Effect of an imaginary combination coefficient on the global image variance in SPECT

Image reconstruction in SPECT with uniform attenuation is theoretically appealing as well as practically important. In this work, we investigated a class of reconstruction algorithms that are indexed by a complex combination coefficient. The class with a real combination coefficient proposed previously can be interpreted as a subclass of this new class. We studied theoretically and evaluated numerically the impact of the introduction of such a complex combination coefficient on the variances in reconstructed images. Specifically, we investigated theoretically as well as quantitatively whether and to what extent the introduction of a complex combination coefficient can further reduce the variances in SPECT images. Using the Shepp-Logan phantom, we evaluate quantitatively the difference of image variances obtained with the quasi-optimal algorithm that we proposed previously and the true optimal algorithm that is generally unobtainable without prior knowledge of the object.