Evaluation of Variable Density and Data-Driven K-Space Undersampling for Compressed Sensing Magnetic Resonance Imaging

Zijlstra, Frank, Viergever, Max A, Seevinck, Peter R


Investigative Radiology 51 (6), p. 410-419


OBJECTIVES: 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.

MATERIALS AND METHODS: 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.

RESULTS: 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.

CONCLUSIONS: 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.