Compressed sensing acceleration of biexponential 3D-T_1ρ relaxation mapping of knee cartilage

Purpose: Use compressed sensing (CS) for 3D biexponential spin-lattice relaxation time in the rotating frame (T_1ρ ) mapping of knee cartilage, reducing the total scan time and maintaining the quality of estimated biexponential T_1ρ parameters (short and long relaxation times and corresponding fractions) comparable to fully sampled scans.

Methods: Fully sampled 3D-T_1ρ -weighted data sets were retrospectively undersampled by factors 2-10. CS reconstruction using 12 different sparsifying transforms were compared for biexponential T_1ρ -mapping of knee cartilage, including temporal and spatial wavelets and finite differences, dictionary from principal component analysis (PCA), k-means singular value decomposition (K-SVD), exponential decay models, and also low rank and low rank plus sparse models. Synthetic phantom (N = 6) and in vivo human knee cartilage data sets (N = 7) were included in the experiments. Spatial filtering before biexponential T_1ρ parameter estimation was also tested.

Results: Most CS methods performed satisfactorily for an acceleration factor (AF) of 2, with relative median normalized absolute deviation (MNAD) around 10%. Some sparsifying transforms, such as low rank with spatial finite difference (L + S SFD), spatiotemporal finite difference (STFD), and exponential dictionaries (EXP) significantly improved this performance, reaching MNAD below 15% with AF up to 10, when spatial filtering was used.

Conclusion: Accelerating biexponential 3D-T_1ρ mapping of knee cartilage with CS is feasible. The best results were obtained by STFD, EXP, and L + S SFD regularizers combined with spatial prefiltering. These 3 CS methods performed satisfactorily on synthetic phantom as well as in vivo knee cartilage for AFs up to 10, with median error below 15%.