Multidimensional signal processing of magnetic resonance image scene sequences.

Abstract

This dissertation develops and studies a set of transformations for image analysis and interpretation of magnetic resonance image (MRI) scene sequences. First, the eigenimage filter (EF) is derived as the transformation that maximizes the signal-to-noise ratio (SNR) while correcting for the partial volume averaging effects. Advantages of this new derivation include: (1) a well-defined contrast criterion; (2) demonstration of exact correction for partial volume averaging effects; (3) simple analytical expressions for the weighting vector and the SNR and contrast-to-noise ratio (CNR) of the eigenimage; and (4) fast and numerically stable calculation of the weighting vector. Second, error propagation in eigenimage filtering is investigated and a method for reducing it is suggested. Third, the derivation developed for the eigenimage filter is adapted to maximize the minimum absolute CNR between a desired feature and multiple interfering processes. Fourth, we provide a unified presentation of, and simplified analytical expressions for, the SNR and CNR of the composite images using the following transforms: principal component analysis; matched; modified-matched; eigenimage; maximum contrast; target point; ratio; log-ratio; and angle image. These expressions are then used to evaluate strengths and weaknesses of the various filtering techniques. Fifth, a new multidimensional, non-linear, edge-preserving filter which uses both inter-frame and intra-frame information to filter the additive noise from multiple spin-echo images is developed. This filter combines the well-known exponential model for the multiple spin-echo images with a trimmed spatial smoothing algorithm which utilizes a Euclidean distance discriminator to preserve edges. Its performance is compared to that of several other pre- and post-processing techniques, including lowpass filtering, median filtering, spatial smoothing, and a combination of vector median and average filtering. Finally, the MRI protocols and pulse sequence parameters are optimized to improve the CNR of the eigenimage. Maximization of a normalized CNR of the eigenimage, along with a set of diagnostic or instrumental constraints on the pulse sequence parameters, defines a non-linear constrained optimization problem, which is solved using the fixed point approach. Simulations, phantoms, and brain images are used for evaluation of the techniques and illustration of the results throughout the thesis.