Compressed sensing MR image reconstruction based on a non-uniform FFD motion-compensated reference

In this paper, we propose a reference driven magnetic resonance (MR) image reconstruction method inspired by compressed sensing (CS) theory. The target MR image is formulated as a linear combination of a motion compensated reference image and a difference image. Both the global and the local deformations are estimated to enhance the sparsity of the difference image. The global motion is estimated by affine transformation. The local motion is described by hierarchical B-spline refinement, and non-uniform control points at each level are used to speed up the registration. In addition, we replace the l₁ norm term with a weighted l₁ norm to further improve reconstruction quality. The proposed method is applied to a numerical phantom data set and an in-vivo data set. The experimental results prove that our method outperforms the other CS based MR image reconstruction methods under the same sampling rate.