Accelerating 3D-T_1ρ mapping of cartilage using compressed sensing with different sparse and low rank models

Purpose: To evaluate the feasibility of using compressed sensing (CS) to accelerate 3D-T_1ρ mapping of cartilage and to reduce total scan times without degrading the estimation of T_1ρ relaxation times.

Methods: Fully sampled 3D-T_1ρ datasets were retrospectively undersampled by factors 2-10. CS reconstruction using 12 different sparsifying transforms were compared, including finite differences, temporal and spatial wavelets, learned transforms using principal component analysis (PCA) and K-means singular value decomposition (K-SVD), explicit exponential models, low rank and low rank plus sparse models. Spatial filtering prior to T_1ρ parameter estimation was also tested. Synthetic phantom (n = 6) and in vivo human knee cartilage datasets (n = 7) were included.

Results: Most CS methods performed satisfactorily for an acceleration factor (AF) of 2, with relative T_1ρ error lower than 4.5%. Some sparsifying transforms, such as spatiotemporal finite difference (STFD), exponential dictionaries (EXP) and low rank combined with spatial finite difference (L+S SFD) significantly improved this performance, reaching average relative T_1ρ error below 6.5% on T_1ρ relaxation times with AF up to 10, when spatial filtering was used before T_1ρ fitting, at the expense of smoothing the T_1ρ maps. The STFD achieved 5.1% error at AF = 10 with spatial filtering prior to T_1ρ fitting.

Conclusion: Accelerating 3D-T_1ρ mapping of cartilage with CS is feasible up to AF of 10 when using STFD, EXP or L+S SFD regularizers. These three best CS methods performed satisfactorily on synthetic phantom and in vivo knee cartilage for AFs up to 10, with T_1ρ error of 6.5%.