Parallel algorithms for maximum a posteriori estimation of spindensity and spin-spin decay in magnetic resonance imaging
Schaewe, T.J.; Miller, M.I.
Medical Imaging, IEEE Transactions on
Volume 14, Issue 2, Jun 1995 Page(s):362 - 373
Digital Object Identifier 10.1109/42.387717
Summary: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 τ 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
View citation and abstract |
Cart
