Fig 1.
Variable density Poisson disk pattern under-sampling k-space mask.
The sampling rate is 21% (acceleration rate is 4.7×). The mask is 256×110 pixels in resolution. The two axes are the two phase-encoding directions, namely transverse and craniocaudal. The frequency encoding direction is antero-posterior, and is continuous (not depicted).
Fig 2.
Craniocaudal maximum intensity projection images of the sum of squares images and brain masks.
(A) Sum of squares image, (B) brain mask, (C) arterial mask and (D) an axial slice of the parenchymal mask.
Fig 3.
Flowchart of the overall image processing and calculation workflow for all image quality metrics.
Fig 4.
Result of the visual evaluation by consensus of two radiologists.
The axes are wavelet coefficient (α) and total variation (TV) coefficient (β). The score (1 to 5) is denoted on each square. The highest ratings concentrate at β = 3.2 × 10−5 and the parameter pair that reconstructed the best image (α = 3.2 × 10−5, β = 3.2 × 10−5) is denoted as a number in white.
Fig 5.
Craniocaudal maximum intensity projections of reconstructed magnetic resonance angiography.
(A) SoS image and sample images from a visual rating of (B) 1 (α = 1.0 × 10−4, β = 3.2 × 10−3), (C) 2 (α = 1.0 × 10−7, β = 1.0 × 10−6), (D) 3 (α = 3.2 × 10−5, β = 1.0 × 10−4), (E) 4 (α = 1.0 × 10−6, β = 1.0 × 10−5) and (F) 5 (α = 3.2 × 10−5, β = 3.2 × 10−5).
Fig 6.
Color plots of all metrics against the regularization parameter pairs of total variation (α) and wavelet coefficients (β).
The vertical axis of each plot is α (1.0 × 10−7 to 3.2 × 10−3 from top to bottom) and the horizontal axis is β (1.0 × 10−7 to 3.2 × 10−3 from left to right). For NMSE and SIFT, lower values reflect better results (i.e. in blue), and vice versa for PSNR, SSIM and CNR (i.e. good results in red). Note the similarity and dissimilarity with visual evaluation (Fig 4).
Fig 7.
Box-whisker plots of all metrics (vertical axis) against the visual score (horizontal axis).
The red boxes and circles indicate how SSIM and SIFT with brain mask and CNR of artery-to-parenchyma show good correlation with the visual rating, especially with the highest rated images (i.e. score of 5) which are most relevant.
Fig 8.
The top 10 values for each metric.
The parameters that generated the visually best image are noted in red and the highest score in blue. The SSIM with brain mask and CNR have ranked the visually best image (reconstructed with α = 3.2 × 10−5 and β = 3.2 × 10−5) on the top. CNR and SIFT have ranked the six highest rated images in the top six and SSIM with brain mask ranked the six highest rated images in the top seven.