Figure 2. Reconstruction results for uniform undersampling without (top row) and with (bottom row) attack. The small perturbation causes no visual difference in the fully-sampled image or the zero-filled image. The reconstructions without attack show some residual aliasing due to the R=4 acceleration. Both CG-SENSE and GRAPPA visibly fail with the small perturbation attack.

Figure 3. Reconstruction results for random undersampling without (top row) and with (bottom row) attack. The small perturbation leads to no visual change in the fully-sampled or zero-filled image. For the input without attack, CG-SENSE has visible and multi-coil CS has subtle aliasing artifacts at R=4. For the attack input, both these reconstructions fail although they are run with the exact same parameters as the non-attack case.

Subtle Crime I Results. (a) CS reconstructions from data subsampled with R=6. The subtle crime effect is demonstrated: the reconstruction quality improves artificially as the sampling becomes denser around k-space center (top to bottom) and the zero-padding increases (left to right). (b) The same effect is shown for CS (mean & STD of 30 images), Dictionary Learning (10 images), and DNN algorithms (87 images): the NRMSE and SSIM improve artificially with the zero-padding and sampling.

Subtle Crime II concept. MR images are often saved in the DICOM format which sometimes involves JPEG compression. However, JPEG-compressed images contain less high-frequency data than the original data; therefore, algorithms trained on retrospectively-subsampled compressed data may benefit from the compression. These algorithms may hence exhibit misleadingly good performance.

Fig.4(A) Voxelwise magnitude correlations between B1_initial (initial position) and B1_gt (ground-truth displaced) [left] and B1_predicted (network predicted displaced) and B1_gt [right]. Small (top), medium (middle) and large (bottom) displacements are shown. Phase data not shown. (B) Magnitude (in a.u.) and phase (radians) B1-maps for the largest displacement. Left, middle and right: B1_initial, B1_gt and B1_predicted, respectively. B1_predicted quality did not depend heavily on displacement magnitude and remained high despite 5 network cascades for evaluation at R-20 A10mm.

Fig.3(A) Motion-induced flip-angle error for pTx pulses designed using B1_initial (conventional method, pink) & B1_predicted (proposed method, blue) at all evaluated positions & slices. Y-axes show nRMSE (% target flip-angle). nRMSE of all pulses_predicted is at/below the shaded region. Asterisks show number of network cascades required for evaluation. (B) Example profiles. Left: evaluation for pulse_initial without motion. Middle & right: evaluations at B1_gt (displaced position) using pulse_initial & pulse_predicted, respectively. Colorscale shows flip-angle (target=70°).

Figure 1. The structure of the proposed network. “A” represents the BUDA forward model, “B” is SENSE-encoding (coil sensitivities and Fourier transform), “VC” represents augmentation of virtual conjugate coils for the phase constraint. Some parameter choices are: the number of iteration K=7, convolution kernel size=7, The number of output channels of the first convolutional layer=64, λ₁ = 1, λ₂ = 0.5.

Figure 2. The reconstruction results of the diffusion data with b=1000s/mm² . Top two rows display reconstructed images, the bottom two rows show error images (10x-amplified). For each shot, 4x in-plane acceleration was applied. Two shots (one blip-up and one blip-down) were used for reconstruction. The reference images were generated by combining 4 shots (2 blip-up and 2 blip-down) through BUDA. Naive SENSE does not include the fieldmap, resulting in distortion near frontal lobes.

Fig. 1. The proposed sparse plus low-rank network (L+S-Net) for dynamic MRI. The L+S-Net is defined by the iterative procedures of Eq.(5). The three layers correspond to the three modules in L+S-Net, which are named as low-rank prior layer, sparse prior layer and data consistency layer respectively. The convolution block in sparse prior layer is shown at the left bottom. The correction term in data consistency layer is shown at the right bottom.

Fig. 3. The reconstruction results of the different methods (L+S, MoDL and L+S-Net) at 12-fold acceleration using multi-coil data. The first row shows, from left to right, the ground truth, the reconstruction result of these methods. The second row shows the enlarged view of their respective heart regions framed by a yellow box. The third row shows the error map (display ranges [0, 0.07]). The y-t image (extraction of the 92th slice along the y and temporal dimensions) and the error of y-t image are also given for each signal to show the reconstruction performance in the temporal dimension.

Fig. 1. Overall framework of our proposed joint deep model-based magnetic resonance image and coil sensitivity reconstruction network (Joint-ICNet).

Fig. 3. Fully sampled and reconstructed (a) FLAIR images and (b) T2 images using zero-filling, ESPIRiT, U-net, k-space learning, DeepCascade, and Joint-ICNet, with the reduction factors R = 4 and R =8, respectively.

FIG_2: Comparison of the single-slice temporal subspace reconstruction with a rank $$$N_\text{b}=30$$$ subspace estimated using PCA (left) and SSA-FARY SE (right). The movie shows a 1.8s snippet of the full time-series. The snippet corresponds to the time-frames highlighted by the orange box in FIG_3. (The movie of the full time-series could not be included here due to file-size limits.)

FIG_4: Real- and imaginary part of the six most significant temporal basis functions $$$T\,1\;-\;T\,6$$$ and the corresponding complex image coefficients for PCA (left) and SSA-FARY SE (right). The temporal basis functions are provided by the columns of the matrix $$$U$$$, see Step 2 of the theory section.

Left: The quantitative Recurrent Inference Machine jointly reconstructs and estimates an R2*-map from sparsely sampled multi-echo gradient echo data. Right: The netwerk architecture of the quantitative Recurrent Inference Machine is shown with the log-likelihood function l(M,R2*,B0) depicted on top.

Example R2* images of the reference image and 12-times accelerated reconstructions using the RIM with least-squares fit, and the proposed method qRIM with integrated reconstruction and parameter estimation.

Figure 4: Reconstruction result from a slice in the test set for $$$R=5$$$ and $$$R=10$$$. Zero-filled reconstruction corresponds to applying $$$A_\phi^H$$$ on $$$z$$$ directly.

Figure 1: Network architecture consisting of nuFFT based encoder (a) and unrolled reconstruction network (b, c). Sampling locations $$$\phi$$$ are shared between encoder and decoder.

Figure 3: The NRMSE over the whole parameters space. In blue the results for the Network I trained on 1D slice-selective SLR pulses for different validation data sets are shown. In red the same principle was extended to Network II, for which SMS pulses were included in the library. The first row ((a)-(c) displays the influence of the BWTP, the second row ((d)-(f)) with respect to the FA and the third row ((g)-(i)) to a varying slice thickness . The last row ((j)-(l)) shows the influence of the slice shift . The relations are evaluated for the magnetization profile, the RF pulse and the gradient.

Figure 2: Representative example for a validation data set with a BWTP of 7, FA of 45°, slice thickness of 7mm and no slice shift used on the pretrained neural network is shown. In (e), (f), (g) the output is compared to the ground truth. The prediction is used for a second Bloch simulation to analyze the difference between the desired and the predicted magnetization in (a), (b), (c), (d). The predicted result is in good agreement with the ground truth for this parameter set.

Figure 1: Illustration of the Multinet architecture, featuring the Multi-image U-net and a traditional U-net. The Multi-image U-net takes in as many images as there are coils, and outputs that many images.

Figure 2: Illustration of the Multi-image U-net, the first component of the Multinet. The number in the boxes indicates the number of channels, while the width and height of the data is displayed to the side. x is the number of channels in the output of the first convolution, i.e. Multinet-16 would have x=16. n is the number of input and output channels of the entire model. For the Multinet, this is the number of coils.

Fig.5 Comparison of reconstructed images between eFREBAS-CNN, Image Domain CNN, ADMM-CSNet and CS iterative. (h) – (m) are the enlarged images of (a) – (f), respectively.

Fig.3 Network architecture and reconstruction flow of eFREBAS-CNN. Three groups are reconstructed by three CNNs, respectively. U-Net2 and U-Net3 that treats Group B and Group C are input lower frequency sub-images as shown in Fig.2.

Figure 2: Simulation of loss landscapes. The loss landscapes of the \(\ell^1, \ell^2,\) and \(\perp\)-loss are shown, respectively. For every \((\phi, \lambda)\) pair, \(10^5\) random complex number pairs were generated. Contours show lines of equal loss. The figures show that \(\perp\)-loss is symmetric around \(\lambda\), whereas the \(\ell^1\) and \(\ell^2\) loss functions have a higher loss for \(\lambda > 1\).

Figure 3: Typical reconstructions. Typical magnitude reconstructions from the \(\ell^1\), \(\ell^2\) and \(\perp\)-loss networks with R=5. Top row shows magnitude target and reconstructions, with respective squared error maps below. The training with our loss function reconstructs smaller details as highlighted by the red arrows. Third row shows phase map target and reconstructions, with respective error maps below. Significant phase artifacts not present in \(\perp\)-loss are highlighted.

Figure 1: Block diagram of the proposed method: First, PCA is applied to compress the VD under-sampled human head data from 30 channel receiver coils to 8 virtual coils. Later U-Net is used to compensate the compression losses of PCA in terms of sensitivity information of 8 virtual coils VD under-sampled images. Later, adaptive coil combination of CS-MRI reconstructed virtual coil images gives the final solution/reconstructed image.

Figure 2: CS-MRI reconstructed 8 virtual coil images obtained from the proposed channel compression and PCA: First the VD under-sampled human head data (AF=2) is compressed from 30 channel receiver coils into 8 virtual coils by the proposed method and PCA. Later, CS-MRI is used for coil-by-coil reconstruction of 8 virtual coil under-sampled images. The reconstructed virtual coil images show minimum compression losses by the proposed method as compared to the PCA.

Fig. 1: The pipeline of MAGIC-Net.

Fig. 4: The reconstruction of MAGIC-Net and CG-SENSE of b = 0 s/mm² and b =1000 s/mm² under different sampling trajectories.

Figure 2: Nlops and automatic differentiation. a) A basic nlop modeled by the operator $$$F$$$ and derivatives $$$\mathrm{D}F$$$. When applied, $$$F$$$ stores data internally such that the $$$\mathrm{D}F$$$s are evaluated at $$$F$$$'s last inputs. b) Chaining two nlops $$$F$$$ and $$$G$$$ automatically chains their derivatives obeying the chain rule. The adjoint of the derivative can be used to compute the gradient by backpropagation. c) Composition of a residual structure $$$F(\mathbf{x}, G(\mathbf{x},\mathbf{y}))$$$ by combine, link and duplicate.

Figure 1: Basic structure of the BART-libraries used for deep learning: Networks are implemented as nlops supporting automatic differentiation. The nn-library provides deep-learning specific components such as initializers. Training algorithms have been integrated BART's library for iterative algorithms. MD-functions act as a flexible, unified interface to the numerical backend. We added many deep-learning specific nlops such as convolutions using efficient numerical implementations. Solid blocks represent major changes allowing deep learning.

Block diagram of the approach. (a) Inside each unrolling step, the pair of variables is updated in an alternating fashion with M steps of CG applied to each variable. The red blocks represent the learnable parameters of Deep J-Sense and are shared across unrolls. The numbers in parentheses corresponding to the four update steps in the text. (b) N unrolls are applied starting from initial values. At each step, the gradient of the loss term is back-propagated to the trainable parameters and an update is performed.

Examples of estimated sensitivity maps and reconstructed coil images output by our method after N = 6 unrolls for a validation sample with R = 4. The first five columns show specific coils and the last columns shows the RSS image obtained from all 15 coils. The first row shows the estimated sensitivity maps, obtained by zero-padding and IFFT of the estimated frequency-domain kernel. The second row shows the sensitivity maps estimated using the auto-ESPIRiT algorithm. The third row shows the reconstructed coil images. The fourth row shows the ground truth (fully-sampled) coil images.

Figure 1. The python program to train a generic prior consists of components illustrated above.

Figure 3. Reconstructions from 60 radial k-space spokes via zero-filled, iterative sense, $$$\ell_1$$$-wavelet, learned log-likelihood (left to right).

Fig.2: Reconstruction result of the random variable density sampling, along with the fully-sampled image, undersampled (zero-padded) image and the corresponding difference images.

Fig.1. Network architecture and the workflow of the proposed complex valued residual neural network. The network is provided with undersampled k-space for each coil, treating each coil as different channel. The network also provided coil-wise k-space as output. The originally acquired data were then replaced in the output k-space as a data consistency step. 2D inverse fast Fourier transform (IFFT) was performed on this k-space to obtain the coil-wise reconstructed images. IFFT was also performed on the fully sampled k-space and then the loss was computed by comparing these images.

Figure 4. Top: Example reconstructions with motion induced at 3% of scanning lines. The Interleaved and Alternating architectures more accurately eliminate the 'shadow' of the moved brain and the induced ringing and blurring compared to the single-space networks.

Bottom: Comparison of all four network architectures on test samples with motion at varying fractions of lines. For nearly every example, the joint architectures (Interleaved and Alternating) outperform the single-space baselines.

Figure 1. Maps of correlation coefficients between a single pixel (circled) and all other pixels in image (left) and frequency (right) space representations of the brain MRI dataset (click to view an animation of correlation patterns at several pixels). Both maps show strong local correlations useful for inferring missing or corrupted data. Frequency space correlations also display conjugate symmetry characteristic of Fourier transforms of real images.

Figure 1. Overview of DeepSlider. Five slab-encoding RF pulses are designed using deep reinforcement learning and gradient descent. The signals from slab-encoding RF pulses can be modeled as a linear system of an encoding matrix and sub-slice signals z. The design objective is to minimize the condition number of the encoding matrix A, improving stability against noise.

Figure 2. Details of generating slab-encoding RF pulses. (a) In a single episode, DRL agent generates an RF pulse as an action, and Bloch equation environment returns a reward for the RF pulse. The reward is composed of slice profile penalty and SAR regularization. The agent is updated using the reward and generates an RF pulse recursively to maximize the reward. (b) DRL-generated RF pulses are randomly grouped into five RF pulses. Then the five RF pulses are optimized to have the lowest condition number in the encoding matrix (and maximize DRL reward term) by gradient descent.

Figure 1. ACS flowchart: AI Module represents the trained AI network; CS Module is for solving the second formula using iterative reconstruction.

Figure 2. T2 FSE 2D of knee with acceleration factors from 2.00x to 4.00x. As acceleration factor increased, quality of CS images degraded more rapidly than ACS.

Figure 1: Schematic of the MRzero framework. Topmost part: An MR image is simulated for given sequence parameters and Bloch parameters (PD, B1 and T1) with an analytic signal equation. The evolution of the signals are mapped pixelwise to B1 and T1 values with a NN. The output is compared to the target (B1 and T1 value) and gradient descent optimization is performed to update sequence parameters TI, Trec, TR, $$$\alpha_{gre}$$$, $$$\alpha_{prep}$$$ and NN parameters.

Figure 4: Pixelwise evaluation of the NN-predicted B1 (A) and T1 (B) maps for the optimized sequence (first column) and the inversion recovery (second column). B1 map from the WASABI measurement as reference (third column). Correlation between WASABI and optimized sequence with correlation coefficient R=0.88 and correlation between WASABI and inversion recovery with correlation coefficient R=0.90 (C). Comparison of obtained T1 values for different tissue ROIs with literature values (D).

Figure 1. Overview of AutoSON. (a) Structure of AutoSON. AutoSON contains an MRI simulator for the generation of training signals and a neural network that extracts target information for the objective. (b) Joint optimization of AutoSON. The distribution of tissue properties and noise conditions were utilized to generate training data. Using this data, joint optimization was performed for scan parameters and weights of the neural network using a loss function for the objective. (c) After the joint optimization, the sequence parameters were optimized for the objective.

Figure 4. Partially spoiled SSFP T2 mapping results of the scan parameters. The AutoSON optimized parameters yielded better performance than the parameters from Wang et al. in a computer simulation, although the mapping was performed by without a neural network.

The architecture of our Attentive Residual Non Local-Network (ARNL-Net) with RCAB as building blocks.

Image reconstructions under cartesian constrained acquisition scheme. Second row demonstrates the results for the joint optimization model.

Figure 1. Artifacts simulated in this work and identified in the low-field dataset. a) Representative input brain slice (b-e) Gibbs ringing and wrap-around artifacts simulated in this work b) Gibbs ringing artifact c) X-axis wrap-around artifact d) Y-axis wrap-around artifact e) Z-axis wrap-around artifact (f-i) Wrap-around artifacts identified in the low-field dataset (j-m) Gibbs ringing artifact identified in the low-field dataset.

Figure 4. Performance evaluation and model explanation via filter visualization for wrap-around artifact identification. (a) Confusion matrix obtained from the validation and test sets; in the case of simulated data, forward modeling parameters were tweaked based on the validation set results to improve performance. (b) Visualization of representative filters for a true-positive (TP), true-negative (TN), false-positive (FP) and a false-negative (FN) input for explainability.

Fig.2 Workflow of smart patient positioning

Fig.1 Placement of Camera in MRI scanner room

Example results from the synthetic test dataset where the uncertainty metric Δy accurately predicted the validity of the corrections: For the input image shown in the top row, the network produces a faithful reconstruction of the ground truth image, which is accurately predicted by the low uncertainty metric. For the center and bottom row, substantial deviations from the ground truth can be observed (marked by arrows), which is accurately predicted by the relatively high uncertainty metric (SD=standard deviation).

Example results on the synthetic test dataset where the uncertainty metric Δy did not accurately predict the validity of the corrections. In particular, multiple local hallucinations can be observed (indicated by red arrows), although the TTA metric values are relatively low (Δy=0.3).

QSM Pipeline: Raw phase and magnitude images from SWI are combined (Bernstein method), the phase is unwrapped (fast phase unwrapping algorithm), background removed (Laplacian boundary value method), and the QSM reconstructed (MEDI).

Comparison of de-Gibbs-ed outputs from MRtrix3 and our UNet model removing the simulated Gibbs artifacts that were generated by truncating 70% of the high frequency k-space components of a full-sized mask from an image with minimal visually detectable Gibbs artifact. The second row is a zoomed in look into the black square on the first row.

Figure 3: Comparison between 4 x 3 accelerated, l2-regularized GRAPPA using 3D kernels trained on a reference scan, and an acceleration matched SPARK acquisition (un-regularized GRAPPA-input). SPARK measured the 30 x 30 undersampled ACS region with 2 x 2 undersampling and the exterior of kspace with 4 x 3 undersampling in the phase encode and partition directions. SPARK exploits the same reference scan used in GRAPPA to achieve improvement at the representative slices.

Figure 4: Comparisons between sense, sense + SPARK, wave encoding, and wave + SPARK reconstructions on a simulated multiband 5, in-plane acceleration 2, acquisition. Wave was simulated with a maximum Gy/Gz gradient amplitude of 16 $$$\frac{mT}{m}$$$ and two cycles. Complex gaussian noise was added to all simulated data. SPARK provides qualitative and quantitative rmse improvement for both the sense and wave reconstructions. Wave + SPARK achieves the best results on both the total slice group and individual slices.

Figure 3 - Qualitative comparison of the models on a selected slice for the whole brain and two selected regions (green and blue boxes). The AHEAD reference is subject 005 slice 158. The ** represents the unoptimized cyclic LR WIMSE.

Table 1 - Comparison of models performance using the MSE and SSIM metrics. MSE: low score refers to high performance, SSIM: high score refers to high performance. Best performances are highlighted.

Figure 4. High-resolution dynamic DMRSI results of rat brain tumors. (a)-(b): Results obtained by the Fourier-based and proposed imaging scheme, including time-dependent concentration maps (left panel), metabolic time courses (middle panel), and time evolution of ²H-spectra (right panel); here, the metabolic time courses and spectra are from voxels at the center of the red and yellow circles within tumor and normal appearing tissues. (c): Differences in the dynamic changes of deuterated Lac (left panel) and Glx (right panel) between tumor and normal-appearing tissues.

Figure 3. In vivo DMRSI results from one healthy rat brain, obtained by (a) conventional Fourier-based imaging scheme, and (b) the proposed imaging scheme. On the left panels are concentration maps of deuterated Glc and Glx at five different time points after the infusion of deuterated glucose; in the middle panels are time courses of deuterated Glc, Glx and Lac at two representative voxels at the center of the red and yellow circles located at the right- and left-hemispheric cortex, respectively; on the right panel is the time evolution of ²H-spectra at the same voxels.

Fig. 1. (a) network architecture of the DNN1. (b) network architecture of the DNN2. Each CNN layer contains convolution (Conv), Rectified Linear Units (ReLU), and batch normalization (BN). The size of each CNN layer is shown on the box. A kernel size of 3*3 is used for each convolution.

Fig. 3. An example of (a) ground-truth image, and (b) denoised image by the DNN1 model, (c) denoised image by the DNN2 model is shown.

Figure 1. An illustration of image quality manifolds for (a) SSIM, (b) data fidelity, and (c) norm of regularization function. As can be seen, all image quality metrics, as a function of λ and ρ, reside in a low-dimensional manifold and thus learnable from training data.

Figure 2. Comparison of reconstruction results obtained from L-curve and the proposed method for image deblurring. Note the reconstruction error was significantly reduced by the proposed method, demonstrating its effectiveness in learning the optimal regularization parameters.

Fig. 1: Noise2Recon complements supervised training (blue pathway) with unsupervised training (red pathway) by enforcing network consistency between reconstructions of both unsupervised data and their noise-augmented counterparts. Unsupervised data is augmented by a noise map ε=U*F*N(0,σ), where σ is selected uniformly at random and the undersampling operator U is determined from the undersampled k-space. Scans with fully-sampled references follow the supervised training paradigm. The total loss is the weighted sum of the supervised (L_sup) and consistency (L_cons) losses.

Fig. 4: Reconstruction performance for 12x (top) and 16x (bottom) undersampled scans corrupted at varying noise levels (σ). Supervised models were trained with one (solid) or fourteen (dashed) supervised scans. Noise2Recon outperformed both 1-subject supervised methods at all noise levels. Noise2Recon achieved similar nRMSE and pSNR as noise-augmented supervised training but outperformed the latter in SSIM. Noise2Recon image quality metrics had low sensitivity to increasing σ and acceleration, which may indicate higher reconstruction robustness in noisy settings.

Fig. 3: ENSURE results on experimental data at 6-fold acceleration factor. Here we show the comparison of unsupervised training using the proposed ENSURE approach with supervised training as well as an existing unsupervised training approach SSDU [5]. The noise variance of the measurements was estimated, followed by the use of the SURE loss for training. The second row shows the zoomed cerebellum region. The third row shows error maps at 3x-scaling for visualization purposes. We observe that the ENSURE results closely match the MSE results with minimal blurring.

Fig. 1: The implementation details of the data-term in the proposed ENSURE approach for unsupervised training. First, we do the regridding reconstruction $$$\boldsymbol u_s$$$, then pass it through the network to get the reconstruction. Here the weighted projection term $$$\mathbf W_s$$$ represents the weighting of the k-space sample together with projection onto range space of $$$\mathcal A_s^H$$$. We note that this data-term does not require the ground truth image.

Figure 3. Representative MIP images of MRCP.

Figure 4. Overall image quality and duct visibility assessment. All values are expressed as the mean ± SD. The dDLR-BH scores for overall image quality, RHD, and LHD were significantly higher than BH (*).

Figure 1: Five reconstructions (DLR, NL2, GA43, GA53, and REF) from each sequence. The labels of the 5 reconstructions were removed and their order is randomized before sharing with 2 MSK specialists for blinded review via a cloud-based webPACS. ROIs and feature profile placements are at identical locations in all 5 images. Mean and the standard deviation of signal intensities within an ROI were used for SNR and CNR calculations while signal profile was used for calculating the full-width-at-half-maximum (FWHM) of the small features.

Figure 3: SNR, CNR, and FWHM measured from DLR, NL2, GA43, GA53, and REF reconstructed images. DLR’s SNR and CNR were statistically higher than those of NL2, GA43, and GA53 (p < 0.001) and not statistically different from that of REF (p > 0.049). DLR’s FWHM is statistically higher than that of REF (p < 0.006) and not statistically different from that of NL2, GA43, and GA53 (p > 0.17).

Figure 4: Comparison of super resolution (SR) results using different network architectures and training datasets in abdominal imaging. HR: high resolution ground truth. L1 GAN: L1+advaserial loss. L1 GAN VGG: L1+adversarial+perceptual loss. Body/Brain indicates the training datasets. The bottom two rows are the zoom-in views from HR and different SR results in a same local region of the full field-of-view HR body image. Note the SR performance difference for small image structures as shown by the red arrows.

Figure 3: Comparison of MSRES2NET based super resolution (SR) results using different loss functions and training datasets in knee imaging. HR: high resolution ground truth. LR: downsampled low resolution input. L1 GAN: L1+advaserial loss. L1 GAN VGG: L1+adversarial+perceptual loss. Knee/Brain(mp)/Brain(all) indicates the training datasets, where brain(mp) denotes to only use MPRAGE data and brain(all) uses all of the brain data. Note the SR results difference for the ligament regions (red circles) and small arteries (red arrows).

Fig. 3 The reconstructed results compared against its ground- truth for undersampled 10%. From left to right, upper to lower: ground-truth, trilinear, SR result of main training and SR result of fine-tuning. For the yellow ROI, (a-b): trilinear and the difference image, (e-f): SR result of the main training and the difference image and (i-j): SR result of after fine-tuning and the difference image. For the red ROI, (c-d): trilinear and the difference image, (g-h): SR result of the main training and the difference image and (k-l): SR result of after fine-tuning and the difference image.

Fig. 1 The schematic diagram along with network architecture in this work. A model is based on U-net with perceptual loss was used for main training. The trained network was fine-tuned using prior scan as a planning scan to obtain high resolution dynamic images during the inference stage. The loss during training and fine-tuning were calculated with the perceptual loss. The output loss at each level of a pre-trained perceptual loss network was calculated using L1 loss.

Architecture of our SRR approach. The generative network offers an HR image excited by an input. The degradation networks degrade the output of the generative network to fit the LR inputs, respectively, with an MSE loss. A TV criterion is used to regularize the generative network. The input can be an arbitrary volume of the same size as the HR reconstruction. The training allows for the SRR tailored to the individual patient as it is performed on the LR images acquired from the specific patient.

Qualitative results on the HCP dataset. Our approach (SSGNN) yielded the best image quality. In particular, SSGNN offered finer anatomical structures of the cerebellum at a lower noise level, and in turn, achieved superior reconstructions to the direct HR acquisitions as well as the five baselines.

Fig. 1. The framework of the proposed algorithm.

Fig. 2. Illustration of SR results for simulated data with different methods. The second row shows the zoom-up views of selected regions in the first row.

Figure 2. Reconstruction results for a representative test slice using CG-SENSE, proposed multi-mask and conventional supervised PG-DL methods. CG-SENSE suffers from noise amplification and significant residual artifacts (red arrows). Conventional supervised PG-DL approach suppresses artifacts further compared to CG-SENSE, but it still exhibits residual artifacts (red arrows) as well. Proposed multi-mask supervised PG-DL approach outperforms conventional PG-DL approach by successfully removing the residual artifacts. Difference images align with the observations.

Figure 4. Reconstruction results for conventional and proposed multi-mask supervised PG-DL. Conventional supervised PG-DL suffers from banding artifacts shown with yellow arrows. Proposed multi-mask supervised PG-DL improves reconstruction quality by significantly suppressing these banding artifacts.

Figure 2: Network Architecture. The VDSR residual network consists of repeated cascades of convolutional (conv) and ReLU layers. The sum of the residual and the low-resolution input creates the high-resolution output estimated images

Figure 4: Representative example of DL network performance. The ground truth movie is labeled with relevant articulators. For each downsampling scale (2x, 3x, and 4x), we show the result of sinc-interpolation (1st column), super-resolution (2nd column), and difference images (3rd and 4th columns) with respect to ground truth. Lip boundaries appear blurred in the super-resolution estimate compared to the ground truth (red arrow). The epiglottis is successfully reconstructed in 2x case but lost/blurred in the 4x case (teal arrow).

Figure 3. Results of the reconstructed MR images by different algorithms on an image example from the IXI dataset. The reference (a) is the full view of the T2 brain slice. The zoom-in area (denoted by red rectangular) of the image based on different methods is displayed on the right. (b) denotes the ground truth, (d) denotes the image upsampled by bicubic interpolation. (c), (e) denotes the recovered images using EDSR without and with applying the OF method, respectively. As can be seen, the dura matter from the ground truth was partly recovered by the proposed method (denoted by red arrows).

Figure 1. An illustration of arriving at synthesis image (d) by applying the estimated optical flow field (c) on the source image (a) (denoted by red lines). The estimated optical flow field (c) is achieved by applying the OF method on source image (a) and target image (b) (denoted by green lines). The colors in (c) denote the field color-coding, where smaller vectors are lighter, and color represents the direction.