Motion-compensated orthonormal expansion ℓ1ℓ1-minimization for reference-driven MRI reconstruction using Augmented Lagrangian methods

• An accurate sparse MRI reconstruction method is proposed.
• The reconstruction method is successful particularly when highly under-sampled.
• Sparsity of the target and motion-compensated residual image are explored.
• Obvious feature displacements between the target and reference are discussed.

Compressed Sensing theory has been found with successful reconstructions of MR images from incomplete measurements by prompting sparsity in MR images. Research works have shown even better reconstructions by taking advantage of prior information from a reference image which has anatomical similarity with the target image.In this work, a novel method for motion-compensated reference-driven MR image reconstruction is presented. The target image is directly reconstructed by solving a convex minimization problem which prompts ℓ1ℓ1-norm sparsity of the target and the motion-compensated difference images. An efficient algorithm is proposed to solve the minimization problem with joint application of Augmented Lagrangian method and alternating direction minimization method. Numerical experiments demonstrate that the proposed framework provides more accurate reconstructions especially in high under-sampling ratios when comparing with commonly used and state-of-the-art methods.