A Positron Emission Mammography (PEM) scanner dedicated to breast imaging is being developed at our laboratory. We have developed a list mode likelihood reconstruction algorithm for this scanner. Here we theoretically study the lesion detection and quantitation. The lesion detectability is studied theoretically using computer observers. We found that for the zero-order quadratic prior, the region of interest observer can achieve the performance of the prewhitening observer with a properly selected smoothing parameter. We also study the lesion quantitation using the test statistic of the region of interest observer. The theoretical expressions for the bias, variance, and ensemble mean squared error of the quantitation are derived. Computer simulations show that the theoretical predictions are in good agreement with the Monte Carlo results for both lesion detection and quantitation.

The objective assessment of image quality is essential for design of imaging systems. Barrett and Gifford [1] introduced the Fourier cross talk matrix. Because it is diagonal for continuous linear shift-invariant imaging systems, the Fourier cross talk matrix is a powerful technique for discrete imaging systems that are close to shift invariant. However, for a system that is intrinsically shift variant, Fourier techniques are not particularly effective. Because Fourier bases have no localization property, the shift-variance of the imaging system cannot be shown by the response of individual Fourier bases; rather, it is shown in the correlation between the Fourier coefficients. This makes the analysis and optimization quite difficult. In this paper, we introduce a wavelet cross talk matrix based on wavelet series expansions. The wavelet cross talk matrix allows simultaneous study of the imaging system in both the frequency and spatial domains. Hence it is well suited for shift variant systems. We compared the wavelet cross talk matrix with the Fourier cross talk matrix for several simulated imaging systems, namely the interior and exterior tomography problems, limited angle tomography, and a rectangular geometry positron emission tomograph. The results demonstrate the advantages of the wavelet cross talk matrix in analyzing shift-variant imaging systems.

Motion artifacts can be a significant factor that limits the image quality in high-resolution PET. Surveillance systems have been developed to track the movements of the subject during a scan. Development of reconstruction algorithms that are able to compensate for the subject motion will increase the potential of PET. In this paper we present a list mode likelihood reconstruction algorithm with the ability of motion compensation. The subject moti is explicitly modeled in the likelihood function. The detections of each detector pair are modeled as a Poisson process with time vary ingrate function. The proposed method has several advantages over the existing methods. It uses all detected events and does not introduce any interpolation error. Computer simulations show that the proposed method can compensate simulated subject movements and that the reconstructed images have no visible motion artifacts.