Quantitative susceptibility mapping using plug-and-play alternating direction method of multipliers

Quantitative susceptibility mapping employs regularization to reduce artifacts, yet many recent denoisers are unavailable for reconstruction. We developed a plug-and-play approach to QSM reconstruction (PnP QSM) and show its flexibility using several patch-based denoisers. We developed PnP QSM using alternating direction method of multiplier framework and applied collaborative filtering denoisers. We apply the technique to the 2016 QSM Challenge and in 10 glioblastoma multiforme datasets. We compared its performance with four published QSM techniques and a multi-orientation QSM method. We analyzed magnetic susceptibility accuracy using brain region-of-interest measurements, and image quality using global error metrics. Reconstructions on glioblastoma data were analyzed using ranked and semiquantitative image grading by three neuroradiologist observers to assess image quality (IQ) and sharpness (IS). PnP-BM4D QSM showed good correlation (β = 0.84, R² = 0.98, p < 0.05) with COSMOS and no significant bias (bias = 0.007 ± 0.012). PnP-BM4D QSM achieved excellent quality when assessed using structural similarity index metric (SSIM = 0.860), high frequency error norm (HFEN = 58.5), cross correlation (CC = 0.804), and mutual information (MI = 0.475) and also maintained good conspicuity of fine features. In glioblastoma datasets, PnP-BM4D QSM showed higher performance (IQ_Grade = 2.4 ± 0.4, IS_Grade = 2.7 ± 0.3, IQ_Rank = 3.7 ± 0.3, IS_Rank = 3.9 ± 0.3) compared to MEDI (IQ_Grade = 2.1 ± 0.5, IS_Grade = 2.1 ± 0.6, IQ_Rank = 2.4 ± 0.6, IS_Rank = 2.9 ± 0.2) and FANSI-TGV (IQ_Grade = 2.2 ± 0.6, IS_Grade = 2.1 ± 0.6, IQ_Rank = 2.7 ± 0.3, IS_Rank = 2.2 ± 0.2). We illustrated the modularity of PnP QSM by interchanging two additional patch-based denoisers. PnP QSM reconstruction was feasible, and its flexibility was shown using several patch-based denoisers. This technique may allow rapid prototyping and validation of new denoisers for QSM reconstruction for an array of useful clinical applications.