title: Parameter estimation using weighted total least squares in the two-compartment exchange model.
abstract: OBJECTIVE
  The linear least squares (LLS) estimator provides a fast approach to parameter estimation in the linearized two-compartment exchange model. However, the LLS method may introduce a bias through correlated noise in the system matrix of the model. The purpose of this work is to present a new estimator for the linearized two-compartment exchange model that takes this noise into account.
  
  
  METHODS
  To account for the noise in the system matrix, we developed an estimator based on the weighted total least squares (WTLS) method. Using simulations, the proposed WTLS estimator was compared, in terms of accuracy and precision, to an LLS estimator and a nonlinear least squares (NLLS) estimator.
  
  
  RESULTS
  The WTLS method improved the accuracy compared to the LLS method to levels comparable to the NLLS method. This improvement was at the expense of increased computational time; however, the WTLS was still faster than the NLLS method. At high signal-to-noise ratio all methods provided similar precisions while inconclusive results were observed at low signal-to-noise ratio.
  
  
  CONCLUSIONS
  The proposed method provides improvements in accuracy compared to the LLS method, however, at an increased computational cost. Magn Reson Med 79:561-567, 2017. © 2017 International Society for Magnetic Resonance in Medicine.
authors.affiliation: Department of Radiation Sciences, Umeå University, Umeå, Sweden.
authors.forename: Anders
authors.initials: A
authors.lastname: Garpebring
authors.affiliation: Department of Radiation Sciences, Umeå University, Umeå, Sweden.
authors.forename: Tommy
authors.initials: T
authors.lastname: Löfstedt
mesh_terms: D000465:Algorithms; D001921:Brain / Q000000981:diagnostic imaging; D001931:Brain Mapping; D002138:Calibration; D003198:Computer Simulation; D003287:Contrast Media / Q000737:chemistry; D038524:Diffusion Magnetic Resonance Imaging; D006801:Humans; D007091:Image Processing, Computer-Assisted; D016018:Least-Squares Analysis; D008279:Magnetic Resonance Imaging; D016011:Normal Distribution; D059629:Signal-To-Noise Ratio
chemical_list: D003287:Contrast Media
keywords: dynamic contrast-enhanced magnetic resonance imaging; parameter estimation; two-compartment exchange model; weighted total least squares