title: Evaluation of Variable Density and Data-Driven K-Space Undersampling for Compressed Sensing Magnetic Resonance Imaging.
abstract: The aim of this study was to investigate the influence of variable density and data-driven k-space undersampling patterns on reconstruction quality for compressed sensing (CS) magnetic resonance imaging to provide recommendations on how to avoid suboptimal CS reconstructions.
  
  
  
  First, we investigated the influence of randomness and sampling density on the reconstruction quality when using random variable density and variable density Poisson disk undersampling. Compressed sensing reconstructions on 1 knee and 2 brain data sets were compared with fully sampled data sets and reconstruction errors were measured. Sampling coherence was evaluated on the undersampling patterns to investigate whether there was a relation between this coherence measure and reconstruction error.Second, we investigated whether data-driven undersampling methods could improve reconstruction quality when 1 or more fully sampled scans are available as a training set. We implemented 3 different data-driven undersampling methods: (1) Monte Carlo optimization of variable density and variable density Poisson disk undersampling, (2) calculating sampling probabilities directly from the k-space power spectra of the training data, and (3) iterative design of undersampling patterns based on CS reconstruction errors in k-space.Two cross-validation experiments were set up using retrospective undersampling to evaluate the 3 data-driven methods and the influence of the size of the training set. Furthermore, in an experiment that included prospective under sampling, we show the practical applicability of 2 of the data-driven methods. Compressed sensing reconstruction quality was measured with both the normalized root-mean-square error metric and the mean structural similarity index measure.
  
  
  
  Different optimal variable sampling densities were found for each of the data sets, showing that the optimal sampling density is data dependent. Choosing a sampling density other than the optimal density decreased reconstruction quality. These results suggest that choosing a sampling density without having any reference scans is likely suboptimal. Furthermore, no meaningful correlation was found between sampling coherence and reconstruction error.For the data-driven methods, the iterative method yielded statistically significantly higher reconstruction quality in both retrospective and prospective experiments. In retrospective experiments, the power spectrum method yielded a reconstruction quality that was comparable with the data-driven variable density method. The size of the training set had only a minor influence on the reconstruction quality.
  
  
  
  Data-driven undersampling methods can be used to avoid suboptimal reconstruction quality in CS magnetic resonance imaging, provided that at least 1 fully sampled scan is available to train the data-driven method. The iterative design method resulted in the highest reconstruction quality.
authors.affiliation: From the Image Sciences Institute, UMC Utrecht, Utrecht, the Netherlands.
authors.forename: Frank
authors.initials: F
authors.lastname: Zijlstra
authors.forename: Max A
authors.initials: MA
authors.lastname: Viergever
authors.forename: Peter R
authors.initials: PR
authors.lastname: Seevinck
mesh_terms: D000465:Algorithms; D001921:Brain / Q000033:anatomy & histology*; D006801:Humans; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D007719:Knee Joint / Q000033:anatomy & histology*; D008279:Magnetic Resonance Imaging / Q000379:methods*; D009010:Monte Carlo Method; D011446:Prospective Studies; D012016:Reference Values; D012189:Retrospective Studies; D018401:Sample Size