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We propose a method to reconstruct the density of a luminescent source in a highly scattering medium from ultrasound-modulated optical measurements. Our approach is based on the solution to a hybrid inverse source problem for the diffusion equation.

Positron emission tomographs (PETs) are currently almost exclusively designed as hybrid systems. The current standard is the PET/CT combination, while prototype PET/MRI systems are being studied by several research groups. One problem in these systems is that the transaxial field-of-view of the second system is smaller than that of the PET camera and does not provide complete attenuation data. Because this second system provides the image for PET attenuation and scatter correction, the smaller FOV causes truncation of the attenuation map, producing bias in the attenuation corrected activity image. In this paper, we propose a maximum-a-posteriori algorithm for estimating the missing part of the attenuation map from the PET emission data. The method is evaluated on five artificially truncated 18F-FDGPET/CT studies, where it reduced the error on the reconstructed PET activities from 20% to less than 7%. The results on a PET/MRI patient study with 18F-FDG are presented as well.

In positron emission tomography (PET) and single photon emission tomography (SPECT), attenuation correction is necessary for quantitative reconstruction of the tracer distribution. Previously, several attempts have been made to estimate the attenuation coefficients from emission data only. These attempts had limited success, because the problem does not have a unique solution, and severe and persistent "cross-talk" between the estimated activity and attenuation distributions was observed. In this paper, we show that the availability of time-of-flight (TOF) information eliminates the cross-talk problem by destroying symmetries in the associated Fisher information matrix. We propose a maximum-a-posteriori reconstruction algorithm for jointly estimating the attenuation and activity distributions from TOF PET data. The performance of the algorithm is studied with 2-D simulations, and further illustrated with phantom experiments and with a patient scan. The estimated attenuation image is robust to noise, and does not suffer from the cross-talk that was observed in non-TOF PET. However, some constraining is still mandatory, because the TOF data determine the attenuation sinogram only up to a constant offset.

This study simulates a multi-pinhole single-photon emission computed tomography (SPECT) system using the Monte Carlo method, and investigates different multi-pinhole designs for quantitative mouse brain imaging. Prior approaches investigating multi-pinhole SPECT were not often optimal, as the number and geometrical arrangement of pinholes were usually chosen empirically. The present study seeks to optimize the number of pinholes for a given pinhole arrangement, and also for the specific application of quantitative neuroreceptor binding in the mouse brain. An analytical Monte Carlo simulation based method was used to generate the projection data for various count levels. A three-dimensional ordered-subsets expectation-maximization algorithm was developed and used to reconstruct the images, incorporating a realistic pinhole model for resolution recovery and noise reduction. Although artefacts arising from overlapping projections could be a major problem in multi-pinhole reconstruction, the cold-rod phantom study showed minimal loss of spatial resolution in multi-pinhole systems, compared to a single-pinhole system with the same pinhole diameter. A quantitative study of neuroreceptor binding sites using a mouse brain phantom and low activity (37 MBq) showed that the multi-pinhole system outperformed the single-pinhole system by maintaining the mean and lowering the variance in the measured uptake ratio. Multi-pinhole collimation can be used to reduce the injected dose and thereby reduce the radiation exposure to the animal. Results also suggest that the nine-pinhole configuration shown in this paper is a good choice for mouse brain imaging.

We present an algorithm that provides a frequency-domain solution of the equation of radiative transfer (ERT) for heterogeneous media of arbitrary shape. Although an ERT is more accurate than a diffusion equation, no ERT code for the widely employed frequency-domain case has been developed to date. In this work the ERT is discretized by a combination of discrete-ordinate and finite-volume methods. Two numerical simulations are presented.