title: An L1-norm phase constraint for half-Fourier compressed sensing in 3D MR imaging.
abstract: OBJECTIVE
  In most half-Fourier imaging methods, explicit phase replacement is used. In combination with parallel imaging, or compressed sensing, half-Fourier reconstruction is usually performed in a separate step. The purpose of this paper is to report that integration of half-Fourier reconstruction into iterative reconstruction minimizes reconstruction errors.
  
  
  METHODS
  The L1-norm phase constraint for half-Fourier imaging proposed in this work is compared with the L2-norm variant of the same algorithm, with several typical half-Fourier reconstruction methods. Half-Fourier imaging with the proposed phase constraint can be seamlessly combined with parallel imaging and compressed sensing to achieve high acceleration factors.
  
  
  RESULTS
  In simulations and in in-vivo experiments half-Fourier imaging with the proposed L1-norm phase constraint enables superior performance both reconstruction of image details and with regard to robustness against phase estimation errors.
  
  
  CONCLUSIONS
  The performance and feasibility of half-Fourier imaging with the proposed L1-norm phase constraint is reported. Its seamless combination with parallel imaging and compressed sensing enables use of greater acceleration in 3D MR imaging.
authors.affiliation: Department of Radiology, Medical Physics, University Medical Center Freiburg, Breisacher Straße 60a, 79106, Freiburg, Germany. guobin.li@uniklinik-freiburg.de.
authors.forename: Guobin
authors.initials: G
authors.lastname: Li
authors.affiliation: Department of Radiology, Medical Physics, University Medical Center Freiburg, Breisacher Straße 60a, 79106, Freiburg, Germany.
authors.forename: Jürgen
authors.initials: J
authors.lastname: Hennig
authors.affiliation: Siemens Healthcare, Erlangen, Germany.
authors.forename: Esther
authors.initials: E
authors.lastname: Raithel
authors.affiliation: Department of Radiology, Medical Physics, University Medical Center Freiburg, Breisacher Straße 60a, 79106, Freiburg, Germany.
authors.forename: Martin
authors.initials: M
authors.lastname: Büchert
authors.affiliation: Siemens Healthcare, Erlangen, Germany.
authors.forename: Dominik
authors.initials: D
authors.lastname: Paul
authors.affiliation: Department of Microsystems Engineering-IMTEK, University of Freiburg, Freiburg, Germany.
authors.forename: Jan G
authors.initials: JG
authors.lastname: Korvink
authors.affiliation: Department of Radiology, Medical Physics, University Medical Center Freiburg, Breisacher Straße 60a, 79106, Freiburg, Germany.
authors.forename: Maxim
authors.initials: M
authors.lastname: Zaitsev
mesh_terms: D000465:Algorithms; D001921:Brain / Q000033:anatomy & histology*; D044962:Data Compression / Q000379:methods*; D005583:Fourier Analysis; D006801:Humans; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D021621:Imaging, Three-Dimensional / Q000379:methods*; D008279:Magnetic Resonance Imaging / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D012815:Signal Processing, Computer-Assisted
keywords: 3D MRI; Compressed sensing; Half-Fourier; L1-norm; Phase constraint