0365
Improving k-t PERRI: a low-rank data-driven fMRI k-t acceleration method1Wellcome Centre for Integrative Neuroscience, FMRIB Centre, University of Oxford, Oxford, United Kingdom, 2Wellcome Centre for Human Neuroimaging, UCL Institute of Neurology, London, United Kingdom
Synopsis
FMRI data quality requires both good image fidelity (conferring spatial specificity), and high temporal resolution (conferring statistical robustness). We present an image reconstruction algorithm that aims to achieve both aims through a spatio-temporal (k-t) image reconstruction. Our approach utilises low-rank reconstruction algorithms and 3D golden angle k-space sampling. Using golden-angle sampling, we demonstrate that data-driven spatial and temporal priors can be incorporated into reconstruction. We demonstrate improvement over previously-proposed methods (k-t FASTER and k-t PSF) that correspond to special cases of our prior-based reconstruction. These results have great potential to improve on time-independent reconstructions currently in use.
Introduction
Accelerating fMRI data acquisition provides increased effective sampling efficiency, which can be used to increase temporal resolution or temporal degrees of freedom, to improve sensitivity to temporal features, reduce physiological noise aliasing, or improve statistical power. Alternatively, the increased efficiency can enable higher spatial resolution reconstructions.Although fMRI data are primarily accelerated through the use of parallel imaging1,2 and simultaneous multi-slice methods3, these approaches are limited by their time-independent reconstructions and their reliance solely on coil sensitivity information. Recently, low-rank methods have also been shown to enable acceleration of fMRI data by leveraging intrinsic spatio-temporal structures (k-t FASTER)4,5, using information from all time points simultaneously to directly reconstruct the fMRI principal component (spatial and temporal) subspaces.
Here, we demonstrate an improved approach to low-rank constrained fMRI reconstruction, k-t PERRI (Prior Enhanced Rank Reliant Inference), which uses L2 penalties on the estimated spatial and temporal component that enforces our prior knowledge of their structures. The key feature of k-t PERRI is the data-driven priors, derived from an initial reconstruction of the same data. We show that k-t PERRI outperforms k-t FASTER and the partially separable functions (k-t PSF)6 reconstruction model in retrospective and prospectively undersampled experiments.
Theory
k-t PERRI reconstructions solve the following optimisation problem:$$argmin_{X,T} \{ ||f(X∗T')–data||^2_2 + λ_X∗||X−X_{prior}||^2_2 + λ_T∗||T−T_{prior}||^2_2 \}$$
X and T correspond respectively to the weighted spatial and temporal components (Fig.1a). The chosen dimensionality of X and T explicitly enforces the rank constraint. The first term ensures data consistency with the undersampled k-t space data, where f( ) captures the sampling transform (using the NUFFT7,8 and coil sensitivities).
The latter terms represent prior regularization. Xprior and Tprior are produced by an initial reconstruction with λX=λT=0 (Fig.1b). These priors are subsequently incorporated into the final reconstruction, weighted in the spatial domain (λX) and temporal domain (λT) (Fig.1b). Essentially, this two-step process iteratively reweights the low-rank reconstruction with an initial estimation based on a k-t FASTER reconstruction. X and T are jointly optimized using alternating minimization.
Methods
k-t PERRI was compared against the k-t FASTER and k-t PSF methods. These methods can be modelled as special cases of k-t PERRI with specific λX and λT: k-t FASTER4,5, low-rank only, with no priors (λX=λT=0); and k-t PSF6, which reconstructs spatial coefficients against a pre-determined temporal basis (T=Tprior, λX=0 and λT=∞). The methods were first evaluated using a highly-realistic simulation from retrospectively undersampled real data (100x100 matrix, 300 TRs, 30s/30s on/off finger-tapping task, rank=16) with acceleration factors of R=31.4, 15.7 and 10.5 (5, 10, and 15 projections/image reconstructions respectively). The spatial and temporal subspaces were directly compared to the (simulated) ground truth components using canonical correlation (principal angles). Further evaluation of the methods in vivo (i.e. using prospective undersabled reconstructions) used TURBINE9 data (100x100 matrix, 6000 radial projections at TR=0.05s, finger-tapping task, rank=16) with acceleration factors of R=7.9 and 15.7 for TRvol=1s (20 projections/image) and TRvol=0.5s (10 projections/image) respectively.For in vivo reconstructions, z-stat maps were generated through FEAT10, null corrected using mixture modelling and evaluated using ROC curves when compared a slow, fully-sampled reconstruction. Optimal λ values for the in vivo reconstructions were selected based on their peak AUC ROC value (Area Under Curve of Receiver Operating Characteristics) (shown in figure 3 for R=15.7).
Results
Fig.2 displays the spatial and temporal subspace correspondences in the retrospective (simulation) data, across a grid of λ values. The canonical correlation peak at optimal λ values predict that k-t PERRI can indeed improve upon k-t FASTER (top left) and k-t PSF (top right), in both the spatial and temporal domains, particularly at higher acceleration (R=31.4-15.7, or 5-10 projections/image).For R=15.7 in vivo reconstructions (10 projections/image), Fig.3 shows the effect of λ selection on z-stat maps at a consistent threshold (top). The AUC of ROC graph (bottom-left) shows a simplified but similar picture. Optimal λ values yield effective reconstructions (with activation regions similar to the slow, fully sampled reconstruction – bottom-right) but deviation from the optima lead to k-t FASTER- and k-t PSF-like maps.
The benefit of k-t PERRI is most noticeable at high acceleration factors, as figures 4 and 5 demonstrate. For R=7.9 reconstructions (20 projections/image) (Fig.4), the benefit is small. For the faster R=15.7 reconstructions (Fig.5), the benefit becomes more pronounced. k-t PERRI provides a much more sensitive reconstruction at virtually every specificity level, indicating that it is better able to characterize the functional information than the alternative low-rank methods.
Conclusion
k-t PERRI has been shown to successfully perform high fidelity reconstructions of task fMRI data at significant acceleration levels, improving upon the k-t FASTER and k-t PSF low-rank approaches.Acknowledgements
This work was supported by funding from the Engineering and Physical Sciences Research Council (EPSRC) and Medical Research Council (MRC) [grant number EP/L016052/1]
The Wellcome Centre for Human Neuroimaging is supported by core funding from the Wellcome [203147/Z/16/Z].
Professor Karla Miller is supported by the Wellcome Trust (202788/Z/16/Z)
Dr. Mark Chiew is supported by the Royal Academy of Engineering (RF201617\16\23)
References
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Figures
1B: A schematic overview of k-t PERRI. The undersampled dataset first undergoes a standard k-t FASTER reconstruction to create Xprior and Tprior. These priors then feed into the final reconstruction, producing the final dataset. The first term of the Eq.1 is represented in the “Data Consistency” box, and the influence of the prior terms are shown via the downwards dotted arrows (weighted by λX and λT).
