Statistical methods for approaching image reconstruction and restoration problems have generated much interest among statisticians in the past decade. In this dissertation, we examine in detail various statistical methods of image reconstruction through the simulation of a multiple-pinhole coded-aperture imaging system for use in emission tomography. We reconstruct each object from a class of 64 total objects, obtaining a reconstruction for each of the 64 originals by several different methods. Among the methods that we use to obtain these reconstructions are maximum likelihood techniques, where we make use of both the popular expectation-maximization (EM) algorithm and a Monte Carlo search routine. We also examine methods that include, in some form, various kinds of prior information. One way of using prior information is through the specification of a prior probability density on the object (or class of objects) to be reconstructed. We investigate the use of Markov random field (MRF) models as a means of specifying the prior densities that will be used to obtain reconstructions. Once given a prior density, these reconstructions are taken to be approximations to the maximum a posteriori (MAP) estimate of the original object. We also investigate reconstructions obtained through other prior densities plus reconstructions obtained by introducing prior information in alternate ways. Once all the reconstructions are obtained, we attempt to answer the important question, "which reconstruction method is 'best'?" We define "best" in this context to be the method that allows a human observer to perform a specified task the most accurately. The task to be performed is to determine whether or not a small protrusion exists on an elliptical object. (This task is motivated by the desire to detect wall-motion abnormalities in the left ventricle of the heart.) We generate 32 objects with protrusions (abnormal objects) and 32 objects without protrusions (normal objects). These objects constitute our class of 64 originals which are reconstructed by the various methods. The reconstruction methods are then analyzed through receiver operating characteristic (ROC) analysis, and a performance index, the area under the curve (AUC), is obtained for each method. Statistical tests are then performed on certain pairs of methods so that the hypothesis that no difference between the AUC's exists can be tested. We found that the reconstruction methods that used the largest amount of (accurate) prior information were generally superior to other methods considered. We also compute calculable figures of merit (FOM) associated with each reconstruction method with the hope that these FOM's will predict the performance of the human observer. Unfortunately, our results indicate that the FOM's that we considered do not correlate well with the performance of the human.

The problems of noise removal, and simultaneous noise removal and deblurring of imagery are common to many areas of science. An approach which allows for the unified treatment of both problems involves modeling imagery as a sample of a random process. Various nonstationary image models are explored in this context. Attention is directed to identifying the model parameters from imagery which has been corrupted by noise and possibly blur, and the use of the model to form an optimal reconstruction of the image. Throughout the work, emphasis is placed on both theoretical development and practical considerations involved in achieving this reconstruction. The results indicate that the use of nonstationary image models offers considerable improvement over traditional techniques.

This work concerns practical quantitative magnetic resonance (MR) imaging techniques and their implementation and use in clinical MR systems. First, background information on MR imaging is given, including the physics of the magnetic resonance, relaxation effects and how imaging is accomplished.Subsequently, the first part of this work describes the estimation of the T2 relaxation parameter from fast spin-echo (FSE) data. Various complications are considered, including partial volume and data from multiple receiver coils along with the effects of the timing parameters on the accuracy of T2 estimates. Next, the problem of classifying small (1 cm diameter) liver lesions using T2 estimates obtained from radially-acquired FSE data collected in a single breath-hold is considered. Several algorithms are proposed for obtaining lesion T2 estimates, and these algorithms are evaluated with a task-based metric, their ability to separate two classes of lesions, benign and malignant. A novel computer-generated phantom is developed for the generation of the data used in this evaluation.The second part of this work describes techniques that perform the separation of water and lipid signals while simultaneously estimating relaxation parameters that have clinical relevance. The acquisition sequences used here are Cartesian and radial versions of Gradient and Spin-Echo (GRASE). The radial GRASE technique is post-processed with a novel algorithm that estimates the T2 of the water signal independent of the lipid signal. The accuracy of this algorithm is evaluated in phantom and its potential use for detecting inflammation of the liver is evaluated using clinical data. Cartesian GRASE data is processed to obtain T2-dagger and lipid fraction estimates in bone which can be used to assess bone quality. The algorithm is tested in phantom and in vivo, and preliminary results are given.In the concluding chapter results are summarized and directions for future work are indicated.

No description available.

This paper proposes a metric to predict edge detection performance when applied to an image with noise. First, models of edges and edge detection linear operators are characterized by their spatial and Fourier domain properties. Second, additive uncorrelated noise on the operator is examined and a metric is developed using the image formation system modulation transfer function (MTF), expected noise power spectral density, and edge detector characterization as inputs. Thirdly, the problem of partially correlated noise is examined. A separate performance metric for simple thresholded operator outputs is proposed. Finally, several discrete edge detectors in noise are evaluated numerically. Both the metric based on signal to noise detector output, and based on thresholding probabilities were useful in predicting previously published performance results. This was true even for many nonlinear detectors based on the linear detectors evaluated here. The specification of a localization criteria was critical for comparisons between detectors.

No description available.

No description available.

No description available.

No description available.

No description available.