global image variances in SPECT

In this work, we studied a class of reconstruction algorithms, which are specified by a complex combination coefficient, in SPECT with uniform attenuation. We studied theoretically and evaluated numerically the impact of such a complex combination coefficient on the variances in reconstructed images. Specifically, we investigated whether and to what extent a complex combination coefficient can further reduce the global image variances in SPECT as compared to a real combination coefficient. We show that the algorithm specified by an optimal complex combination coefficient can provide theoretically a lower global image variance than does the the quasi-optimal algorithm that is specified by a real combination coefficient. However, because such a reduction of global image variance is only a few percent, and because the optimal complex combination coefficient is generally unobtainable without prior knowledge of the object, it is concluded that the quasi-optimal algorithm probably should be used for image reconstruction in SPECT with uniform attenuation.