Fast reconstruction for multichannel compressed sensing using a hierarchically semiseparable solver

Stephen F. Cauley, Yuanzhe Xi, Berkin Bilgic, Jianlin Xia, Elfar Adalsteinsson, Venkataramanan Balakrishnan, Lawrence L. Wald, Kawin Setsompop

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


Purpose: The adoption of multichannel compressed sensing (CS) for clinical magnetic resonance imaging (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× 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.

Original languageEnglish (US)
Pages (from-to)1034-1040
Number of pages7
JournalMagnetic resonance in medicine
Issue number3
StatePublished - Mar 1 2015

Bibliographical note

Publisher Copyright:
© 2014 Wiley Periodicals, Inc.


  • Compressed sensing
  • Hierarchically semiseparable
  • Parallel imaging

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