title: Structured errors in reconstruction methods for Non-Cartesian MR data.
abstract: BACKGROUND
  Reconstruction methods for Non-Cartesian magnetic resonance imaging have often been analyzed using the root mean square error (RMSE). However, RMSE is not able to measure the level of structured error associated with the reconstruction process.
  
  
  METHODS
  An index for geometric information loss was presented using the 2D autocorrelation function. The performances of Least Squares Non Uniform Fast Fourier Transform (LS-NUFFT) and gridding reconstruction (GR) methods were compared. The Direct Summation method (DS) was used as reference. For both methods, RMSE and the loss in geometric information were calculated using a digital phantom and a hyperpolarized (13)C dataset.
  
  
  RESULTS
  The performance of the geometric information loss index was analyzed in the presence of noise. Comparing to GR, LS-NUFFT obtained a lower RMSE, but its error image appeared more structured. This was observed in both phantom and in vivo experiments.
  
  
  CONCLUSIONS
  The evaluation of geometric information loss together with the reconstruction error was important for an appropriate performance analysis of the reconstruction methods. The use of geometric information loss was helpful to determine that LS-NUFFT loses relevant information in the reconstruction process, despite the low RMSE.
authors.affiliation: Department of Information Engineering-EIT, University of Pisa, Pisa, Italy; GE Global Research, Munich, Germany. Electronic address: f.gibiino@gmail.com.
authors.forename: Fabio
authors.initials: F
authors.lastname: Gibiino
authors.forename: Vincenzo
authors.initials: V
authors.lastname: Positano
authors.forename: Florian
authors.initials: F
authors.lastname: Wiesinger
authors.forename: Giulio
authors.initials: G
authors.lastname: Giovannetti
authors.forename: Luigi
authors.initials: L
authors.lastname: Landini
authors.forename: Maria Filomena
authors.initials: MF
authors.lastname: Santarelli
mesh_terms: D006801:Humans; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D008279:Magnetic Resonance Imaging / Q000379:methods*; D008962:Models, Theoretical
keywords: Autocorrelation; Hyperpolarized (13)C; Image structures; Magnetic resonance imaging; Non-Cartesian MRI reconstruction