We consider the problem of optimizing collimator characteristics for a simple emission tomographic imaging
system. We use the performance of two different ideal observers to carry out the optimization. The first ideal
observer applies to signal detection when signal location is unknown and background is variable, and the second
ideal observer (one proposed previously by our group) to the more realistic task of signal detection and localization
with signal location unknown and background variable. The two observers operate on sinogram data to deliver
scalar figures of merit AROC and ALROC, respectively. We considered three different collimators that span a
range of efficiency-resolution tradeoffs. Our central question is this: For optimizing the collimator in an emission
tomographic system, does adding a localization requirement to a detection task yield an efficiency-resolution
tradeoff that differs from that for the detection-only task? Our simulations with a simple SPECT imaging
system show that as the localization requirement becomes more stringent, the optimal collimator shifts from
a low-resolution, high efficiency version toward higher resolution, lower efficiency version. We had previously
observed such behavior for a planar pinhole imaging system. In our simulations, we used a simplified model of
tomographic imaging and a simple model for object background variability. This allowed us to avoid the severe
computational complexity associated with ideal-observer performance calculations. Thus the more realistic task
(i.e. localization included) resulted for this case in a different optimal collimator.
Tomosynthesis mammography is a potentially valuable technique for detection of breast cancer. In this simulation study, we investigate the efficacy of three different tomographic reconstruction methods, EM, SART and Backprojection, in the context of an especially difficult mammographic detection task. The task is the detection of a very low-contrast mass embedded in very dense fibro-glandular tissue - a clinically useful task for which tomosynthesis may be well suited. The project uses an anatomically realistic 3D digital breast phantom whose normal anatomic variability limits lesion conspicuity. In order to capture anatomical object variability, we generate an ensemble of phantoms, each of which comprises random instances of various breast structures. We construct medium-sized 3D breast phantoms which model random instances of ductal structures, fibrous connective tissue, Cooper's ligaments and power law structural noise for small scale object variability. Random instances of 7-8 mm irregular masses are generated by a 3D random walk algorithm and placed in very dense fibro-glandular tissue. Several other components of the breast phantom are held fixed, i.e. not randomly generated. These include the fixed breast shape and size, nipple structure, fixed lesion location, and a pectoralis muscle. We collect low-dose data using an isocentric tomosynthetic geometry at 11 angles over 50 degrees and add Poisson noise. The data is reconstructed using the three algorithms. Reconstructed slices through the center of the lesion are presented to human observers in a 2AFC (two-alternative-forced-choice) test that measures detectability by computing AUC (area under the ROC curve). The data collected in each simulation includes two sources of variability, that due to the anatomical variability of the phantom and that due to the Poisson data noise. We found that for this difficult task that the AUC value for EM (0.89) was greater than that for SART (0.83) and Backprojection (0.66).