Accelerating 3D-T 1ρ mapping of cartilage using compressed sensing with different sparse and low rank models

To evaluate the feasibility of using compressed sensing (CS) to accelerate 3D-T mapping of cartilage and to reduce total scan times without degrading the estimation of T relaxation times. Fully sampled 3D-T 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 parameter estimation was also tested. Synthetic phantom (n = 6) and in vivo human knee cartilage datasets (n = 7) were included. Most CS methods performed satisfactorily for an acceleration factor (AF) of 2, with relative T 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 error below 6.5% on T relaxation times with AF up to 10, when spatial filtering was used before T fitting, at the expense of smoothing the T maps. The STFD achieved 5.1% error at AF = 10 with spatial filtering prior to T fitting. Accelerating 3D-T 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 error of 6.5%.