
TITLE: Analytic Estimates of Precision with
Multipinhole cameras AUTHORS: David
Graff ___________________________________________________________________ ABSTRACT PURPOSE: 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. METHODS AND MATERIALS: 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. RESULTS: 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 intrinsicresolution 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. Conclusions: 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. CONCLUSIONS: FUNDING SOURCES: 