title: A framework for generalized reference image reconstruction methods including HYPR-LR, PR-FOCUSS, and k-t FOCUSS.
abstract: OBJECTIVE
  To investigate the relationships among highly constrained back projection (HYPR)-LR, projection reconstruction focal underdetermined system solver (PR-FOCUSS), and k-t FOCUSS by showing how each method relates to a generalized reference image reconstruction method. That is, the generalized series model employs a fixed reference image and multiplicative corrections-that model is extended here to consider reference images more broadly, both in image space and in transform spaces (x-t and x-f spaces), and that can evolve with iteration.
  
  
  METHODS
  Theoretical relationships between the methods were derived. Computer simulations were done to compare HYPR-LR to one iteration of PR-FOCUSS. The generalized reference approaches applied in the x-t or x-f domain were compared using computer simulation, five cardiac cine imaging datasets, and six myocardial perfusion datasets.
  
  
  RESULTS
  PR-FOCUSS and HYPR-LR gave comparable errors, with PR-FOCUSS slightly outperforming HYPR-LR. The baseline image is important to the performance of k-t FOCUSS and x-t FOCUSS, as demonstrated by results from cardiac cine imaging. For cardiac perfusion reconstructions with the use of a temporal average image as the baseline image, k-t FOCUSS gave lower errors than x-t FOCUSS.
  
  
  CONCLUSIONS
  HYPR-LR and PR-FOCUSS are closely related: both work for radial sampling and use reference images in the x-t domain; HYPR-LR is an approximate implementation of the generalized reference framework, while PR-FOCUSS is a conjugate gradient implementation of the generalized reference framework. The superiority of generalized reference approaches applied in the x-t or x-f domain was sensitive to the characteristics of the acquired data and to the baseline image used.
authors.affiliation: Department of Bioengineering, University of Utah, Salt Lake City, Utah 84108, USA.
authors.forename: Liyong
authors.initials: L
authors.lastname: Chen
authors.forename: Alexey
authors.initials: A
authors.lastname: Samsonov
authors.forename: Edward V R
authors.initials: EV
authors.lastname: DiBella
mesh_terms: D000465:Algorithms; D016477:Artifacts; D003198:Computer Simulation; D003952:Diagnostic Imaging / Q000379:methods; D006801:Humans; D007089:Image Enhancement / Q000379:methods; D007091:Image Processing, Computer-Assisted / Q000379:methods* / Q000592:standards; D008279:Magnetic Resonance Imaging / Q000379:methods*; D015233:Models, Statistical; D009206:Myocardium / Q000473:pathology*; D016011:Normal Distribution; D010477:Perfusion