Unlike the attenuation densities which are estimated in conventional xray tomography the signals estimated and measured in magnetic resonance (MR) imaging are inherently timevarying. Any method for reconstructing the free induction decay (FID) signals within particular voxels of an object must take this into account. In spite of this, Fourier MR imaging methods involve decoding procedures for spatial localization of spin density and exponential decay parameters which assume that the signal amplitudes are constant in time, an assumption which is valid only under the condition that the data collection window is very small with respect to the signal decay rate. This forces conventional Fourier methods to generate images from small slices of the full FID time signal (on the order of lO msec). We have recently demonstrated in NMR spectroscopy [1] that fitting the FIB to exponentially decaying sinuosoid models with unknown amplitude,frequency and decay parameters using the method of maximumlikelihood yields far more accurate estimates of the parameters than those based on Fourier methods. This ofcourse requires collection and fitting of the entire FID time signal. Following these ideas, we now describe a new method for reconstructing spin density and T2 images from data collected in the hydrogen MR imaging mode, which models the FID from every voxel of the image as a sinusoid with unknown amplitude and decay. The paper first presents a signal model for the FID signals collected from hydrogen MR imaging based on previous work with collaborators [2], which is at the heart of our new algorithm for maximum likelihood estimation of the image parameters. Then the major focus of this paper is to describe the maximum likelihood estimation of the spin density and T2 decay images, and present its solution via an iterative expectation maximization algorithm. Finally we show the reconstruction of a simulated 2 dimensional phantom imaged using conventional phase and frequency encoding. We conclude by showing results which demonstrate the major advantage of the ML method over conventional Fourier based techniques for producing MR images.