Figure 1.
Visualisation of matrix unfolding of a tensor.
(a) Visualises the matrix unfolding of a third-order tensor and, (b) visualises a third-order tensor multiplied by matrix.
Figure 2.
(a) Shows HOSVD on a third-order tensor and, (b) shows HOSVD on a fourth-order tensor. The left of (b) shows a four dimensional cardiac dataset denoted as A. The four dimensions are labelled as i1, i2, i3 and i4. The right of (b) presents tensor S and the unitary matrices U1 U2 U3 and U4, that were obtained by performing HOSVD operation on A. S is also a fourth-order tensor, the dimensions of which are marked as i1, i2, i3 and i4.
Figure 3.
Several frames of the datasets obtained at different time instants (as indicated).
From top to bottom: (a) Dataset A, (b) Dataset B and, (c) Dataset C. In (c), images obtained at four time instants (as indicated by t3) are presented row by row, and images obtained at four z positions (as indicated by z, along axial direction (base-apex)) are presented column by column. The regions of interest of each dataset are marked within the red rectangles and, the regions of myocardial and blood pool used for averaged signal intensity comparison are marked with yellow and light blue colours, respectively.
Figure 4.
Outline of the reconstruction algorithm.
Figure 5.
Reconstructions of Dataset A at reduction factor 6.
(a) and (b) show the averaged normalised signal intensity at the myocardial and blood pool regions, respectively, and (c) shows the images (region of interest only) at the peak signal intensity of myocardial (the 54th frame, top row) and blood pool (the 14th frame bottom row). The left of (a) and (b) shows the averaged signal intensity of the fully sampled images (black line), k-t SLR reconstruction (blue line) and, the reconstruction of the proposed method (red line); the right of (a) and (b) shows the averaged signal intensity of the fully sampled images (black line), the k-t SPARSE reconstruction (blue line) and, the reconstruction of the proposed method (red line).
Figure 6.
Reconstructions of Dataset A at reduction factor 11.
(a) and (b) show the averaged normalised signal intensity at the myocardial and blood pool regions, respectively, and (c) shows the images (region of interest only) at the peak signal intensity of myocardial (the 54th frame, top row) and blood pool (the 14th frame bottom row). The left of (a) and (b) shows the averaged signal intensity of the fully sampled images (black line), k-t SLR reconstruction (blue line) and, the reconstruction of the proposed method (red line); the right of (a) and (b) shows the averaged signal intensity of the fully sampled images (black line), the k-t SPARSE reconstruction (blue line) and, the reconstruction of the proposed method (red line).
Figure 7.
Reconstructions of Dataset B at reduction factor 6.
(a) and (b) show the averaged normalised signal intensity at the myocardial and blood pool regions, respectively, and (c) shows the images (region of interest only) at the peak signal intensity of myocardial (the 13th frame, top row) and blood pool (the 24th frame bottom row). The left of (a) and (b) shows the averaged signal intensity of the fully sampled images (black line), k-t SLR reconstruction (blue line) and, the reconstruction of the proposed method (red line); the right of (a) and (b) shows averaged the signal intensity of the fully sampled images (black line), the k-t SPARSE reconstruction (blue line) and, the reconstruction of the proposed method (red line).
Figure 8.
Reconstructions of Dataset B at reduction factor 11.
(a) and (b) show the averaged normalised signal intensity at the myocardial and blood pool regions, respectively, and (c) shows the images (region of interest only) at the peak signal intensity of myocardial (the 13th frame, top row) and blood pool (the 24th frame bottom row). The left of (a) and (b) shows the averaged signal intensity of the fully sampled images (black line), k-t SLR reconstruction (blue line) and, the reconstruction of the proposed method (red line); the right of (a) and (b) shows the averaged signal intensity of the fully sampled images (black line), the reconstruction of k-t SPARSE (blue line) and, the reconstruction of the proposed method (red line).
Figure 9.
The averaged normalised signal intensity achieved by the proposed method at reduction factor 11.
(a) The myocardial signal intensity of the fully sampled images and the reconstructed images provided by the proposed method; (b) the blood pool signal intensity of the fully sampled images and the reconstructed images provided by the proposed method.
Figure 10.
The reconstruction of Dataset C (region of interest only) achieved by the proposed method at reduction factor 11.
(a) Presents several fully sampled images, and (b) presents the corresponding reconstructed images. In (a), images obtained at four time instants (indicated by t) are present row by row; and images obtained at four z positions (indicated by z along axial direction (base-apex)) are presents column by column. Likewise, (b) presents the reconstructed images at the corresponding time instants (indicated by t) and z positions (indicated by z).