Fast joint estimation of local magnitude, decay and frequency from single-shot MRI

By acknowledging local decay and phase evolution, single-shot parameter assessment by retrieval from signal encoding (SS-PARSE) models each datum as a sample from (k, t)-space rather than k-space. This more accurate model promises better performance at a price of more complicated reconstruction computations. Normally, conjugate-gradients is used to simultaneously estimate local image magnitude, decay, and frequency. Each iteration of the conjugate-gradients algorithm requires several evaluations of the image synthesis function and one evaluation of gradients. Because of local decay and frequency and the non-Cartesian trajectory, fast algorithms based on FFT cannot be effectively used to accelerate the evaluation of the image synthesis function and gradients. This paper presents a fast algorithm to compute the image synthesis function and gradients by linear combinations of FFTs. By polynomial approximation of the exponential time function with local decay and frequency as parameters, the image synthesis function and gradients become linear combinations of non-Cartesian Fourier transforms. In order to use the FFT, one can interpolate non-Cartesian trajectories. The quality of images reconstructed by the fast approach presented in this paper is the same as that of the normal conjugate-gradient method with significantly reduced computation time.