Fast reconstruction for multichannel compressed sensing using a hierarchically semiseparable solver

Abstract

Purpose

The adoption of multichannel compressed sensing (CS) for clinical magnetic resonance imaging (MRI) hinges on the ability to accurately reconstruct images from an undersampled 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 math formula speedup 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. Conclusions

The proposed HSS-Inverse method is highly efficient and should enable real-time CS reconstruction on standard MRI vendors' computational hardware.