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2.
J Magn Reson B ; 107(3): 210-21, 1995 Jun.
Artigo em Inglês | MEDLINE | ID: mdl-7788095

RESUMO

A maximum-likelihood (ML)-based magnetic-resonance-imaging (MRI) reconstruction algorithm is established, based on frequency- and phase-encoded data. The model on which the ML method is based is a superposition of exponentially decaying, sinc-modulated sinusoids, arising from the basic Bloch equations for MR spectroscopy, modified to account for the distribution of resonance frequencies and phases used for spatial localization in the image field. Spatial-localizing gradients are assumed to be known linear functions of spatial coordinate position, with the x-encode (frequency) gradient applied continuously during the full duration of data collection, and the y-encode (phase) gradient applied during varying time periods before data collection. A single-voxel emitter becomes sinc-modulated in the x, y directions at rates proportional to voxel size and gradient strengths in the x-encode and y-encode directions. The full two-dimensional MRI signal becomes a superposition of sinc-modulated, exponentially decaying, single-sinusoid emitters, one for each voxel. The ML estimation of spin-density and spin-spin relaxation decay time images becomes a nonlinear least-squares optimization problem; it is solved using an iterative expectation-maximization algorithm for estimating multiple modulated sinusoids in noise. Phantom studies are presented, demonstrating the accuracy of the model and the application of the algorithm to spin-density and spin-spin relaxation decay time profiles.


Assuntos
Funções Verossimilhança , Imageamento por Ressonância Magnética , Algoritmos , Modelos Teóricos
3.
IEEE Trans Med Imaging ; 14(2): 362-73, 1995.
Artigo em Inglês | MEDLINE | ID: mdl-18215839

RESUMO

A maximum a posteriori (MAP) algorithm is presented for the estimation of spin-density and spin-spin decay distributions from frequency and phase-encoded magnetic resonance imaging data. Linear spatial localization gradients are assumed: the y-encode gradient applied during the phase preparation time of duration tau before measurement collection, and the x-encode gradient applied during the full data collection time t>/=0. The MRI signal model developed in M.I. Miller et al., J. Magn. Reson., ser. B (Apr. 1995) is used in which a signal resulting from M phase encodes (rows) and N frequency encode dimensions (columns) is modeled as a superposition of MN sinc-modulated exponentially decaying sinusoids with unknown spin-density and spin-spin decay parameters. The nonlinear least-squares MAP estimate of the spin density and spin-spin decay distributions solves for the 2MN spin-density and decay parameters minimizing the squared-error between the measured data and the sine-modulated exponentially decay signal model using an iterative expectation-maximization algorithm. A covariance diagonalizing transformation is derived which decouples the joint estimation of MN sinusoids into M separate N sinusoid optimizations, yielding an order of magnitude speed up in convergence. The MAP solutions are demonstrated to deliver a decrease in standard deviation of image parameter estimates on brain phantom data of greater than a factor of two over Fourier-based estimators of the spin density and spin-spin decay distributions. A parallel processor implementation is demonstrated which maps the N sinusoid coupled minimization to separate individual simple minimizations, one for each processor.

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