title: SHARP edges: recovering cortical phase contrast through harmonic extension.
abstract: OBJECTIVE
  To recover local phase contrast at the edges of the brain (e.g., cortex), where it is otherwise unavailable with the conventional form of the technique sophisticated harmonic artifact reduction for phase data (SHARP).
  
  
  METHODS
  A harmonic potential field, such as the magnetic "background" field, is an analytic field and can thus be represented by a convergent power series. Using SHARP to obtain an initial estimate of the harmonic background field over a reduced inner portion of the brain, a three-dimensional Taylor expansion was performed to extend field coverage to the brain edges. The method, called Extended-SHARP, was quantitatively assessed through a numerical field-forward simulation and qualitatively demonstrated in vivo.
  
  
  RESULTS
  Using a typical spherical kernel (6 mm radius), Extended-SHARP recovered on average 26% more in vivo brain volume than SHARP. When applied to the numerical model, local field contrast around an otherwise lost edge source was recovered, with the resulting error comparable to that of conventional SHARP.
  
  
  CONCLUSIONS
  The lost field values near the edges of the brain can be recovered through an easily implemented adaptation to conventional SHARP.
authors.affiliation: Department of Biomedical Engineering, University of Alberta, Edmonton, Alberta, Canada.
authors.forename: Ryan
authors.initials: R
authors.lastname: Topfer
authors.forename: Ferdinand
authors.initials: F
authors.lastname: Schweser
authors.forename: Andreas
authors.initials: A
authors.lastname: Deistung
authors.forename: Jürgen R
authors.initials: JR
authors.lastname: Reichenbach
authors.forename: Alan H
authors.initials: AH
authors.lastname: Wilman
mesh_terms: D000465:Algorithms; D016477:Artifacts; D001185:Artificial Intelligence; D001921:Brain / Q000033:anatomy & histology*; 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*; D010363:Pattern Recognition, Automated / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity
keywords: SHARP; harmonic extension; phase imaging; susceptibility mapping