title: Comparison of phase-constrained parallel MRI approaches: Analogies and differences.
abstract: OBJECTIVE
  Phase-constrained parallel MRI approaches have the potential for significantly improving the image quality of accelerated MRI scans. The purpose of this study was to investigate the properties of two different phase-constrained parallel MRI formulations, namely the standard phase-constrained approach and the virtual conjugate coil (VCC) concept utilizing conjugate k-space symmetry.
  
  
  METHODS
  Both formulations were combined with image-domain algorithms (SENSE) and a mathematical analysis was performed. Furthermore, the VCC concept was combined with k-space algorithms (GRAPPA and ESPIRiT) for image reconstruction. In vivo experiments were conducted to illustrate analogies and differences between the individual methods. Furthermore, a simple method of improving the signal-to-noise ratio by modifying the sampling scheme was implemented.
  
  
  RESULTS
  For SENSE, the VCC concept was mathematically equivalent to the standard phase-constrained formulation and therefore yielded identical results. In conjunction with k-space algorithms, the VCC concept provided more robust results when only a limited amount of calibration data were available. Additionally, VCC-GRAPPA reconstructed images provided spatial phase information with full resolution.
  
  
  CONCLUSIONS
  Although both phase-constrained parallel MRI formulations are very similar conceptually, there exist important differences between image-domain and k-space domain reconstructions regarding the calibration robustness and the availability of high-resolution phase information.
authors.affiliation: Research Center Magnetic-Resonance-Bavaria (MRB), Würzburg, Germany.
authors.forename: Martin
authors.initials: M
authors.lastname: Blaimer
authors.affiliation: Department of Experimental Physics 5, University of Würzburg, Würzburg, Germany.
authors.forename: Marius
authors.initials: M
authors.lastname: Heim
authors.affiliation: Research Center Magnetic-Resonance-Bavaria (MRB), Würzburg, Germany.
authors.forename: Daniel
authors.initials: D
authors.lastname: Neumann
authors.affiliation: Research Center Magnetic-Resonance-Bavaria (MRB), Würzburg, Germany.|Department of Experimental Physics 5, University of Würzburg, Würzburg, Germany.
authors.forename: Peter M
authors.initials: PM
authors.lastname: Jakob
authors.affiliation: Siemens Healthcare, Erlangen, Germany.
authors.forename: Stephan
authors.initials: S
authors.lastname: Kannengiesser
authors.affiliation: Research Center Magnetic-Resonance-Bavaria (MRB), Würzburg, Germany.
authors.forename: Felix A
authors.initials: FA
authors.lastname: Breuer
mesh_terms: D000465:Algorithms; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D008279:Magnetic Resonance Imaging / Q000295:instrumentation / Q000379:methods*; D012815:Signal Processing, Computer-Assisted
keywords: ESPIRiT; GRAPPA; conjugate symmetry; parallel MRI; phase-constrained reconstruction; virtual coil