title: Fast reconstruction for multichannel compressed sensing using a hierarchically semiseparable solver.
abstract: OBJECTIVE
  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 >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.
authors.affiliation: Athinoula A. Martinos Center for Biomedical Imaging, Department of Radiology, Massachusetts General Hospital, Charlestown, Massachusetts, USA.
authors.forename: Stephen F
authors.initials: SF
authors.lastname: Cauley
authors.forename: Yuanzhe
authors.initials: Y
authors.lastname: Xi
authors.forename: Berkin
authors.initials: B
authors.lastname: Bilgic
authors.forename: Jianlin
authors.initials: J
authors.lastname: Xia
authors.forename: Elfar
authors.initials: E
authors.lastname: Adalsteinsson
authors.forename: Venkataramanan
authors.initials: V
authors.lastname: Balakrishnan
authors.forename: Lawrence L
authors.initials: LL
authors.lastname: Wald
authors.forename: Kawin
authors.initials: K
authors.lastname: Setsompop
mesh_terms: D000465:Algorithms; D001921:Brain / Q000033:anatomy & histology*; D044962:Data Compression / Q000379:methods*; D006801:Humans; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D008279:Magnetic Resonance Imaging / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D012815:Signal Processing, Computer-Assisted
keywords: SENSE; compressed sensing; hierarchically semiseparable; parallel imaging