title: An augmented Lagrangian based compressed sensing reconstruction for non-Cartesian magnetic resonance imaging without gridding and regridding at every iteration.
abstract: BACKGROUND
  Non-Cartesian trajectories are used in a variety of fast imaging applications, due to the incoherent image domain artifacts they create when undersampled. While the gridding technique is commonly utilized for reconstruction, the incoherent artifacts may be further removed using compressed sensing (CS). CS reconstruction is typically done using conjugate-gradient (CG) type algorithms, which require gridding and regridding to be performed at every iteration. This leads to a large computational overhead that hinders its applicability.
  
  
  METHODS
  We sought to develop an alternative method for CS reconstruction that only requires two gridding and one regridding operation in total, irrespective of the number of iterations. This proposed technique is evaluated on phantom images and whole-heart coronary MRI acquired using 3D radial trajectories, and compared to conventional CS reconstruction using CG algorithms in terms of quantitative vessel sharpness, vessel length, computation time, and convergence rate.
  
  
  RESULTS
  Both CS reconstructions result in similar vessel length (P = 0.30) and vessel sharpness (P = 0.62). The per-iteration complexity of the proposed technique is approximately 3-fold lower than the conventional CS reconstruction (17.55 vs. 52.48 seconds in C++). Furthermore, for in-vivo datasets, the convergence rate of the proposed technique is faster (60±13 vs. 455±320 iterations) leading to a ∼23-fold reduction in reconstruction time.
  
  
  CONCLUSIONS
  The proposed reconstruction provides images of similar quality to the conventional CS technique in terms of removing artifacts, but at a much lower computational complexity.
authors.affiliation: Department of Medicine (Cardiovascular Division), Beth Israel Deaconess Medical Center and Harvard Medical School, Boston, Massachusetts, United States of America.
authors.forename: Mehmet
authors.initials: M
authors.lastname: Akçakaya
authors.affiliation: Department of Medicine (Cardiovascular Division), Beth Israel Deaconess Medical Center and Harvard Medical School, Boston, Massachusetts, United States of America; Surgical Technologies, Medtronic, Inc., Littleton, Massachusetts, United States of America.
authors.forename: Seunghoon
authors.initials: S
authors.lastname: Nam
authors.affiliation: Department of Medicine (Cardiovascular Division), Beth Israel Deaconess Medical Center and Harvard Medical School, Boston, Massachusetts, United States of America.
authors.forename: Tamer A
authors.initials: TA
authors.lastname: Basha
authors.affiliation: Department of Medicine (Cardiovascular Division), Beth Israel Deaconess Medical Center and Harvard Medical School, Boston, Massachusetts, United States of America; Department of Medicine (Section of Cardiology), University of Chicago, Chicago, Illinois, United States of America.
authors.forename: Keigo
authors.initials: K
authors.lastname: Kawaji
authors.affiliation: School of Engineering & Applied Sciences, Harvard University, Cambridge, Massachusetts, United States of America.
authors.forename: Vahid
authors.initials: V
authors.lastname: Tarokh
authors.affiliation: Department of Medicine (Cardiovascular Division), Beth Israel Deaconess Medical Center and Harvard Medical School, Boston, Massachusetts, United States of America.
authors.forename: Reza
authors.initials: R
authors.lastname: Nezafat
mesh_terms: D000328:Adult; D000465:Algorithms; D044962:Data Compression; D005260:Female; D006801:Humans; D007091:Image Processing, Computer-Assisted; D021621:Imaging, Three-Dimensional; D008279:Magnetic Resonance Imaging / Q000379:methods*; D008297:Male; D008875:Middle Aged; D019047:Phantoms, Imaging; D013997:Time Factors; D055815:Young Adult