Non‐local low‐rank constraint‐based self‐consistent PMRI reconstruction using eigenvector maps

Abstract Eigenvector‐based SPIRiT (ESPIRiT) can estimate multiple sets of coil sensitivity maps from the calibration matrix constructed from the auto‐calibration data. Recently, the L1 norm and total variation were combined with the ESPIRiT model to improve the reconstruction quality of magnetic resonance (MR) images. To further improve the reconstruction performance, the non‐local low‐rank regularisation term is incorporated into the ESPIRiT model (NLR‐ESPIRiT) is proposed. The proposed NLR‐ESPIRiT model takes full advantage of the non‐local self‐similarity features of MR images. The resulting optimisation problem can be transformed into a gradient problem and a denoising problem with low‐rank constraints using the operator splitting technique. The weighted nuclear norm (WNN) is applied as a surrogate of the rank. Then the denoising subproblem with the WNN can be effectively solved by using the alternating direction method of multipliers technique. For practical applications, a parameter‐selecting method is proposed to obtain almost optimal parameters for the same kind of MR images. Simulation experiments on in vivo data sets demonstrate that the proposed NLR‐ESPIRiT outperforms all competing traditional model‐based algorithms in terms of three objective metrics and visual comparison.