Figure 1.
Block schematic of the proposed autocalibrating MRI reconstruction technique.
Figure 2.
Bandwidth of a spatial sensitivity profiles and calibration kernels.
Top row: two coils profiles and their (regularized) pointwise division. Bottom row: corresponding operations in Fourier/k-space. The images were taken from a SENSE dataset. Note how the Fourier domain support size of the division is both larger than that of the typical calibration kernel and larger than the support size of the Fourier domain support of both coil profiles.
Figure 3.
Results from noise measurements on 10 000 repeated acquisitions of a 2 shot spiral: the trajectory (a) box plot of per 100 measurement variance estimates on each k-space point (b) the absolute error matrix between two sets of 100 measurements over a short timescale (c) the absolute error matrix between two sets of 100 measurements on a longer timescale (d) the crosscorrelation matrix between k-space points overall (e).
Figure 4.
K-space points considered for noise level estimation indicated in red.
Left: Subsampled spiral, Right: pMRI GRAPPA sequence.
Figure 5.
Demonstration of how the signal level is estimated.
A crude reconstruction is made (left), which can contain aliasing, then a histogram is made of its pixel values and a mixture of 2 Gaussian distributions is fit to its histogram (right).
Figure 6.
Left, a 2D grid of k-space sampling coordinates, Right, its Voronoi tesselation.
Figure 7.
Detail of the Voronoi tesselation in Figure 6 showing the principle of the density estimation.
Figure 8.
A 25% subsampled Spiral trajectory for a 256×256 image.
The blue points are all the data points, the red portion of points signifies the automatically detected autocalibration region.
Figure 9.
PSNR, in function of acceleration factor, with respect to the reconstruction at acceleration factor 1.
The distinction between realistic and perfect calibration is with respect to the data used for calibrating the pMRI reconstruction. Realistic calibration uses only the undersampled dataset, perfect calibration uses the fully sampled dataset, before the simulated undersampling.
Figure 10.
Visual comparison between ‘perfect calibration’ SPIRIT, ‘realistic calibration’ SPIRIT, ESPIRIT and the proposed method for reconstruction of some of the datapoints that make up_ Figure 9 the acceleration factor (AF) is shown on the left.
Figure 11.
PSNR, in function of acceleration factor, with respect to the reconstruction at acceleration factor 1.
The dashed line is the proposed method, the full line is SPIRIT with fully sampled knowledge of calibration data.
Figure 12.
pMRI reconstruction results for the GE hardware phantom: a visual comparison between proposed reconstruction and ‘perfect calibration’ SPIRIT reconstruction for some of the graph points that make up the graph in Figure 11, for AF = 1 and AF = 4.
Figure 13.
Contrast enhanced reconstruction from GRAPPA experiment.
For both the high SNR and the low SNR case the contrast was adjusted for maximal visibility. Top: reference GRAPPA reconstruction, Bottom: Proposed.
Figure 14.
Illustration of an estimated coil sensivity profile.
Top left: a crop from the noisy GRAPPA reconstruction, in high contrast indexed colormap Top right: a crop from proposed reconstruction, in high contrast indexed colormap Bottom left: estimated coil profile from coil 1, Bottom right: logarithmically scale power spectral density of the coil profile in the bottom left.
Figure 15.
Reconstruction experiment for a simulated random subsampling of phase encoding lines to 34% of the Nyquist rate.
GRAPPA, SPIRIT and the proposed method use autocalibration. The COMPASS method uses exact knowledge of the simulated coil profiles.
Figure 16.
Reconstruction experiment for a simulated random subsampling of phase encoding lines to 20% of the Nyquist rate.
Figure 17.
Reconstruction from a simulated subsampled Archimedean spiral pMRI acquisition.
(left) Ground truth, (middle left) maximum likelihood sum of squares reconstruction (19.2dB), (middle right) proposed method (21.9dB), (right) k-space sampling pattern detail, notice the spiral arms being too distant to allow for conventional autocalibration.
Figure 18.
K-space trajectory used in the 3D stack of spiral experiment.
The red points constitute the automatically detected autocalibration area. Left: side view, Right: top view.
Figure 19.
Reconstruction experiments from an autocalibrated 3D stack of spirals reconstruction.
Top row: saggital view of slice 32. Middle row: saggital view of slice 16. Bottom row: coronal view of slice 64.