Reconstruction of magnetic resonance images by iterative methods

Abstract

AbstractIn MRI based on the time‐varying gradient magnetic field, the image must be reconstructed from the sampled values which are distributed in k‐space with nonuniform intervals. If there exists any static field inhomogeneity, gradient field nonlinearity, or patient motion, the image must be reconstructed considering these effects, thereby preventing the deterioration of the reconstructed image.This paper proposes a new MRI image reconstruction method to cope with the forementioned problems in a unified way. The proposed method of reconstruction is based on the principle whereby the imaging equation representing the relation between the spin density distribution and FID signal is solved directly by an iterative least‐squares method. The proposed reconstruction method strictly considers that mathematically the measured data are the finite number of sampled values of the FID signal. The minimum norm solution is obtained as the reconstructed image. Also, a method is proposed which improves the convergence of the iterative least‐squares method by utilizing the information concerning the density of the sampling point distribution in k‐space. An image reconstruction experiment is shown assuming the spiral k‐trajectory.