William Scott Hoge

An Adaptive Signal Processing Approach to Dynamic Magnetic Resonance Imaging Subject:

Date: Defended May 14, 2001

Abstract

Magnetic resonance imaging (MRI) is a powerful non-invasive imaging tool that has found extensive use in medical diagnostic procedures. Dynamic MRI refers to the acquisition of multiple images in order to observe changes in tissue structure over time. Clinical applications include the observation of the early flow of contrast agent to detect tumors and real time monitoring of surgical interventions and thermal treatments. The primary goal of our research is to reduce the acquisition time of dynamic MRI sequences through the application of signal processing concepts. These concepts include adaptive filtering techniques, system subspace identification, and subspace tracking. Presented in this thesis are methods to find estimates of the true sequence images from a limited amount of acquired data using optimization of multiparameter function techniques. The methods build on the linear MRI system response model first proposed by Panych and Zientara. Three new methods related to dynamic MRI are presented. First, because medically significant changes are typically limited to a small region of interest (ROI), a static ROI estimation problem is presented along with a numerical solution algorithm. This static problem has parallels to matrix completion problems in the field of linear algebra. Second, a general adaptive image estimation framework for dynamic MRI is described. Analysis shows that most previous low-order methods are special cases of this general framework. Third, two methods are presented for identifying suitable MR data acquisition inputs to use with the adaptive estimation framework: one relies on a conjugate gradient algorithm constrained to the Stiefel manifold; the second relies on linear prediction. The combination of the adaptive estimation framework and dynamic input identification methods provide a mechanism to efficiently track changes in an image slice, potentially enabling significant acquisition time savings in a clinical setting.