Magnetic resonance (MR) spectroscopy and imaging data are most often analyzed using Fourier transforms. Although computationally efficient, such methods fail to take into account the fact that the signals to be analyzed are not simple sinusoids. A deterministic signal model for magnetic resonance imaging is developed in this thesis as an extension of the exponentially decaying sinusoid model used in the analysis of signals in magnetic resonance spectroscopy. The model describes the influence of the image parameters of spin density and spin-spin relaxation on the observed signal, as well as the sinc function modulation of the sinusoidal signal components induced by frequency and phase encoding gradient fields. Experimental verification of the imaging signal model is presented.; The technique of maximum-likelihood (ML) estimation, which requires prior information about the received signal in the form of a parameterized probability density on the data, is applied to the problem of magnetic resonance image reconstruction. Iterative expectation-maximization algorithms which compute the image estimates are derived. A coordinate transformation on the observed data is introduced which leads to a highly efficient parallel reconstruction algorithm.; The iterative ML image estimation algorithms are implemented on a mesh-connected parallel computer. The performance characteristics of the ML algorithm are investigated by comparing image estimates from experimental and simulated data with results produced using Fourier-transform based techniques.
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