Figure 1. Overview of the MoDL-based UNN framework for radial CINE image reconstruction used in the study. Sensitivity maps are derived with ESPIRiT method, proximal block is designed with the proposed network architecture, data-consistency block (DC) is designed with conjugate gradient descent iterations.

Figure 3. Representative results of radial CINE reconstructions from synthetized images in short-axis view. The data was 18.8-fold accelerated with the trajectory shown in the bottom-left. The proposed method (number of unrolls=10, ConvLSTM) is compared to inverse gridding, Short CNN (number of unrolls=5, Conv2D+1D) and Long CNN (number of unrolls=10, Conv2D+1D). Proposed method provides improved reconstruction quality and sharper cardiac motion in the y-t profile image.

Overview of proposed workflow. VCN centers and crops the input pair of cine-MRI frames. Tissue labels generated by CarSON are used to build an anatomical model. Motion estimates derived from CarMEN are used to calculate strain measures, and these estimates are combined with the anatomical model to enable global and regional strain analyses.

Subject-wise regional application. Circumferential end-systolic strain (ESS) in healthy and myocardial infarction subjects shows that infarcts (red arrows) can result in diffused (center) and focal (right) strain reduction.

Figure 1. MyoMapNet architecture: MyoMapNet uses a fully-connected neural network for estimating voxel-wise T₁ values from T₁-weighted images collected after a single look-locker inversion pulse. For each voxel, the signal values from 5 T₁-weighted images are concatenated with their corresponding look-locker times and used as the network input (i.e. 10×1) for native T₁ mapping. The input values are fed to a fully-connected network with 5 hidden layers with 400, 400, 200, 200, and 100 nodes each layer, respectively. The output is the estimated T₁ value at each voxel.

Figure 3. Native T₁ maps from three patients, reconstructed using MOLLI-5 (using only 5 T₁ weighted images with 3-parameter fitting), MyoMapNet, and MOLLI-5(3)3 with a 3-parameter fitting model. MoyMapNet yield maps with more homogenous signal compared to MOLLI-5.

Fig. 1: Proposed generative adversarial super-resolution (SR) framework with cascaded Enhanced Deep Residual Network for SR (EDSR) generator, trainable discriminator and perceptual loss network. Non-rigid motion-compensated CMRA data is acquired to form the low-resolution (1.2x3.6x3.6mm³ or 1.2x4.8x4.8mm³; superior-inferior x left-right x anterior-posterior) input image/patch which is reconstructed to the high-resolution output (0.9mm³ or 1.2mm³).

Fig. 2 [animated]: Prospective SR reconstruction: Coronal and coronary reformat of low-resolution acquisition (1.2x4.8x4.8mm³) acquired in ~50s, high-resolution acquisition (1.2mm³) acquired in ~7min, bicubic interpolation (1.2mm³), and proposed super-resolution reconstruction (1.2mm³) in a patient with suspected CAD for a prospective acquired low-resolution scan of ~50s scan time (prospective cohort).

Figure 1: Top: Pipeline. 1. 4D flow data is pulled from server 2. Dicoms are loaded and the velocity standard deviation is input into the eddy current and noise masking CNNs. 3. Velocity data is fed into the antialiasing CNN. 4. Phase contrast MR angiogram (PCMRA) is calculated and input into the segmentation CNN. 5. Outputs are generated. 6. Results pushed back to the server. Bottom: example outputs. A: PCMRA, B: segmentation preview, C: velocity MIP, D: data preview, E: mean velocity flow curve.

Figure 2: Example outputs. Top left: healthy subject, Top right: bicuspid aortic valve (BAV) and coarctation patient. Bottom left: BAV and stenosis patient, Bottom right: tricuspid valve patient. For each patient, peak systolic velocity maximum intensity projections for manual workflow (left) and CNN pipeline (right) are shown, as well as mean velocity curves for manual (red) and CNN (blue). In the 3D mask comparison, grey is shared, red volumes are larger in the manual, and blue volumes are larger in the CNN.

Figure 1: Overview of the proposed system based on an example. A SAX TI scout series is used as an input for the system. By applying the localization, style transfer and segmentation network, the time point where the mean pixel intensities from myocardium signal is minimum is selected as TI_null. By examining the 80ms window starting from the TI_null, the time point where the difference between the average LV, RV blood pool and myocardium signal is highest, is selected as TI_contrast.

Figure 4: Qualitative results of the system output and the observers' annotation. The illustrated images show the first 16 phases of the standardized TI scout series. In a), b) the results on 1.5T are shown. In c), d) the results of 3.0T data are shown. In d) the observer 2 was selected one frame later than TI_contrast. However, the deviation is negligible. In e) series acquired without- while in f) with compressed sensing on the same patient with 4min 30s in between.

Figure 2: Animation of the tracking network output. The left panel shows a cropped image of the input grid tagged data. This middle panel shows the tracked points overlayed on the image throughout cardiac cycle. The right panel shows the displacement vectors of the tracked points (only 25% of points included for visibility).

Figure 4: A) E_cc maps for both tracking methods, where similar values can be seen, with less blurring on the voxel tracked map. B) Corresponding E_cc curve from (A), where very similar values are seen. C) E_rr maps from both methods, where voxel tracking corresponds to higher values and less blurring. D) E_rr curves for this case, where higher E_rr is evident.

Figure.1 Flow pattern visualization of the intracranial aneurysm (IA) and adjacent parent artery (APA) were performed by (A) streamlines, maximum velocity point and the largest cross-section of IA were showed in (B) APA and (D) IA. Hemodynamic measurements within contours were conducted in (C) APA and (E) IA.

Figure.3 The receiver operating characteristic (ROC) curves of logistic regression models: (A) Single characteristic predict stable IA using GLM model, (B) hemodynamic characteristics predict stable IA using GLM model (C) six significant characteristics predict stable IA using GLM model. (D-F) SVM model respectively. (D) Single characteristic predict stable IA using SVM model, (E) hemodynamic characteristics predict stable IA using SVM model (E) six significant characteristics predict stable IA using SVM model.

Table I. Quantitative comparison of all models

Fig. 2. Visualization of model performance comparison where the proposed method achieved a better result: dashed block (a) and (b) are two 3-slice examples from a vessel segment. The 1st column is the original consecutive MRI slices (s1, s2, and s3), the 2nd to the last columns show the ground truth and estimated segmentation from each model of the corresponding MRI slice, respectively. Black represents the background, grey represents the vessel wall, and white represents the lumen.

Fig. 2. The ML aided k-t SENSE processing.

Stage I – the $$$M_{x,f}^2$$$ estimation. Both flow encoded ($$$y_{k,t}^{'}$$$) and compensated ($$$y_{k,t}^{''}$$$) data were processed as described [2]. The u-net results were combined for the final x-f signal estimation. Stage II – k-t SENSE: the linear conjugate gradient solver was used to minimise [1] and produce the final PCMR results.

Fig. 3. Imaging results.

$$$U_w$$$ reconstructions presented with smaller or larger artefacts: visible reconstruction patch boundary, signal removal. These are not visible on the $$$U_w^M$$$ results. In two cases $$$U_w$$$ removed heart structures (i.e. the bottom row). In these hard cases temporal blurring can be observed in the $$$U_w^M$$$ results. This had a small effect on the k-t SENSE magnitude results. However, it resulted in blurring of the extracted phase data Fig. 4.

Figure 1 Representative images of the segmentation results of the two deep learning models (U-net and V-net).

Table 1 the three quantitative indicators of the model to reflect the accuracy of the results.

Figure 2. Representative example of vessel contouring performed by manual and DL segmentation in MPA and AO.

Figure 1. Schematic representation of the proposed segmentation model. A 2D U-net model with 3 encoder-decoder blocks is trained to regress heatmaps directly from input complex difference images to localize vessel center. A second 2D U-net model with 5 encoder-decoder blocks is trained to segment out the vessel using cropped magnitude images as input.

Fig.1 Simulated DWI image corresponding to a noise-free simulation randomly selected, the noisy image of SNR = 5~25 after adding Gaussian white noise, and the results after denoising

Fig.2 Parameter estimations of helix angle (HA) from the simulated, noisy and denoised (ANLM, LPCA, MPPCA) images.

Figure 1: A) Deep-learning identification of valve insertion points on long axis cine (see blue markers, indicated by white arrows). B) Processing of valve locations to obtain IVRT and e’, along with a’ and s’. C) Blinded qualitative analysis of atrial LGE: one subject had only mild atrial enhancement (left), while the other had extensive enhancement (right, arrows).

Figure 2: Extensive LA LGE was associated with longer IVRT time (15 ±4.5% vs. 9.9± 4%, p=0.032), and lower |a’/s’| values (0.78 ±.25 vs. 1.0 ±0.28, p<0.05), reflecting the impact of atrial fibrosis on diastolic function.

Figure 2. Comparison of fSNAP and CNN fSNAP

Figure 1. The 3D FuseUnet used in this study. The real and imaginary parts of IR-TFE and fSNAP are used as input 1 and input 2 respectively and the loss for the network is MSE.

Figure 1. Summary of comparisons between genotype-positive (G⁺) individuals and controls (G^?). Values shown are mean±SEM, unless otherwise indicated. LVEF-left ventricular ejection fraction, RVEF-right ventricular ejection fraction, LGE-late gadolinium enhancement, sECV-synthetic extracellular volume. *p<0.05.

Figure 2. Native T1 maps in A) G^? control and B) G⁺ variant-positive individuals. Representative patients were selected as those with the median native T1 value across each group. While subtle, elevated T1 values in the myocardium of the G⁺ patient left ventricle (LV) are evident.

Fig. 1. The four chamber view of ground truth and the recovered images from the simulated tagged images. Top row: the original size of the image; bottom row: magnified image of the highlighted area.

Fig. 2. The four chamber view of real tagged image and the recovered results. Top row: the original size of the image; bottom row: magnified image of the highlighted area.

Figure 2. Peak systolic magnitude image from one subject, reconstructed with zero filling (ZF) and the DCCNN for all trajectories and acceleration rates 2X and 6X (3X and 4X omitted for space).

Figure 4. Global radial (top), circumferential (middle), and longitudinal (bottom) strains derived from images reconstructed from each of the three trajectories across all acceleration rates. Statistically significant differences (*p<0.05) from the fully-sampled reference were found for high acceleration rates when employing the CD trajectory.

Figure 1: The architecture of the 2DVet network.

Figure 4: The representative images and segmentation results from two clinical cases. Case A and Case B represent the images with anterior circulation and posterior circulation, respectively.

Figure show the ROC for the ML model and cox regression model with a random sample of 80:20. Table show the result of ML model and cox regression model in 5 fold cross validation. C-statistic will be used to evaluate the result of our model in the table.

table show the non-linear test for strain index. It is clear that there are a non linear relationship of 3D Systolic Apical long Strain.

Figure 1: Vessel ROI pixel-by-pixel velocity difference compared to FS (% of VENC) measured in percent error for acceleration rates 5-10x. The maximum, minimum, and medians (variance) for both the upper and lower bounds on the 95% confidence intervals are displayed for each acceleration rate (red), as well as the median flow difference (bias) for the 8 folds (blue).

Table 1: Vessel ROI pixel-by-pixel velocity (% of VENC), peak velocity (%), and total flow (%) differences compared to FS for acceleration rates 5-10x. For each flow metric, the bias (median flow differences) for all 8 folds are reported.

Figure 1. (A) The original DL-ESPIRiT⁹ reconstruction pipeline with an unrolled network architecture that alternates between a Data Consistency update and a CNN-based denoising step. (B) The CNN was comprised of (2+1)D convolutional layers as described in ⁹. Both PC-MRI velocity encodings, $$$I_1$$$ and $$$I_2$$$, were used to generate a quantitative phase difference image using either the proposed (C) Phase Contrast DL-ESPIRiT (PC-DLE) or (D) Complex Difference DL-ESPIRiT (CD-DLE) reconstruction pipelines.

Figure 2. Representative velocity movies for (A) FS and 8x undersampled data reconstructed using (B) L1E, (C) PC-DLE, and (D) CD-DLE. Pixel-by-pixel velocity difference movies are shown for (E) FS vs. L1E, (F) FS vs. PC-DLE, and (G) FS vs. CD-DLE. Both DL frameworks present significantly lower error (F, G), especially at the cardiac phases with high flow.

Figure 2: 3D SWI images of the lenticulostriate artery (LSA) region with (a) and without dDLR (b). With dDLR, noises were removed for better depiction of LSA vessels (arrows).

Figure 3: Width colormap of VESA identified blood vessels before and after exercise.

Figure 1: Workflow. All 4D flow data (Figure 1A) underwent standard 4D flow preprocessing and used to generate 3D phase contract (PC) MRAs (Figure 1B). The 3D PCMRA was used to generate the ground-truth via manual or automated segmentation of the aorta (utilizing a completely independent CNN) and manually labeling the ascending aorta (AAo), arch, and descending aorta (DAo) (Figure 1C). The 3D PCMRA was, also, used as the input for the CNN, generating automated segmentations (Figure 1D). Training and testing were performed through 10-fold cross validation.

Figure 2: Examples of the Manual and Automated segmentations as well as a difference map between them. Each example showcases a unique geometry of the aorta and distinct placements of the aortic arch. In Figure 2A, the arch is located at the peak of the aorta, while Figure 2B has a wider aortic arch, and for Figure 2C, the arch is slightly left of the top of the aorta. The Dice scores for Figure 2A were AAo: 0.95, arch: 0.95, DAo: 0.98; for Figure 2B, AAo: 0.95, arch: 0.88, DAo: 0.96; and Figure 2C, AAo: 0.95, arch: 0.86, DAo: 0.96

Figure 1 : Comparison of total epicardial fat volume against 4-chamber surface measured on systolic or diastolic frame across the three cohorts merged for the database.

Figure 3 : Representative automated segmentation results for each of EAT surface population quartile. White arrows shows network segmentation errors.

Figure 1. Features selection using SFS and exhaustive search: (a) Sequential forward selection. There are five selected features, and they correspond to Velocity Angle in AAo, Velocity Angle in AArch, Forward Velocity in AAo, Regurgitation Fraction in pDAo, and Helicity Density in AAo. (b) Feature Space in 3D. The selected features are certain hemodynamic features. We can see that the separability is ‘good’ between both classes (volunteers and BAV patients).

Table 2. Average accuracy and standard deviation of different combinations of classifiers and features. Each experiment was done using 10 group cross-validation and repeated 10 times with confidence interval 95%.

Figure 1. Schematic representation of the PINN. From the MR data, anatomy, microstructure, tissue and circulation properties are defined. A dense neural network is generated with a preselected number of FM bases as the last layer. The bases are set as fixed network weights which are not updated during training. The PINN is trained to provide the deformation consistent with cardiac mechanics and it is then coupled to a lumped-parameter model of the systemic circulation to predict cardiac deformation and the corresponding functional metrics

Figure 5. Comparison of pressure-volume loops for 4 of the 60 new different anatomies different cases from the PINN (5 hidden layers, 5 neurons per layers, 10 FM basis) FE model

Figure 1. A schematic illustration of the proposed PS-VN reconstruction pipeline. (a). The part of solving spatial basis images U in classical PS model is substituted by a variational network. (b). An unrolled layer of PS-VN consists of a data fidelity block and a regularization block. The parameters are tuned by backpropagation during network training. (c). PS-VN recovers the corrupted spatial basis images U. A^Hb is used to be the initial value U⁽⁰⁾ as the input of VN. The reconstructed images can be obtained by multiplying spatial basis U with temporal basis V.

Table 1. Summary statistics of different reconstruction methods. The metrics are averaged over 4200 time frames on the test set. Generally, PS reconstruction show the best nRMSE, PSNR and SSIM; however, it takes around 10 min to reconstruct a single slice. The addition of TV constraints into PS model reduced the reconstruction time to less than 4 min, while at the cost of decrease in PSNR and SSIM. PS-VN produce higher PSNR and SSIM than PS+TV method, and consumes only around 10 seconds.

Overlay of predicted segmentation masks over transformed versions of an input image. Each row has images with the same transformation but different parameters (e.g. first row rotations by different angles). The ground truth segmentation mask for this image is shown in Figure 1.

Quantitative effect on the dice score for each class over the parameter space of three transformations. A: Rotation, positive values denote a rotation counter-clockwise while negative ones denote a rotation clockwise. B: Zoom, a value of 480px is the default scale. Larger values mean zooming out while smaller values mean zooming in. C: Brightness, a value of 0.5 denotes no change in brightness while a value of 0 means completely dark (all black) and 1 means full brightness (all white).

Fig. 5 Reformatted coronary arteries from 9x accelerated CMRA reconstructed using non-rigid PROST and the proposed MoCo-MoDL. First row: the test patient shown in Fig. 4; second row: one of the test healthy subjects.

Fig. 4 Whole-heart 9x accelerated CMRA from one representative test patient, reconstructed using non-rigid PROST (left) and the proposed MoCo-MoDL (right).

Figure 5. Representative images from the prospective study. Multiplanar reformats of the ascending aorta (AAO), descending aorta (DAO), main pulmonary artery (MPA), left pulmonary artery (LPA) and right pulmonary artery (RPA).

Figure 1. (A) Estimation of the intensity ratio between low-dose data (LD-MRA) and high-dose data (HD-MRA). T: thresholding followed by morphological opening. M: compute mean over ROI for both images. (B) Generation of synthetic low-dose (SLD-MRA) images, using the estimated intensity ratio, to be paired with the corresponding high-dose (HD-MRA) images for training.

MRA orthogonal views of a 31-year-old female subject: blue patches are the ones which are retained in the anatomically-informed sliding-window approach. (top-right): 3D schematic representation of sliding-window approach; out of all the patches in the volume (white patches), we only retain those located in the proximity of the Willis polygon (blue ones).

(left): 24 landmark points (in pink) located in specific positions of the Willis polygon (white segmentation) in MNI space. (right): same landmark points co-registered to the MRA space of one subject

Figure 1: Overall concept of using DL of DENSE datasets to predict intramyocardial displacement from contour motion. (A) Training of FlowNet2 using DENSE data, and (B) addition of a through-time correction network.

Figure 4: Example myocardial displacement movies for FlowNet2, DT-FlowNet2, TC-DT-FlowNet2 and DENSE ground truth.

Workflow of the proposed fully automated cardiac strain and function analyses.

Summary of global and segmental Ell and Ecc using fastSENC and autoFT for oncology and non-oncology patients. Mean (std) numbers are reported.

Figure 1. Overview of the background phase offset correction method. (A) Magnitude and velocity images were used as input to generate masked images of magnitude, velocity, and static tissue using a 60% signal intensity threshold. (B) The resulting static tissue mask was then used to generate a polynomial fit velocity image, which provides an estimated background phase offset image that can be used to correct the acquired velocity image.

Figure 2. Pixel-by-pixel histogram differences demonstrate the magnitude of the reconstruction induced background phase offset bias, $$$\phi_{R}$$$ (cm/s), for L1E, PC-DLE and CD-DLE (A) within static tissue and (B) inside the vessel ROIs. The median (blue line) and 95%-CIs (lines) of $$$\phi_{R}$$$ are plotted as a function of the acceleration rate.

Figure 2 - The structure of our network. A Conv Block consists of a CNN layer, a batch normalization layer, and an active function ReLU. The kernel size of each convolution layer: 7*7, 3*3, 3*3, 3*3. A feature map with the size of (128, 7, 7) is outputted from the last Conv Block, and will then be reshaped into (128, 1) after max pooling. The number of total param of the network is 129600.

Figure 4 - Feature map of validation samples with normal/abnormal clusters in 2D space using t-SNE. Each dot represents an average feature of 5 slices in MRI scans, as described in the "inference" part. The colors (red for normal, blue for abnormal (aneurysm), green for ectasia, and yellow for normal validation samples) are painted to show the type of each dot. (a) and (b) show 2 normal validation samples, and (c) and (d) show 2 ectasia samples. The clusters' position can vary due to the t-SNE algorithm, as shown in (c) and (d), but the distance between features will be truly presented.

(A) The CMRA data acquisition and motion correction pipeline using a VD-CASPR trajectory and performing translational motion correction estimated from 2D iNAVs. (B) CSMs and the undersampled k-space data are used as network inputs. The variational network structure for one gradient step: the filters k are learned for the real and complex plane and a linear activation function combines the responses of the filters on those planes. The loss function is the MSE of the 3D-VNN reconstruction and the fully sampled.

CMRA reconstructions for 5-fold undersampling for two representative subjects. 3D-VNN reconstruction is compared against the CS, iterative SENSE, CS and 3D CG MoDL-U-Net for a representative subject. Fully sampled and zero-filled reconstructions are also included for comparison.

Schematic of automated, multi-stage system for prescribing cardiac imaging planes comprised of DCNN modules. 1) AXLocNet to localize the mitral valve (MV) and apex from the axial stack to prescribe a vertical long-axis, 2) LAXLocNet to localize the MV and apex from long-axis views to prescribe a SAX stack, 3) SAXLocNet to localize the mitral valve, tricuspid valve, and aortic valve to prescribe the 4, 3, and 2-chamber views.

Left: Comparison of plane angulation differences from A) 4-chamber, B) 3-chamber, or C) 2-chamber planes acquired by an MRI technologist (teal) or SAXLocNet (coral).

Right: Exemplar vertical long-axis images displaying radiologist ground truth (yellow), technologist acquired (teal), and SAXLocNet predicted (red) A) 4-chamber, B) 3-chamber, or C) 2-chamber planes. Ground truth and SAXLocNet predicted localizations are shown as dots yellow and red, respectively.

Figure 2: Top row : a) Raw TOF, b) CW segmentation, c) Propagation of CW labels in the brain; Bottom row: 3D rendering of a full arterial segmentation; Right: Legend indicating artery labels with their corresponding color.

Figure 3: CW from a TOF-MRA raw (a) alongside its manual annotation (b) and the neural network prediction (c)

Figure 2. Coronal MIP 3D tsSOS-QISS MRA images showing the impact of 3D SCRC SR DNN reconstruction on image quality for 2- to 4-fold reduced of axial spatial resolution with respect to ground truth data (left-most column) and input lower resolution (LR) data (right-most upper panels). Insets show magnified views of the right middle cerebral artery. Note the markedly improved image quality and spatial resolution of the 3D SCRC SR DNN with respect to input LR volumes.

Figure 1. Architectures of the deep neural networks used for super-resolution reconstruction. ReLU = rectified linear unit. Training batch sizes for networks (a) through (d) were 400, 80, 400 and 20, whereas the number of trainable parameters for networks were 540,073, 436,521, 185,857 and 556,801, respectively.

Figure 1: Proposed CNN system. The long-axis CMR images are forwarded to the first CNN which localizes the region of interest. After cropping and rotation, the second CNN regresses the time-resolved mitral valve annulus landmarks from Gaussian heatmaps. Finally, the motion parameters are extracted.

Figure 2: a) Feature extraction 2D Residual and 3D convolution blocks. Each residual block consists of a spatial convolution(CONV)(3x3), Batch Normalization (BN) and Leaky Rectified Linear Units (LReLU) activation layers. The 3D block consist of double spatial and temporal CONV(3x3x3)-BN-LReLU operations. b) Localization CNN architecture based on 2-D UNet with 3 encoder-decoder blocks. c) Landmark tracking Fully CNN architecture details based on 3-D UNet.For down-sampling asymmetrical max-pooling layers were applied into temporal and spatial dimensions.

Figure 2. Four IA segmentation examples. Each row represents a patient in the test set. Six columns from left to right represent TOF-MRA, T1-VISTA, ground truth (GT), segmentation from the model with dual inputs, segmentation from the model with TOF-MRA alone and segmentation from the model with T1-VISTA alone.

Figure 3. Aneurysm segmentation evaluation across different combinations of image inputs: dual inputs, TOF-MRA alone and T1-VISTA alone. (A) Sørensen–Dice coefficient (DSC); (B) sensitivity; (C) positive predictive value (PPV); and (D) specificity. Paired Student’s t-tests were performed with the notation *: P < 0.05; **: P < 0.005; ***: P < 0.0005.

Fig 1. Workflow of AI-CASCADE

Fig 3. Visualization of composition segmentation. Blue-Ca, yellow-LRNC, orange-IPH.

(a) C-SENSE T2W-BB (b) CS-AI-T2W-BB

Figure 1. Representative high resolution T2W-BB images using the C-SENSE and CS-AI reconstructions.

(a) C-SENSE strong (b) CS-AI weak (c) CS-AI medium (d) CS-AI strong

Figure 2. High resolution T2W-BB images reconstructed by C-SENSE with denoising level = strong (a) and CS-AI with denoising level = weak, medium, and strong for (b), (c), and (d), respectively.

Figure 1.- Long axis views of 3D MDE series, reconstructed with a standard 3D Cartesian method (left) and the proposed Deep Learning framework (right).

Figure 4.- Top: Logarithmic joint histograms of the voxel-wise relative standard deviation, in the reference Cartesian and DL reconstructions shown in figure 1. Notice how most voxels are located below the identity line, indicating SNR improvement. Bottom: Line profile illustrating the preservation of structure edges with the regularized reconstruction.

Figure 3. Examples of results for the different DL networks from four testing cases. The segmentation results generated by the 3D inputs are qualitatively better than those generated by the 2D inputs.

Figure 2. The overall process of DL segmentation for (A) 2D and (B) 3D inputs. The LA LGE and reference masks extracted from manual contours were used as input and reference to train the DL network. For testing, the LA LGE images were fed into the trained network to get the DL segmented masks.

Diagram of an encoder-type convolutional neural network to estimate linear and constant phase corrections for motion-corrupted DENSE and it’s training using data generated with the DENSE simulator.

Bloch-equation-based simulations show the various effects of free breathing during the acquisition of DENSE images (top row of images). Motion-compensation based on Equation 4 demonstrates the validity of the motion model and its ability to achieve motion correction if the phase correction values are known (bottom row of images).

Figure 2(a,b,c): Bayesian networks learned through NOTEARS structure learning algorithm for each subgroup pair of the data. Each node represents a feature variable, and each directed edge encodes causal influence in the form of conditional probability dependence.

Figure 1(a,b,c): SHAP value plots computed for each Random Forest classification, representing a rank of feature importances. The x-axis gives the SHAP value, i.e. the impact on the model output (for a positive classification). Red indicates higher feature values, while blue indicates lower values.

Figure1 Feature selection and dimension reduction process.

ICC: intraclass correlation coefficient, LASSO: the least absolute shrinkage and selection operator.

Figure 2 Correlogram of the relationship among the selected texture features.

Smaller and/or lighter circles represent lower correlation. On the contrary, larger and/or darker circles indicate higher correlation. GLRLM: gray level run length matrix, GLDM: gray level dependence matrix, GLCM: gray level co-occurrence matrix; LRE: Long Run Emphasis; SRE: Short Run Emphasis; SDHGLE: Small Dependence High Gray Level Emphasis; LDE: Large Dependence Emphasis; H: high wavelet filter; L: low wavelet filter