title: Robust reconstruction of B1 (+) maps by projection into a spherical functions space.
abstract: OBJECTIVE
  Several parallel transmit MRI techniques require knowledge of the transmit radiofrequency field profiles (B1 (+) ). During the past years, various methods have been developed to acquire this information. Often, these methods suffer from long measurement times and produce maps exhibiting regions with poor signal-to-noise ratio and artifacts. In this article, a model-based reconstruction procedure is introduced that improves the robustness of B1 (+) mapping.
  
  
  METHODS
  The missing information from undersampled B1 (+) maps and the regions of poor signal to noise ratio are reconstructed through projection into the space of spherical functions that arise naturally from the solution of the Helmholtz equations in the spherical coordinate system.
  
  
  RESULTS
  As a result, B1 (+) data over a limited range of the field of view/volume is sufficient to reconstruct the B1 (+) over the full spatial domain in a fast and robust way. The same model is exploited to filter the noise of the measured maps. Results from simulations and in vivo measurements confirm the validity of the proposed method.
  
  
  CONCLUSIONS
  A spherical functions model can well approximate the magnetic fields inside the body with few basis terms. Exploiting this compression capability, B1 (+) maps are reconstructed in regions of unknown or corrupted values.
authors: Imaging Division, University Medical Center Utrecht, Utrecht, The Netherlands.
authors: Alessandro
authors: A
authors: Sbrizzi
authors: Hans
authors: H
authors: Hoogduin
authors: Jan J
authors: JJ
authors: Lagendijk
authors: Peter
authors: P
authors: Luijten
authors: Cornelis A T
authors: CA
authors: van den Berg
mesh_terms: D000465:Algorithms; D000818:Animals; D016477:Artifacts; D001931:Brain Mapping / Q000379:methods; D003198:Computer Simulation; 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*; D008954:Models, Biological; D019047:Phantoms, Imaging; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity
keywords: B1+ mapping; Helmholtz equation; parallel transmit; radiofrequency field mapping; spherical harmonics