Fast Reconstruction for Multi-channel Compressed Sensing Using a Hierarchically Semiseparable Solver - Cauley, Stephen F. (2014)
PURPOSE: The adoption of multi-channel compressed sensing (CS) for clinical MRI hinges on the ability to accurately reconstruct images from an under-sampled dataset in a reasonable time frame. When CS is combined with SENSE parallel imaging, reconstruction can be computationally intensive. As an alternative to iterative methods that repetitively evaluate a forward CS+SENSE model, we introduce a technique for the fast computation of a compact inverse model solution. METHODS: A recently proposed Hierarchically Semiseparable (HSS) solver is used to compactly represent the inverse of the CS+SENSE encoding matrix to a high level of accuracy. To investigate the computational efficiency of the proposed HSS-Inverse method, we compare reconstruction time with the current state-of-the-art. In vivo 3T brain data at multiple image contrasts, resolutions, acceleration factors, and number of receive channels were used for this comparison. RESULTS: The HSS-Inverse method allows for > 6× speed-up when compared to current state-of-the-art reconstruction methods with the same accuracy. Efficient computational scaling is demonstrated for CS+SENSE with respect to image size. The HSS-Inverse method is also shown to have minimal dependency on the number of parallel imaging channels / acceleration factor. CONCLUSION: The proposed HSS-Inverse method is highly efficient and should enable real-time CS reconstruction on standard MRI vendors’ computational hardware.