PARALLEL ALGORITHMS FOR MAXIMUM A-POSTERIORI ESTIMATION OF SPIN-DENSITY AND SPIN-SPIN DECAY IN MAGNETIC-RESONANCE-IMAGING

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 localiza tion gradients are assumed: the y-encode gradient applied during the p hase preparation time of duration tau before measurement collection, a nd the x-encode gradient applied during the full data collection time t greater than or equal to 0, The MRT signal model developed in [22] i s used in which a signal resulting from M phase encodes (rows) and N f requency encode dimensions (columns) is modeled as a superposition of MN sine-modulated exponentially decaying sinusoids with unknown spin-d ensity 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 d ecay signal model using an iterative expectation-maximization algorith m. A covariance diagonalizing transformation is derived which decouple s the joint estimation of MN sinusoids into M separate N sinusoid opti mizations, yielding an order of magnitude speed up in convergence, The MAP solutions are demonstrated to deliver a decrease in standard devi ation of image parameter estimates on brain phantom data of greater th an a factor of two over Fourier-based estimators of the spin density a nd spin-spin decay distributions. A parallel processor implementation is demonstrated which maps the N sinusoid coupled minimization to sepa rate individual simple minimizations, one for each processor.