Fig 1.
Flowchart of the reconstruction algorithm.
Example is shown for reconstructing axial abdominal MRI images at successive timepoints.
Fig 2.
Comparison of compression via spatial versus temporal subspaces.
It is assumed M subspace vectors are used to represent the dataset. Only the coefficients for the subspace vectors are considered. Top row: the format of the stored data for no compression. Middle row: each coefficient represents the weighting of a temporal subspace vector for a particular pixel. Each spatial location must have M coefficients, resulting in x*y*M total coefficients. Bottom row: each coefficient represents the weighting of a spatial subspace vector. Each temporal location must have M coefficients, resulting in M*T total coefficients. Note that we only count the number coefficients stored since these are what are learned in the final high-spatial, high-temporal resolution reconstructions of SPARS and GRASP-Pro.
Fig 3.
Comparison of reconstruction RMSE’s from proposed spatial subspace approach (SPARS) versus GRASP-Pro.
RMSE at each point in time over all space (row 2) and at each point in space over all of time (rows 4 and 5). The simulated brain dataset is on the left, and the simulated abdomen dataset is on the right. For reference, the mean of the ground truth signals across all of space at each point of time is shown in row 1, and across all of time for each point in space in row 3.
Fig 4.
Comparison of reconstructed images from proposed spatial subspace approach (SPARS) versus GRASP-Pro.
Reconstructions are shown for the time point corresponding to the highest error in SPARS (row 2) in the brain (left) and abdomen (right).
Fig 5.
Comparison of estimated DCE-MRI signal-time curves for the proposed spatial subspace approach (SPARS) versus GRASP-Pro with perfect temporal subspace information.
The ground truth DCE-MRI is shown for comparison in the brain at a single pixel in the thalamus (left) and in the abdomen at a single pixel in the aorta (right).
Fig 6.
Reconstruction RMSE for SPARS as a function of the number of basis vectors.
The RMSE over all space for the first 500 time points in the brain (row 2) and abdomen (row 4) of simulated reconstructions using 10, 20, and 40 estimated basis vectors. Only the first 500 time points are used, because the error does not increase in the last 500 time points. For reference, the mean of the ground truth signal across all of space at each point in time are shown in rows 1 and 3.
Table 1.
Comparing times for estimating subspace basis vectors and final reconstruction for the first in-vivo dataset.
Table 2.
Comparing times for estimating subspace basis vectors and final reconstruction for the second in-vivo dataset.
Fig 7.
Reconstructed images of in-vivo human liver DCE-MRI for dataset 1.
Comparison of GRASP, GRASP-Pro, and SPARS. Select timepoints are shown before, during, and after signal enhancement.
Fig 8.
Reconstructed images of in-vivo human liver DCE-MRI for dataset 2.
Comparison of GRASP, GRASP-Pro, and SPARS. Select timepoints are shown before, during, and after signal enhancement.
Fig 9.
Temporal liver and aorta dynamics from in-vivo DCE-MRI reconstructions for dataset 1.
Comparison of signal-time curves for GRASP-Pro, SPARS, and a low-temporal resolution GRASP reconstruction.
Fig 10.
Temporal liver and aorta dynamics from in-vivo DCE-MRI reconstructions for dataset 2.
Comparison of signal-time curves for GRASP-Pro, SPARS, and a low-temporal resolution GRASP reconstruction.