A new mathematical framework is introduced for combining the linear compartmental models used in pharmacokinetics with the spatiotemporal distributions of activity that are measured in single photon emission computed tomography (SPECT) and PET imaging. This approach is global in the sense that the compartmental differential equations involve only the overall spatially integrated activity in each compartment. The kinetics for the local compartmental activities are not specified by the model and would be determined from data. It is shown that an increase in information about the spatial distribution of the local compartmental activities leads to an increase in the number of identifiable quantities associated with the compartmental matrix. These identifiable quantities, which are important kinetic parameters in applications, are determined by computing the invariants of a symmetry group. This group generates the space of compartmental matrices that are compatible with a given activity distribution, input function, and set of support constraints. An example is provided where all of the compartmental spatial supports have been separated, except that of the vascular compartment. The question of estimating the identifiable parameters from SPECT and PET data is also discussed.

Multimodality imaging is becoming increasingly important in medical imaging. Since the motivation for combining multiple imaging modalities is generally to improve diagnostic or prognostic accuracy, the benefits of multimodality imaging cannot be assessed through the display of example images. Instead, we must use objective, task-based measures of image quality to draw valid conclusions about system performance. In this paper, we will present a general framework for utilizing objective, task-based measures of image quality in assessing multimodality and adaptive imaging systems. We introduce a classification scheme for multimodality and adaptive imaging systems and provide a mathematical description of the imaging chain along with block diagrams to provide a visual illustration. We show that the task-based methodology developed for evaluating single-modality imaging can be applied, with minor modifications, to multimodality and adaptive imaging. We discuss strategies for practical implementing of task-based methods to assess and optimize multimodality imaging systems.

Adaptive imaging systems alter their data-acquisition configuration or protocol in response to the image information received. An adaptive pinhole single-photon emission computed tomography (SPECT) system might acquire an initial scout image to obtain preliminary information about the radiotracer distribution and then adjust the configuration or sizes of the pinholes, the magnifications, or the projection angles in order to improve performance. This paper briefly describes two small-animal SPECT systems that allow this flexibility and then presents a framework for evaluating adaptive systems in general, and adaptive SPECT systems in particular. The evaluation is in terms of the performance of linear observers on detection or estimation tasks. Expressions are derived for the ideal linear (Hotelling) observer and the ideal linear (Wiener) estimator with adaptive imaging. Detailed expressions for the performance figures of merit are given, and possible adaptation rules are discussed.

Tracking is a necessity for interactive virtual environments. Marker-based tracking solutions involve the placement of fiducials in a rigid configuration on the object(s) to be tracked, called a tracking probe. The realization that tracking performance is linked to probe performance necessitates investigation into the design of tracking probes for proponents of marker-based tracking. A challenge involved with probe design is predicting the accuracy of a tracking probe. We present a method for predicting the accuracy of a tracking probe based upon a first-order propagation of the errors associated with the markers on the probe. Results for two sample tracking probes show excellent agreement between measured and predicted errors.

Imaging is often used for the purpose of estimating the value of some parameter of interest. For example, a cardiologist may measure the ejection fraction (EF) of the heart in order to know how much blood is being pumped out of the heart on each stroke. In clinical practice, however, it is difficult to evaluate an estimation method because the gold standard is not known, e.g., a cardiologist does not know the true EF of a patient. Thus, researchers have often evaluated an estimation method by plotting its results against the results of another (more accepted) estimation method, which amounts to using one set of estimates as the pseudogold standard. In this paper, we present a maximum-likelihood approach for evaluating and comparing different estimation methods without the use of a gold standard with specific emphasis on the problem of evaluating EF estimation methods. Results of numerous simulation studies will be presented and indicate that the method can precisely and accurately estimate the parameters of a regression line without a gold standard, i.e., without the x axis.

In this work, we describe a method that uses the linear phase acquired during the readout period due to chemical shift to generate individual magnetic resonance (MR) images of chemically shifted species. The method utilizes sets of Fourier (or k-space) data acquired with different directions of the readout gradient and a postprocessing algorithm to generate chemical shift images. The methodology is developed for both Cartesian data acquisition and for radial data acquisition. The method is presented here for two chemically shifted species but it can be extended to more species. In this work, we present the theory, show the results in phantoms and in human images, and discuss the artifacts and signal-to-noise ratio of the images obtained with the technique.

The filtered backprojection (FBP) algorithm is widely used in computed tomography for inverting the two-dimensional Radon transform. In this paper, we analyze the processing of an inconsistent data function by the FBP algorithm (in its continuous form). Specifically, we demonstrate that an image reconstructed using the FBP algorithm can be represented as the sum of a pseudoinverse solution and a residual image generated from an inconsistent component of the measured data. This reveals that, when the original data function is in the range of the Radon transform, the image reconstructed using the FBP algorithm corresponds to the pseudoinverse solution. When the data function is inconsistent, we demonstrate that the FBP algorithm makes use of a nonorthogonal projection of the data function to the range of the Radon transform.