Analytic Estimates of Precision with Multi-pinhole cameras



David Graff






We optimized the number of pinholes, their diameter, and the collimator magnification for precise quantitation of the tracer concentration in small lesions in multipinhole SPECT.



The criterion used in the optimization was the precision of an ideal observer in the low noise regime.  Since the ideal observer performs equally well with the set of projection images as with a reconstruction, we focused the projection images of a simplified "mouse". We solved for a relation between the magnification and pinhole size that optimizes the detection efficiency of the 

multipinhole collimator without sacrificing resolution.  Unlike single pinhole cameras, which perform best at the highest magnification that avoids truncation, multipinhole cameras have a lower optimal magnification: packing more images into the same detector increases the efficiency while sacrificing some resolution.

Fisher information is a statistical technique that determines the expectation value of the precision of some estimation.  We applied this technique to analytic projection images from multipinhole cameras with different design parameters assuming that the uptake in the mouse is constant except for a small lesion. We derived the expected precision of a hypothetical estimation of tracer concentration as a function of the collimator parameters. The optimal collimator has the number of pinholes, pinhole diameter, and  collimator magnification that maximize the precision.



When the specified resolution is finer than the intrinsic resolution of the detector, the detection efficiency is maximized  when the pinhole and detector contribute equally to the system resolution.  The precision is maximized when the overlap of the multipinhole projection, or multiplexing, is of the order of the 

lesion contrast.  To quantify the concentration of a 0.5 mm lesion with a 1mm intrinsic-resolution detector, the optimal pinhole size is 0.3 mm with a magnification of 3, independent of the lesion contrast or size of the mouse.  The ideal number of pinholes is the lesion contrast times the ratio of the detector area to the area of the field of view projected on the detector.



We derive the optimal number of pinholes, their aperture size, and the collimator magnification to best measure the tracer concentration in a small lesion.  This information will allow us to determine the best possible pinhole pattern and observing strategy for our camera.  The mathematical techniques we employed can easily be adapted to other multipinhole imaging tasks.