title: MRI reconstruction of multi-image acquisitions using a rank regularizer with data reordering.
abstract: OBJECTIVE
  To improve rank constrained reconstructions for undersampled multi-image MRI acquisitions.
  
  
  METHODS
  Motivated by the recent developments in low-rank matrix completion theory and its applicability to rapid dynamic MRI, a new reordering-based rank constrained reconstruction of undersampled multi-image data that uses prior image information is proposed. Instead of directly minimizing the nuclear norm of a matrix of estimated images, the nuclear norm of reordered matrix values is minimized. The reordering is based on the prior image estimates. The method is tested on brain diffusion imaging data and dynamic contrast enhanced myocardial perfusion data.
  
  
  RESULTS
  Good quality images from data undersampled by a factor of three for diffusion imaging and by a factor of 3.5 for dynamic cardiac perfusion imaging with respiratory motion were obtained. Reordering gave visually improved image quality over standard nuclear norm minimization reconstructions. Root mean squared errors with respect to ground truth images were improved by ∼18% and ∼16% with reordering for diffusion and perfusion applications, respectively.
  
  
  CONCLUSIONS
  The reordered low-rank constraint is a way to inject prior image information that offers improvements over a standard low-rank constraint for undersampled multi-image MRI reconstructions.
authors.affiliation: UCAIR, Department of Radiology, University of Utah, Salt Lake City, Utah 84108.
authors.forename: Ganesh
authors.initials: G
authors.lastname: Adluru
authors.affiliation: IBM Almaden Research Center, San Jose, California 95120.
authors.forename: Yaniv
authors.initials: Y
authors.lastname: Gur
authors.affiliation: Advanced MRI Technologies, Sebastpool, California, 95472.
authors.forename: Liyong
authors.initials: L
authors.lastname: Chen
authors.affiliation: Advanced MRI Technologies, Sebastpool, California, 95472.
authors.forename: David
authors.initials: D
authors.lastname: Feinberg
authors.affiliation: UCAIR, Department of Radiology, University of Utah, Salt Lake City, Utah 84108.
authors.forename: Jeffrey
authors.initials: J
authors.lastname: Anderson
authors.affiliation: UCAIR, Department of Radiology, University of Utah, Salt Lake City, Utah 84108 and Department of Bioengineering, University of Utah, Salt Lake City, Utah 84112.
authors.forename: Edward V R
authors.initials: EV
authors.lastname: DiBella
mesh_terms: D003198:Computer Simulation; D066264:Datasets as Topic; D006257:Head / Q000033:anatomy & histology; D006801:Humans; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D008279:Magnetic Resonance Imaging / Q000379:methods*; D009010:Monte Carlo Method; D009038:Motion; D055414:Myocardial Perfusion Imaging / Q000379:methods; D012119:Respiration