Figure 1 (A) Pulse sequence diagram and phase diagram of the proposed method. (B) Sequence diagrams of blip-up/down acquisition and schematic diagram of reconstructing distortion-free image from the blip-up/down images. (C) Schematic diagram of echo-shifting with echo-shifting factor of six.

Figure 2 (A) Spin echo and stimulated echo signal evolutions of four different tissues with five [TE, TM] combinations. (B) Schematic diagram of analytic fitting process. (C) Schematic diagram of unsupervised parameter estimation with neural network (a) and detailed structure of the quantification network (b). As input of Bloch generator, outputs of quantification network, B₁ from analytic fitting and brain mask are used.

Figure 2. (a) Results of DeepTSE-T₂ and conventional EPG_SLR fitting with extra B1⁺ information. B1⁺ maps in the fourth and fifth columns are used for the EPG_SLR fitting. In the acquired B1⁺ map, values above 1 were flipped with respect to 1, assuming symmetry. (b) NRMSE, PSNR, SSIM of the T₂ maps with respect to the labels. DeepTSE-T₂ provides a high-quality T₂ map, comparable to those of the EPG_SLR fitting with B1⁺ map from MESE.

Figure 5. Results of χ-separation using DeepTSE-T₂ map: ALIC - anterior limb of internal capsule, CN - caudate nucleus, GP - globus pallidus, ND - nucleus dorsomedialis, PLIC - Posterior limb of internal capsule, Pul - pulvinar, Put - putamen, RN - red nucleus, and SN - substantia nigra. In the case of 2 mm slice thickness, the positive and negative susceptibilities using DeepTSE-T₂ show similar results with those using MESE. 1 mm slice χ-separation using DeepTSE-T₂ is also illustrated, demonstrating feasibility of high resolution χ -separation.

Fig.4. MRF reconstructions of in-vivo data using EPG and RNN generated dictionaries. [First, second and third rows] ,$$$T_1, T_2$$$, and $$$abs(PD)$$$ maps for the in-vivo brain data, respectively. NRMSEs are reported on the top-right corner of the difference maps.

Fig.1. RNN structure for learning the EPG model. (a) RNN architecture with 3 stacked Gated Recurrent Units (GRU) for the n-th time step. At each time step, GRU1 receives inputs x(n) including tissue parameter θ and time-varying sequence parameter β(n). The hidden states h₁(n), h₂(n), h₃(n), all with size of 32x1, are computed and used for the next time step. A Linear layer is added after GRU3 to compute the magnetization and derivatives using h₃(n). (b) An initial linear layer, Linear_Init, is used for computing the initial hidden state h₁(0), h₂(0), h₃(0) from initial magnetization M₀.

Figure 3: Shown from top left to bottom right: (a) Conventionally obtained amplitude image of a multi-echo GRE scan, (b) Network predicted amplitude parameter map, (c) Ratio of predicted to conventionally obtained amplitude images, (d) Conventionally obtained R2* image of a multi-echo GRE scan, (e) Network predicted R2* parameter map, (f) Difference in R2* maps between conventionally obtained and network trained methods, (g) the frequency prediction map, (h) the phase offset prediction, (i) the gradient offset prediction

Figure 2: Shown from top left to bottom right: (a) predicted magnitude image of the 10th echo of the multi-echo GRE scan (at network output layer), (b) expected magnitude image of the input multi-echo GRE scan, (c) magnitude image discrepancy, (d) predicted phase image, (e) expected input phase image, (f) phase image discrepancy.

Figure 1. The schematic diagram of MoG-QSM. Blue blocks play the role of the proximal operator. They are shared weights and replace with convolutional neural network. The output of each generator performs a physical model operation (green block). The final output and label are feed into the discriminator to distinguish if the image is true or not.

Figure 2. Comparison of different QSM reconstruction methods on a healthy subject. The red arrow pointed to the blur cortex susceptibility contrast reconstructed by the LPCNN.

Figure 1: The schematic demonstration of the CNN framework implementing RELAX. A cyclic workflow was constructed to enforce self-supervised learning. The physics models and additional constraints can be incorporated into the framework to guide the learning of CNN mapping function to extract the latent image parameter maps from undersampled images.

Figure 3: Representative T1 maps estimated using RELAX in one simulated brain dataset at three different experiment conditions, respectively. RELAX successfully suppressed the noises at 5% noise level (NL) and removed the undersampling artifacts at R=5 through self-supervised deep learning reconstruction, providing image quality that is comparable to the noise/artifact-free ground truth (G.T.) T1 map. The NLLS was applied to zero-filling reconstructed images at R=5.

Figure 1: MR signal is simulated for given sequence and spin system, reconstruction and T1 mapping is performed with a NN. The output is compared to the target and gradient descent is performed to update TI/Trec and NN. Architecture: NN takes as input the complex k-space of all measurements and outputs a T1 map. The first two convolutional layers act as decomposed transform (DT) layers for image reconstruction, as described in ². Magnitude of the output of the reconstruction part is calculated and feed into a three-hidden-layer multilayer perceptron for T1 quantification.

Figure 3: Optimized TI and Trec times (a,b) starting from a standard inversion recovery and resulting T1 maps (e,f) are compared to optimization from minimal TI and Trec times (c,d,g,h). The CNN provides T1 values in good agreement with literature values at 3T for both approaches (I,j & k,l).

Figure 1. Network design. (a) The proposed combined training of two synthetic networks using cycle consistency loss. (b) Separate training of the networks without cycle consistency loss.

Figure 3. A sample case of synthetic quantitative maps from a patient with multiple sclerosis using CNN with or without cycle loss. (a) T1 map, (b) T2 map, (c) proton density map. The black arrows show a lesion.

Comparisons on perfusion error between the kinetic model with gamma dispersion effect and NN_dispersion in simulation experiments. The top row shows the perfusion error for the dispersion KM at Low ATT (0-0.5s), Mid ATT (0.5-1.8s) and High ATT (1.8-2.0s) respectively for various SNR levels. The second row shows the errors estimated by NN_dispersion. Both models performed well, with little overall bias, for short and mid ATT, but exhibited some bias at longer ATT and lower SNR. The bias was comparable between NN_dispersion and dispersion KM and variance in estimates was consistent.

Comparisons on ATT error between the kinetic model with gamma dispersion effects and NN_dispersion in simulation experiments. The plot on the left shows the ATT error for the gamma dispersion KM for various SNR levels. The plot on the right shows the errors estimated by NN_dispersion. Both models performed well, with little overall bias for all cases. The bias was comparable between gamma dispersion KM and NN_dispersion and variance in ATT estimates was consistent.

Representation of the framework. Top: The RL loop, where states, rewards and actions are exchanged between the learning agent and the environment. Top-left: the environment keeps track of the reconstructed streamlines and computes states and rewards accordingly. Top-right: The agent uses states and rewards received to improve itself and output actions. Bottom: Reconstructed tractograms are iteratively more plausible as training goes on.

Results for experiment 2. A, B, C refer to the same methods as in Figure 3. D refers to Neher et al.^15,16, E refers to Benou et al.¹⁷, F refers to Wegmayr et al. (2020)¹⁸. ISMRM2015 refers to the mean results of the original challenge¹¹. (GT) indicates that the method was trained on the ground-truth bundles. X indicates measures that were not reported by the original authors. Reported metrics are the same as in Figure 3.

Figure 1: a) Overview of qMTNet-2, qMTNet-1 and qMTNet⁺ approach: qMTNet-2 comprises of 2 separate sub-networks. qMTNet-1 is a single integrated network to directly predict qMT parameters from undersampled MT images. qMTNet⁺ consists of a single network that can produce both values of interest. b) Structure of qMTNet⁺. Unless stated in the caption, the layer includes 100 hidden neurons with rectified linear unit (ReLU) activation and batch normalization. Different color signifies different computation path in the network.

Figure 3: Qualitative comparison between qMTNet+ and qMTNet output against dictionary fitted qMT parameters on inter-slice MT data. Dictionary specifies qMT parameters obtained from dictionary fitting of acquired MT data and is considered as the label. The numbers at the bottom of the images are the peak signal-to-noise ratio. The top two rows show result for k_­f and the bottom two rows show result for F. The first row shows qMT parameters from the different fitting methods and the second row shows the 5 times magnified absolute differences. Details of the networks are explained in text.

Figure 1. a) The overview of the propose GLDDL network. b) The GLDDL block. The global spatiotemporal encoder and decoder layers are used before and after the local DL network, respectively. c) The details of the local DL network.

Figure 3. The comparative MWF maps of the DLTG, CRNN, and GLDDL reconstructions at R = 6 from one subject. The NMSE are showed at the bottom of the corresponding images.

Figure 4. The estimated parametric maps for selected cartilage ROIs overlaid on the reconstructed T_1ρ-weighted images at TSL = 5 ms for R = 9.2 from Data 2. The mean values and the standard deviations of the ROI maps are also provided.

Figure 1. Overview of the proposed framework.

Figure 2: An example of the generated synthetic data. Top row shows the model parameters, second row shows the generated signals and third row shows generated spatial transformations.

Figure 1: A flowchart detailing the proposed pipeline for generation of large scale 3D synthetic datasets for multi-component T2 distributions within the naturally occuring bounds, with a spatially varying sampling model.

Figure 1. Proposed network architecture. Unrolled ADMM network (a) reconstructed multi-echo images from the under-sampled multi-coil multi-echo kspace data. Sampling pattern learning network (b) optimized the kspace undersampling pattern with a straight-through estimator to improve back-propagation.

Figure 3. QSMs of optimal and manually designed sampling patterns with 13% and 23% sampling ratios, with fully sampled (100%) QSM as the reference. QSM sampled by the optimal pattern captures more details in the image such as veins (red arrow) compared to the manual pattern. With 13% under-sampling ratio, both QSMs by the optimal and manual patterns lose some detailed structures (red arrow).

Overall processing pipeline for the quantitative evaluation scheme. The post-contrast 3D T1W (CE) and DL-CE volumes were skull-stripped, interpolated and co-registered to anatomical template. The volumes are then processed with the BRATS pre-trained volume through the NGC interface to obtain the Tumor Core (TC) segmentation masks.

CE and DL-CE shown side-by-side with the segmented Tumor Core (TC) (green overlay). Individual Dice scores are shown below each image pair. The segmentation mask of DL-CE in image (F) is different from that of CE, even though the enhancement patterns look similar.

Fig.1: Representative axial slice of the reconstructed parameters: oxygen extraction fraction OEF, deoxygenated blood volume dBV, transverse relaxation rate R₂, non-blood susceptibility χ_nb and magnitude after excitation S₀. Reconstruction is based on combined QSM and qBOLD and done with four different approaches: a voxel wise quasi-Newton (QN) approach, QN initialized with the results from an initial fit on clusters of voxels with similar signal development (Cluster), an artificial neural network (ANN), and QN initialized with the results from the ANN (ANN+QN).

Fig.2: Normalized histograms of reconstructed parameters in gray matter (left) and white matter (right) of the same test subject as in figure 1. Parameters are oxygen extraction fraction OEF, deoxygenated blood volume dBV, transverse relaxation rate R₂, non-blood susceptibility χ_nb and magnitude after excitation S₀. Reconstruction approaches are: voxel wise quasi-Newton (QN), QN initialized with an initial fit on clusters of voxels with similar signal development (Cluster), an artificial neural network (ANN), and QN initialized with the results from the ANN (ANN+QN).

Figure 1: Overview of the proposed approach. a) Pipeline for training and testing the self-supervised convolutional-neural-network (CNN). b) Equations of the lambda layers used to synthesize the T1w, T2w, PDw, T2*w and FLAIR images from the previously computed parametric maps and with sequence parameters of Table 1. m(x) is the signal intensity of the corresponding weighted image at pixel x. Note that the CNN is pre-trained exclusively with synthetic data, as described in Ref⁷, and that PDw, T2*w, and FLAIR images are only used to compute the loss function and are not input to the CNN.

Figure 3: A representative axial slice of the synthesized and the corresponding acquired weighted images for each test patient. a-e) T1w, T2w, PDw, T2*w, and FLAIR images synthesized by the self-supervised CNN. f-j) Corresponding images synthesized by the standard CNN. k-o) Corresponding acquired images. The self-supervised CNN achieves better structural information and contrast than the standard CNN obtaining higher quality synthesis. Specifically, for the PDw, T2*w, and FLAIR which had the lowest quality synthesis in the standard CNN. See the CSF of the PDw, T2*w, and FLAIR.

Figure 2. The flowchart of training sample generation and reconstruction of T₂ mapping. (a) The single contrast abdomen MRI images from TCGA-LIHC are preprocessed first to generate T₂ and M₀ templates, and then the simulated MOLED acquisition is implemented on MRiLab. (b) U-Net is trained to reconstruct T₂ maps from MOLED data.

Figure 3. Reconstructed abdomen T₂ maps from single-shot MOLED images. (a) T₂ maps with contrast enhancement, the kidney, skeletal muscle, liver and spleen are circled in orange, red, yellow and purple, respectively. (b) T₂ maps without contrast enhancement.

Figure 1. MWF maps from the brain imaging of a young participant. Results are displayed for three different axial slices. (A) represents the MWF maps calculated from BMC-mcDESPOT method (the reference method). (B) represents MWF maps calculated using our trained neural network (NN) model. (C) shows the absolute difference map between the reference and the NN methods.

Figure 3. Mean MWF values calculated within representative white matter brain regions using the NN (blue) and BMC-mcDESPOT (orange) methods. Results are shown for both the young (A) and elderly (B) participants, and indicate that NN- and BMC-mcDESPOT-derived MWF exhibit virtually similar values for all regions evaluated.

Figure 3: T₂ weighted images and T₂ maps for two slices acquired using the second high-resolution in vivo brain scan. Left / right columns show the pre- / post-denoising images and T₂-maps (window size 15x15).

Figure 4: T₂ weighted images and T₂ maps of a selected slice acquired using a high resolution in vivo knee scan (matrix size=448x280, FOV=192x120 mm²). The left column shows the original images and T₂-maps, and the right column shows the corresponding images and T₂ maps after MP-PCA image denoising (window size 20x10).

Figure 1: Proposed framework: The proposed model to synthesize arbitrary FLASH MRI contrasts using a CNN and a FLASH forward model from three input image contrasts. As a consequence of using the FLASH model, the output of the CNN can be interpreted as estimates of the tissue parameters (T1,T2* and PD).

Figure 2: Contrast Synthesis: Test error in synthesis of image contrasts estimated from three input images over 100 test datasets. The boxplots in 2a and 2b, plot the MAE and the images in 2c. show the reference, proposed estimate and fixed acq. network estimate. The images in 2c. show a slice from the test dataset, with the reference estimated from 3 flip 4 echo scan and predicted contrast from both random and fixed networks.

Figure 4. Representative T1, T2, B1 and PD maps of numerical and real NIST system phantom obtained using three reconstruction methods.

Figure 5. Mean estimated value of T1, T2, and their relative errors in each region of numerical and real NIST system phantoms as function of their true and nominal value each other.

Figure 1. The illustration of DAINTY framework. (A) The under-sampled k-space data are first processed by L-Block and S-Block to impose the low rank and sparsity constraint. Then they are processed through R-Block to generate refined T1 maps. The physical model G-Block is used to transform T1 map back to T1 weighted images to further improve the reconstruction quality. After k iterations the clear T1 map and high-quality T1 weighted images can be both obtained. (B) The structure of DenseAttention UNet. The number of feature maps for encoder and decoder block 1-4 are 256, 128, 64, and 32.

Figure 3. MR images of in-vivo human brain. (A) T1 weighted images from GOAL-SNAP sequence using DAINTY, NK-CS, kt-SS and L+S method; (B) Reconstructed T1 and M0 maps and error maps from GOAL-SNAP sequence using DAINTY, NK-CS, kt-SS and L+S methods with least-square fitting and direct deep learning mapping. T1 and M0 maps from IR-TSE are as the reference.

Figure 1: Network architecture of LP-CNN. In the ResNet, there are 8 stacks of residual blocks. Each residual block contains 2 convolutional layers, 2 batch normalization layers, and 2 ReLU layers with 1 skip connection for residual learning. The forward pass of LP-CNN for STI contains 3 iterations.

Figure 3: Principal eigenvector (PEV) maps of the reconstructed susceptibility tensors in anisotropic regions using different methods and the associated ECSE maps. The color represents the PEV direction, and the ECSE maps show the angle difference between the reconstructed PEV and the ground-truth PEV.

Figure 1. The network architecture for 3D MULTIPLEX data reconstruction. The model includes five convolutional blocks and each block contains five 3D convolutional layers and one data consistency layer. The feature maps are 48 for the first four 3D convolutional layers and 2 for the last 3D convolutional layer in each block. The x, y indicate image and kspace, respectively. The real and imaginary numbers of complex values are transformed into two channels and fed into the network.

Figure 2. Examples of reconstructed MULTIPLEX echo images by the proposed deep learning method at 3X and 5X accelerations. FA₁ and FA₂ indicate two different flip angle configurations. Three (Echo1, Echo4 and Echo7) out of seven echo configures are showed due to space constraints. All errors are multiplied by 50 for better visualization. The same 2D axial slice from each 3D image is plotted.

Figure 1. Illustration of the proposed attention-gated neural network for cardiac T1 mapping. Inputs to the network have dimensions of B x CH x 1 x T. CH = 2 corresponds to T1 weighted values and their inversion times. T corresponds to the number of input T1 images and inversion times for pre-contrast (T = 5) and post-contrast (T = 4) acquisitions. B = 1024 is the batch size. Scanner generated T1 maps were used as the reference.

Figure 2. Network generated T1 maps in comparison to scanner generated reference T1 maps and their corresponding difference images for (A) pre-contrast T1 maps and (B) post-contrast T1 maps from two test patients. T1 maps are shown in milliseconds.

Figure 2: Performance of 3 and 4-echo pipelines in predicting fully sampled T2 maps in an example of holdout set. Pearson’s r is calculated for each map with respect to ground truth. (a) Predicted 4-echo pipeline maps showed fidelity to ground truth up to R=6, and for (b) the 3-echo pipeline, up to R=3. Up to these acceleration factors, maps reconstitute T2 values and preserve NP/AF delineation, and can thus quantitatively assess disc health and reflect early degenerative changes.

Figure 1: Recurrent encoder-decoder architecture used to predict T2 maps from spatially undersampled MAPSS T2 echos. Initial recurrent network includes connections between processing streams of each echo to exploit temporal correlations. Subsequent encoder-decoder network exploits spatial correlation and predicts final T2 map. The network could be configured for any number of input T2 echos, but the number of filters throughout the encoder-decoder network portion are presented as for 4-echo inputs.

The reconstructed lesions probability maps are overlayed on the magnitude date in color encoding for all five different patients from the test set. Manual annotation is depicted in blue. Below the probability map is binarized and depicted in yellow in addition. The dice coefficient and white matter lesion detection rate is depicted for every patient and healthy subject for both sites. The average lesions detection rate is 0.83 and dice coefficient is 0.67 for all patients.

Visualization of the reconstruction during the training. The reconstructed T₁, T₂*, WM-, GM and Lesion-probability maps are depicted for 1, 5, 15, 30, 70 and 100 training epochs (white number) and the dictionary matching reference maps are shown on the right side. On the bottom the Dice coefficient (blue) and the lesion detection rate (orange) is depicted over the 50 training epochs.

Figure 1. Contrasts obtained from fourteen different MPRAGE protocols in one example subject. Five equally spaced flip angles were investigated (between 5° and 13°) for two different combinations of repetition and inversion times (TR/TI = 2300/900 ms and 1930/972 ms). Five equally spaced read-out bandwidths were also investigated (between 160 and 320 Hz/Px) for TR/TI=2300/900 ms.

Figure 2. Variation of similarity losses in four experimental scenarios shown in Table 2. SSIM loss is defined as the inverse of SSIM. Segmentation loss is defined as the relative absolute error in the thalamus volume estimation. LPIPS(VGG16) represents a learned similarity metric based on a perceptual loss. Highlighted x-axis ticks indicate the corresponding reference image. *: p < 0.05, **: p < 0.01, ***: p < 0.001

Fig 2. Comparative reconstruction methods for two oncology patients alongside corresponding CMRA images. Aligning the scanner-provided μ-map to the CMRA image removes a defect mimicking artefact in P1 (magenta arrows), while applying motion compensation improves contrast and sharpness in the inferior myocardium (blue arrows). Using either unguided or MR-guided regularization (β=400) reduces noise, however MR-guidance results in better edge-preservation and contrast (green arrows).

Fig 4. Example short-axis views of the reconstructed PET images for two cardiac patients, and corresponding 2D LGE images showing the extent of myocardial scarring. Using the proposed MC-guided MAPEM (with automatic β selection) method improves image quality while maintaining the appearance of myocardial defects (cyan arrows). Note that LGE images are shown only for comparison and did not provide any information for the MR-guided PET reconstructions, which instead used high resolution CMRA images (also shown here).

Comparison of net influx rate (K_i) between original dynamic PET data and transformed dynamic PET data. Heart polar-map comparison is shown in a) & b). Correlation scatter plot shows significant correlation with correlation coefficient = 0.959 in c).

Comparison of net influx rate (K_i) between original and transformed images at 4 different segments (left anterior descending artery, left circumflex artery, right coronary artery, apex) of heart and 3 different time points (before the lipid infusion, during the lipid infusion and after the lipid infusion).

Fig 3. Comparison of PET images with both conventional & proposed denoising methods. The images are reconstructed using TOF-OSEM with 1mm isotropic resolution. Top row images are filtered by a Gaussian filter with 4mm cut off freq. Bottom row images are filtered with the proposed method using anatomical priors. A neighborhood within 3 mm radius around each voxel was searched to find the 25 nearest neighbors. A Gaussian filter with 2mm spatial cut-off freq. was then applied to remove any remaining high freq. noise. The KNN and the Gaussian filter were applied 2 times iteratively.

Fig 4. Comparison of PET images with conventional and proposed denoising methods on a prostate cancer subject imaged with 5 mCi of PSMA. The PET images are reconstructed using TOF-OSEM with 1mm isotropic resolution. Top row images are filtered by a Gaussian filter with 4mm cut off freq. Bottom row images are filtered with the proposed method using anatomical priors. A neighborhood within 3 mm radius around each voxel was searched to find the 25 nearest neighbors of that voxel. A Gaussian filter with 2mm spatial cut-off frequency was then applied to remove any remaining high frequency noise.

Figure 1: Comparison of whole-body attenuation maps of a healthy volunteer. Left: Breath-hold protocol. Right: Free-breathing protocol. The first two bed positions were acquired in breath-hold and free-breathing respectively. The last bed position was acquired using the breath-hold protocol without breath-hold command. In both cases the attenuation map consisting of five compartments (air, lung tissue, soft tissue, fat tissue and bone) could be generated successfully. The truncated arms were recovered as well as described in [2].

Figure 2: Comparison of Dixon image quality. Left Column: Dixon water, acquisition with breath-hold protocol. Right Column: Dixon water, free-breathing acquisition. Free-breathing images show a more distinct boundary of the liver dome and appear to be sharper in the coronal and sagittal reformats (middle and bottom rows). The image quality in the axial plane (top row) is comparable. Images were acquired after a clinical study, Gadovist was given as part of the scan protocol prior to the shown acquisitions.

Figure 3: (A-F) show images generated at three field strengths when no restriction is put on the repetition time. (A,D): TR=7ms,FA=60,SNR$$$\approx$$$6 (B,E):TR=6ms,FA=50,SNR$$$\approx$$$10 (C,F):TR=5ms,FA=30,SNR$$$\approx$$$14 (G-L) are generated with repetition time restricted such that the intra-TR phase wrap is no more than $$$\pi/3$$$ with an inhomogeneity of 0.5ppm. (G,J): same as A (H,K):same as B (I,L):TR=4ms,FA=23,SNR$$$\approx$$$5 (G-L) A significant decrease can be seen in the SNR at 3T due to this restriction.

Figure 5: Optimized SNR plots for both the unrestricted case (left) and case where TR is restricted such that banding is limited to $$$\pi/3$$$ (right). Both plots also show the expected scaling according to coil dominated and noise dominated SNR scaling laws. Note that bandwidth (BW) changes with the optimization. In both cases SNR scales better than the linear case at low fields. These results also approximately match the images generated in Figure 3, with a drop in SNR seen in the restricted case at 3T.

Figure 1 - Simulated CPMG Signal

Figure 2 - Simulated Stimulated Echo Signal

Figure 2. Original, preprocessed, extracted brain images of infants at various age month. Top row shows the original T1W images at 0.35T. Middle row shows preprocessed images after de-nosing and N3 bias correction. Bottom row shows the extracted brain with the skull removed.

Figure 5. Quantitative calculation results of ROI volume, cortical thickness after brain labeling. (a) Automated labeling results on voxel-wise image (hippocampus). (b) Quantitative calculation of hippocampus volume for five cases. (c) Labeling ROIs on cortical surface on surface-based (superior frontal gyrus (dorsal)). (d) Cortical thickness for superior frontal gyrus (dorsal) of different cases.

Algorithm results.

The algorithm progressively denoises the image.

Figure 1: The summary of the proposed approach. (a) The training data is generated by creating a pair of original noisy and noisier images. The additional noise is simulated by simply feeding the raw data with higher noise to the reconstruction pipeline. (b) Once the pair is generated, the noisier images are fed to U-net like architecture to regress noisy images.

Figure 3: The reconstructions for DWI images for b=890 for a patient with pathology. The residual maps show the difference between noisy and the denoised images, highlighting the content that was removed. Both proposed and BM3D showed effectiveness, however, the proposed approach was able to preserve sharpness better.

Figure 1: Illustration of nonlinearity arising from B₁ gradients. (a) Standard MRI phase encoding gradients are built to be linear in amplitude and phase. (b) Example nonlinear B₁ gradient generated by single loop surface coil is nonlinear in amplitude and phase.

Figure 3: Nonlinear RF gradient encoding leads to geometric and intensity distortions in the image, which can be corrected. (a) Numerical phantom plotted with linear and nonlinear RF gradients. (b) Fourier reconstruction of Bloch simulation using linear RF gradient shows no distortions whereas nonlinear RF gradient encoding does. (c) Geometric distortions are corrected using interpolation. (d) Intensity distortion is corrected by Jacobian scaling.

Figure 2: Prospective undersampling. Two examples of a) fully sampled images, b) corresponding prospectively undersampled images, c) U-net reconstructed images, and d) squared error of reconstructed images using U-net versus fully sampled image.

Figure 1: Retrospective undersampling. Two examples of a) fully sampled images, b) corresponding retrospectively undersampled images, c) U-net reconstructed images, and d) squared error of reconstructed images using U-net versus fully sampled image.

Fig. 2. A) Illustration of proposed connectome-based NLM filter. The filtered value for any given voxel is computed by a weighted value for every brain voxel. This weighting is based on voxel-wise PET intensity similarity³ and connectivity strengths between each pair of parcellations (coloured cubes). B) Top: schematic demonstration of computation of intensity similarity matrix, distant and local connectivities. These 3 matrices are combed to form the total weight. Bottom: a realistic example.

Fig. 3. A) Ground-truth simulated PET phantom and AAL parcellations¹⁰. B-D) Left: PET image; right: intensity difference relative to ground-truth, calculated based on grey matter only. B) Reconstructed PET image with noise. C) Smoothing performed by non-local means filter without connectivity information.¹¹ D) Smoothing performed by the proposed CONN-NLM filter.

Figure 2. Representative tau PET images and their corresponding T1-weighted MR image in a patient with significant cortical uptake. The synthesized PET images show greatly reduced noise compared to the low-dose PET image, while the images generated from the Tau Network and the Fine-tuned Network were superior in reflecting the underlying anatomical patterns of the tau tracer uptake. The image obtained directly from the Amyloid Network performed less well, with more image blurring.

Figure 1. A schematic of the CNN used in this work and its input and output channels. The arrows denote computational operations and the tensors are denoted by boxes with the number of channels indicated above each box.

Figure 3. Examples of reference PET CBF and corresponding synthetic CBF maps generated with different loss functions and network settings.

Figure 1. Our 3D convolutional encoder-decoder network for predicting PET CBF maps from multi-contrast MRI scans.

Figure 1. CALIPER’s (A). Graphical user interface consisting (B). PET vessel accumulation, (C) and (D) MRI vessel segmentation prior to (E). co-registration, selection of a region of interest from internal carotid arteries and extracting a (F). IDIF corrected for PVE and spill-in contamination.

Figure 3. (A) IDIFs generated using TOF MR images and AIF of a healthy human control indicating the shape of the entire curve and the initial peak from 0 to 1000 s. (B). Two-sample t-test indicates no significant changes in the ratio of AUC between IDIF and PBAIF for IDIFs generated using TOF and MPRAGE MRI vessel masks.

Figure 2. Comparison of registration methods. The left column shows the MR target and reference bins. Top row images are deformations (Def.) of the reference bin image to match the target bin using different image registration tools. Bottom row images represent the difference (Diff.) between the true MR target bin and the deformed images from the top row. The Q.Freeze2 registration results in lower residual error than MIRT and elastix.

Figure 4: Residual error between warped and original MR bins. The left column shows the regions of interest (ROI) considered. The center and right columns show the normalized root mean squared error (NRMSE) as a function of the target bin for each ROI. The shaded region around the curves corresponds to three standard deviations, estimated via bootstrap of the ROI pixels. Q.Freeze2 results in lower error, especially for bins further from the reference bin (i.e. bin 12).