The invention discloses a method for quickly reconstructing magnetic
resonance images on the basis of adaptive structure low-rank matrixes, and relates to the technical field of
magnetic resonance imaging. The quality of reconstructed images can be improved by the aid of the method. The method includes steps of (1), acquiring partial k spatial data; (2), solving partial derivatives and constructing Toeplitz matrixes; (3), building image reconstruction models; (4), deforming the Toeplitz matrixes and decomposing characteristic values; (5), computing
weight coefficient matrixes and leading the
weight coefficient matrixes into the reconstruction models; (6), introducing auxiliary variables and Lagrange multipliers and carrying out iterative solution by the aid of ADMM (alternating direction method of multipliers) algorithms; (7), judging whether convergence conditions are met by reconstruction results or not; (8), acquiring ultimate magnetic
resonance images when iterative times are reached, or updating the Toeplitz matrixes by the current reconstructed images obtained by means of iteration, and returning the step (4) to continue operation. Compared with first-order and second-
order structure low-rank and total-variation methods, the method has the
advantage that the reconstructed images with high quality can be obtained by the aid of the method under the condition of identical under-sampling multiples.