title: Frequency response of multipoint chemical shift-based spectral decomposition.
abstract: OBJECTIVE
  To provide a framework for characterizing the frequency response of multipoint chemical shift based species separation techniques.
  
  
  METHODS
  Multipoint chemical shift based species separation techniques acquire complex images at multiple echo times and perform maximum likelihood estimation to decompose signal from different species into separate images. In general, after a nonlinear process of estimating and demodulating the field map, these decomposition methods are linear transforms from the echo-time domain to the chemical-shift-frequency domain, analogous to the discrete Fourier transform (DFT). In this work we describe a technique for finding the magnitude and phase of chemical shift decomposition for input signals over a range of frequencies using numerical and experimental modeling and examine several important cases of species separation.
  
  
  RESULTS
  Simple expressions can be derived to describe the response to a wide variety of input signals. Agreement between numerical modeling and experimental results is very good.
  
  
  CONCLUSIONS
  Chemical shift-based species separation is linear, and therefore can be fully described by the magnitude and phase curves of the frequency response. The periodic nature of the frequency response has important implications for the robustness of various techniques for resolving ambiguities in field inhomogeneity.
authors.affiliation: Department of Radiology, University of Wisconsin, Madison, Wisconsin 53705-2275, USA. brodskye@cae.wisc.edu
authors.forename: Ethan K
authors.initials: EK
authors.lastname: Brodsky
authors.forename: Venkata V
authors.initials: VV
authors.lastname: Chebrolu
authors.forename: Walter F
authors.initials: WF
authors.lastname: Block
authors.forename: Scott B
authors.initials: SB
authors.lastname: Reeder
mesh_terms: D000273:Adipose Tissue / Q000737:chemistry*; D000465:Algorithms; D001834:Body Water / Q000737:chemistry*; D005583:Fourier Analysis; D006801:Humans; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D008279:Magnetic Resonance Imaging / Q000379:methods*; D008956:Models, Chemical; D015233:Models, Statistical; D008962:Models, Theoretical; D019047:Phantoms, Imaging; D012828:Silicones / Q000737:chemistry
chemical_list: D012828:Silicones