Fig 1.
A schematic of the SMS-COOKIE objective function in Eq 3.
(a) Data consistency term (depicted with blue box) enforces consistency with the acquired k-space data κSMS, (b) Split slice-GRAPPA consistency term (depicted with maroon box) provides noisy but reliable estimates of individual k-space slices, (c) SPIRiT term (depicted with green box) further enforces coil self-consistency and improves the individual k-space estimations. An SMS acceleration factor of n = 3 is shown and regularization terms are not depicted.
Fig 2.
Representative T1 weighted images with low SNR from a retrospectively SMS-accelerated dataset, reconstructed using RO-SENSE-GRAPPA, split slice-GRAPPA, proposed SMS-COOKIE and proposed regularized SMS-COOKIE.
Single band images are shown in the top row as reference, and difference images are obtained by subtracting them from the reconstructions. Regularized SMS-COOKIE shows the lowest error and visually similar results compared to single band reference images.
Table 1.
Average PSNR and SSIM metrics over all subject, 15 images and all three slices.
Regularized SMS-COOKIE shows the highest PSNR performance with 23.2%, 20.5% and 10.3% improvement compared to RO-SENSE-GRAPPA, split slice-GRAPPA and SMS-COOKIE. Likewise, regularized SMS-COOKIE shows the highest SSIM among all methods, with 21.1%, 19.7% and 9.5% improvement compared to RO-SENSE-GRAPPA, split slice-GRAPPA and SMS-COOKIE.
Fig 3.
Representative leakage and g-factor maps from a retrospectively SMS-accelerated dataset.
(A) Highest leakage is exhibited in RO-SENSE-GRAPPA (up to 6.5%), which is reduced using split slice-GRAPPA (up to 6.2%). The least amount of leakage is observed with SMS-COOKIE (up to 3.5%). (B) Highest g-factor values are observed in RO-SENSE-GRAPPA (mean = 3.76), corresponding to highest noise amplification, while the lowest g-factor values are shown in SMS-COOKIE (mean = 2.84). Leakage analysis and g-factor quantification require linearity in image reconstruction, therefore regularized SMS-COOKIE cannot be included in these analyses.
Fig 4.
Quantitative pixel-wise tissue characterization as T1 maps of the three slices covering the heart in a retrospectively three-fold SMS and two-fold in-plane accelerated imaging.
Single band, RO-SENSE-GRAPPA, split slice-GRAPPA, proposed SMS-COOKIE amd proposed regularized SMS-COOKIE results are shown. Regularized SMS-COOKIE exhibits closer match to single band image in terms of visual quality and shows less noise compared to other reconstruction methods.
Fig 5.
Bullseye representation of myocardial T1 times and T1 spatial variability over all subjects in retrospectively SMS accelerated study.
Among non-regularized SMS methods, SMS-COOKIE shows the lowest spatial variability. When regularization is included, SMS-COOKIE further improves the spatial variability.
Fig 6.
Quantitative evaluation as T1 maps of the three slices covering the heart in a prospectively accelerated SMS acquisition.
All 4 reconstructions are shown with single band as the reference tissue characterization on the leftmost column. Regularized SMS-COOKIE s hows the closest visual quality to single band references.
Fig 7.
Prospectively SMS accelerated study with bullseye representation of myocardial T1 times and T1 spatial variability over all subjects.
SMS-COOKIE shows the lowest spatial variability compared to non-regularized SMS reconstruction methods. Additionally, regularized SMS-COOKIE further improves the spatial variability compared to existing methods and showed less spatial variability compared to single band reference.
Fig 8.
Quantitative pixel-wise tissue characterization as T1 maps of the three slices covering the heart in a simulation study with three-fold SMS and two-fold in-plane acceleration.
Regularized SMS-COOKIE improves upon all methods and shows closest image quality to reference images depicted as single band images.
Fig 9.
Bullseye representation of myocardial T1 times and T1 spatial variability in 3-fold SMS and 2-fold in-plane accelerated simulation study.
SMS-COOKIE shows the least spatial variability among non-regularized SMS methods, which is further improved by regularized SMS-COOKIE.
Table 2.
Average PSNR and SSIM metrics over 15 images and all three slices for simulation study at 3-fold SMS and 2-fold in-plane acceleration.
Regularized SMS-COOKIE shows the highest PSNR and SSIM performance compared to non-regularized methods.