Figure 5 (animation): Comparison of manifold regularization and low rank regularization schemes reconstructed using 3arms/frame (or time resolution of 15 ms). Shown are the dynamic animations and temporal profile cuts from two subjects. We observe good fidelity and under-sampling artifact robustness in the manifold scheme compared to the low rank scheme. This is attributed to efficiently exploiting the similarities in local or distant image frames within the dataset without any explicit binning strategies.

Figure 2: Dynamic images can be modeled as points on a smooth nonlinear manifold embedded in a high dimensional ambient space. This is demonstrated in the dynamic free speech task of serially counting numbers. Similar images are neighbors on the 2D manifold even if they occur at different times (see red and green squares), whereas dissimilar images are distant on the 2D manifold even if they occur consecutively in time. The manifold regularization thus exploits the similarity of points that are close to each other on this manifold.

Figure 1. Representative RT-MRI frames from three subjects. The mid-sagittal image frames depict the event of articulating the fricative consonant [Θ] in the word “uthu” where the tongue tip hits the teeth. (a) and (b) are considered to have very high quality (based on high SNR and no noticeable artifact). (c) is considered to have moderate quality (based on good SNR and mild image artifacts); The white arrows point to blurring artifact due to off-resonance while the yellow arrows point to ringing artifact due to aliasing.

Figure 3. Inter-speaker variability (two representative subjects). The image time profiles shown on the top-right side of each panel correspond to the cut marked by the horizontal dotted line in the image frame shown on the left. The time profile and audio spectrum correspond to the sentence “She had your dark suit in greasy wash water all year”. Green arrows point to several time points where the tongue tip makes contact with teeth. Although both speakers share the critical articulatory events (green arrows), the timing and pattern vary depending on the subject.

Figure 4. (A) Dynamic HP-¹³C EPI data of [1-¹³C]pyruvate, [1-¹³C]lactate, and [¹³C]bicarbonate signals from a healthy brain volunteer before (‘Orig.') and after applying GL-HOSVD (‘DN’). (B) Pyruvate-to-lactate (k_PL) and pyruvate-to-bicarbonate (k_PB) conversion rate maps before and after applying GL-HOSVD. (C) Dynamic traces of the original and denoised bicarbonate signals from 2 selected voxels, indicated by an arrow in the k_PB maps, and the fitted k_PB values. The denoised images show a 2-fold increase in spatial coverage of k_PB maps with acceptable fit quality.

Figure 2. Comparative results between GL-HOSVD and Tensor Rank Truncation-Image Enhancement (TRI) methods for denoising simulated image data. (A) Pyruvate and lactate images at an early (t = 12 s) and late (t = 36 s) timepoints before and after denoising. (B) Relative mean values of signal-to-noise ratios of the noise-added and denoised lactate signals from 500 simulated datasets, showing 2 - 3 times higher SNR gain by using GL-HOSVD versus TRI.

(a) Schematic diagram of KWIA with 3 rings. When KWIA is applied to the selected time frame, 5 frames within the KWIA window are weighted averaged and synthesized to a KWIA-filtered k-space. The weighting function and KWIA-filtered k-space are given. (b) Predicted theoretical SNR improvement of KWIA with 2, 3, and 4 rings. SNR improvement increases with greater number of rings and smaller ratio of the first ring to the full radius. (C) Simulated SNR improvements under 7 MRI conditions that are consistent with expected ratios.

Comparison of the original and KWIA-filtered 15-delay pCASL perfusion images. Two-fold SNR improvement was achieved by KWIA resulting in better image quality and dynamic visualization. No obvious degradation of spatial and temporal resolution was found.

Figure 4. TTSR trained without adversarial loss could lead to higher PSNR and SSIM, yet was visually more blurred than standard TTSR with adversarial loss. Nevertheless, TTSR trained without adversarial loss still resulted in sharper images than the EDSR.

Figure 1. Schematic illustration of the developed method. The input low-resolution image is first used to find a similar high-resolution reference in the database, then the low-resolution image and its high-resolution reference are together input to the transformer based neural network, which internally extracts their texture features, fuses the features with attention, and generates high-resolution output images. Note that the reference image search is done by comparing the distance of GIST features, and thus is extremely fast (<1s per thousand images)

Results of one subject’s lower neck DW msh-EPI at different b-values and the corresponding ADC maps, comparing SPIR, IDEAL, and the proposed method. B₀ maps are estimated through b = 0 s/mm² source images. Both SPIR and IDEAL suffered from severe B₀ inhomogeneities in certain regions (marked by red arrows), leaving behind artifacts in both supposed water-only and associated ADC maps. The proposed algorithm mitigates the artifacts and produced more reliable results.

Comparison between IDEAL and the proposed algorithm of one subject’s leg at different b-values. The two B₀ maps are estimated from non-diffusion measurements. In the water/fat overlapping regions, IDEAL left rim-like artifacts (marked by red arrows and emphasized in sub-figures at lower level/window) in both water and B₀ maps. The proposed eliminates this artifact and produces a better water/fat separation with corrected fat maps locations.

Figure 2: Upper left shows a Cartesian high resolution bFFE scan of the ankle in a healthy volunteer to visualize trabecularization of the bone. The remaining images originate from a 3D UTE stack-of-stars acquisition (middle left) processed with all available 7 TEs (orange block) and with the later 5 TEs (green block). In both cases the field map obtained from the 5TEs (lower left) was used for the initialization. The difference maps (blue block) showed higher PDFF and higher R₂^* values for regions with higher bone densities (indicated with white arrow).

Figure 3: Signal decay for selected regions of the calcaneus (left). Middle column (red) shows the signal fitted with all TEs, the right column shows the fitting with the later 5 TEs (green). The cavum calcanei (ROI 1) has a high fat content¹⁶ and minor differences using different TE regimes were visible. In regions with high trabecularization (T12, L2) signal deviations at the first TE compared to the fitted curve based on later TEs were observed. In the tuber calcanei (ROI 3-4), characterized by lower fat content but also less trabecularized bone, the signal deviation was still visible.

Fig. 3: ZTE MRI of a water bottle using long RF excitation pulses. In conventional ZTE, for gaps ≥ 4 dk, amplification of noise and aliased signal create artifacts that dominate the images. However, PPE-ZTE preserves image quality, even with long sweep pulses. The linear grey-scaling is normalized to the maximum of each image separately.

Fig. 5: In-vivo PPE-ZTE MRI in the head. ZTE is limited to proton-density contrast due to the low flip angle reached with short block pulses, even at maximum power. However, PPE-ZTE allows the use of longer sweep pulses that create larger flip angles and consequently T1 contrast, in this case mostly between the cerebrospinal fluid and brain tissues. Furthermore, short-T2 signal of the eye lenses stands out against the vitreous body. Remaining low intensity variation are likely to stem from residual model violations.

Figure 3. Transversal images from a representative volunteer acquired with the shortest TR (4000ms). Top row (left to right) shows the INV1 (suppressed WM), INV2 (suppressed CSF), and UNI images. Bottom row (left to right) displays the FLAWS_min, FLAWS_hc, and FLAWS_hco images. 240 slices were acquired with a slice partial Fourier of 6/8 and a GRAPPA factor of 3. FOV was 207mmx207mm. The scan duration was under 8.5 minutes. A 32-channel TX/RX head coil was used.

Figure 1. The total INV1 and UNI CNR for the simulations given in Table 1 are plotted. Each total CNR value represented by a coloured disk is the maximum found over the range of flip angles tested. The plots indicated that smaller TI₁ values would result in higher CNRs.

Fig.2: Acquisition schemes presented used in this work, presented as a set of b-value ($$$b$$$) and b-shape ($$$b_\Delta$$$) shells. For the platonic-solid sampling scheme, b-tensor directions sets are shown as black dots (electrostatic repulsion)^8,9 or colored dots (platonic solids).^15,16 Other sampling schemes feature unspecific blue dots for directions. The conventional electrostatic sampling scheme was generated by setting the intra/inter shell optimization strength from Ref.[9] to $$$\alpha=0.75$$$.

Fig.3: Histograms showing the median and interquartile range over 50 Rician noise realizations at signal-to-noise ratio SNR=30 of the DTD statistical descriptors of interest estimated in the numerical systems of Fig.1 using the acquisition schemes of Fig.2, namely the electrostatic ("Elst.", blue), platonic-solid ("Plat.", green) and Frobenius-optimized ("Frob.", red) schemes. Purple lines: ground-truth values.

Figure 4. (a) Distortion due to a simulated linear field perturbation was applied on the fully-sampled reference frame from in vivo data. (b) In-plane accelerated data were synthesised by retrospectively undersampling at R=2, 4. Multiband data were synthesised by adding the data across two slices (R=3x2). Field perturbation leads to calibration inconsistency, manifested as strong unaliasing artefacts. The perturbation was estimated and the data were corrected, yielding a reconstructions that have significant reduced unaliasing artefacts and corrected geometric distortion.

Figure 1. Linear magnetic field perturbation is cast as a linear shift of the k-space data for each navigator line at the reference frame (green dots), yielding shifted navigator lines (red dots). Separate GRAPPA operators (Gx, Gy) trained on calibration data to map each k-space point to their adjacent point across the orthogonal Cartesian grid can shift points on the grid (blue arrows). Partial shifts (red arrows) can be cast as fractional powers of the operators. Field perturbations were estimated by finding the shifts between navigators at each frame and those at the reference frame.

Figure 1: Data Sorting/Temporal subdivision methods for golden angle radial sampled pattern: (a) GRASP based method subdivides the acquired spokes into multiple frames according to the temporal order while there are no repeated spokes among frames; (b) proposed method subdivides the acquired spokes with a temporal windowing function. In the example above, frames 4 in the proposed method contains the similar pattern as frame 2 in general method while the number of frames has been increased 2 times.

Figure 3: Three contrast phases of DCE-MRI liver images reconstructed by Racer-GRASP and the Proposed Method. Our method provides better reconstruction quality about tissue details (straight-line arrows) with less artefacts. Meanwhile, L+S decomposition is able to present the dynamic MRI naturally while better dynamic contrast was observed in the proposed method. The dynamic contrast in arterial region is better than RACER-GRASP (dashed-line arrows). The signal intensity of the arterial region signed by red circle was selected as the standard for evaluating dynamic contrast.

Figure 4. APTw images of a healthy volunteer calculated from the source images in Figure 3. a: The APTw images using data acquired with AF=2×2 and ACS data for all frames were treated as ground truth. b-c: APTw images reconstructed from GRAPPA (b) and KIPI (c) using variably-accelerated data, i.e. AF=2×2 for the +3.5-ppm frame with ACS data and AF=2×4 for the other frames without ACS data. Red arrows indicate severe artifacts in GRAPPA APTw images (b).

Figure 2. Flowchart for implementing the KIPI method with variably-sampled frames. A solid rectangle represents an operation, and a solid rounded rectangle means the input or output data to an operation. The black triangles highlight the steps of reconstruction results. The dashed contour above explains the sampling strategy, and the one below shows the reconstruction pipeline. The k-space reconstruction can use GRAPPA, and the image-space reconstruction can use SENSE. AF stands for acceleration factor, and ACS refers to auto-calibration signal.

Figure 1. Original structural weighting matrix (left) and downsampled structural weighting matrix (right) in the $$$x$$$-direction. Note that the white regions (equal to 1) enforce edge requirements on the susceptibility solution while the black regions (equal to 0) do not.

Figure 2. Central slice of control MEDI, MEDI-d with a downsampling factor of 2 and 3 different regularization parameters, and MEDI-SMV. Note the reduction of shadowing causes loss of detail that occurs beyond $$$\lambda_2$$$ = 1000.

Fig.4: Typical axial maps of the ground-truth statistical descriptors of interest, $$$\chi=\mathcal{S}_0,\mathrm{E}[D_\mathrm{iso}],\mathrm{E}[D_\Delta^2],\mathrm{V}[D_\mathrm{iso}]$$$, along with the corresponding median (greyscale), bias (black-to-green) and uncertainty (black-to-red-to-yellow) parameter maps estimated across noise realizations in the original and denoised datasets. For a given statistical descriptors, all maps of a given colormap type share identically bounded color bar limits, for comparison.

Fig.3: Histograms showing the median and interquartile range of the following DTD statistical descriptors estimated in the voxels of interest of Fig.2 in the "original" and "denoised" (dn) datasets: $$$\mathcal{S}_0$$$, mean diffusivity $$$\mathrm{E}[D_\mathrm{iso}]$$$, squared normalized anisotropy $$$\mathrm{E}[D_\Delta^2]$$$, and the variance of isotropic diffusivities $$$\mathrm{V}[D_\mathrm{iso}]$$$. While $$$D_\mathrm{iso}$$$ denotes the isotropic diffusivity, $$$D_\Delta$$$ is the normalized anisotropy.²⁶ Green lines: ground-truth values.

Figure 2 Representative images of (a, e) magnitude image of the first echo in magnetization-prepared multiple spoiled gradient echo sequence, (b, f) white matter image, (c, g) myelin water fraction map, and (d, h) susceptibility map in patients with Alzheimer’s disease and healthy control groups.

Figure 1 Schematic flowchart of preprocessing for simultaneous voxel-based myelin water, magnetic susceptibility, and morphometry analysis. The magnitude image of the first echo in MP-mSPGR, which has strong T1 contrast, is segmented and normalized for voxel-based morphometry (VBM). Myelin water fraction map is estimated from the magnitude image corrected macroscopic field inhomogeneity. The susceptibility map is estimated from multiple phase images. The MWF and susceptibility maps were spatially normalized using the same transformation parameter for VBM.

Figure 1. (a) Radial turbo-spin echo T2w in-vivo brain image quality improvements with CAMP (rightmost column) compared to CG (middle column) and KWIC (leftmost column) reconstructions shown at an example echo time of 75 ms with undersampling factors 6.3, and 12.6 (rows 2 and 3) respectively. Panel (b) shows T2-maps generated from KWIC, CG, and CAMP. NRMSE and HFEN ⁵ values are shown for the undersampled maps. Panel (c) shows an example of the undersampling pattern used in (a) and (b).

Figure2. (a) Cartesian spin-echo brain data shows image quality improvements when T2w-images are reconstructed with CAMP (right column) compared to regularized CG (left column) at undersampling factors 4 and 8 (middle and bottom rows). (b) Exponential fits of undersampled images propagate the undersampling artifacts of the image series, but these are reduced in T2-maps generated by CAMP reconstruction as evidenced by the halving of NRMSE at R=8. Panel (c) shows an example of the undersampling pattern used in (a) and (b).

Figure 3: The first eigenvectors for the HCP dataset and for the multiple TE dataset. The constrained model is described by 2 components, despite being a four-parameter model. The first 5 eigenvectors of the unconstrained model show little contrast among themselves, suggesting that the acquisition cannot disentangle all model parameters. Bottom row shows the eigenvectors for data with varying b-tensors and TE. The contrast between images shows that additional information is captured by the acquisition.

Figure 1: Parameter maps (diffusivities in mm²/s) obtained with maximizing the inner product for the two HCP datasets (top and middle row) and for the b-tensor dataset (bottom row). The constrained estimation (top row) enforces D_par > D_perp, leading to coherent-looking parameter maps by forcing the model into a lower dimensional space, which is not supported as well by the unconstrained version. The b-tensor encoded dataset suffers less from this degeneracy by providing an additional sample dimension.

Figure 3: ESM parameter $$$a,b$$$ maps and relaxation parameter $$$T_2$$$ maps. Gold standard, calculated and relative error for $$$a$$$ solution (a-c), $$$b$$$ solution (d-f), and $$$T_2$$$ (g-i) depicted in columns from left to right respectively. Color is applied for better visibility of different $$$T_2$$$ values.

Figure 1: A example of the signal ellipse. The orange curve represents the signal ellipse. The blue curve represents the transformation of the signal ellipse $$$I_i$$$ with points $$$P_i$$$ to a circle with points $$$Q_i$$$. The blue curve center is indicated by the geometric cross-point $$$M$$$, and its radius by $$$|M|a=|MQ_i|$$$.

Figure 1. A framework of g-CAMP algorithm with four m_ps, where the color of the k-space-lines represents acquisition at a different ∆TE. g-CAMP applies the CAMP algorithm to the center bands first (cycle 1) until it converges. Then g-CAMP grows the number of m_ps to include band 'a' (cycle 2) and finally, it includes all the bands (cycle 3).

Figure 2. Simulation results showing the ground truth T2 maps versus the maps reconstructed using g-CAMP, with the difference images and the masked absolute differences (showing errors inside the brain). In addition, regression analyses are plotted between pixel values of the g-CAMP T2 maps versus those of the ground truth.

Figure.4 Comparison between aT₁W images and T₁ FLAIR images with TI=750ms.

Figure.1 Simulated signal changes as a function of T₁ values, based on simplified Eq.1 with M₀, E₂ set as 1, TR=10ms, and α₁/α₂=6°/48°. All signals are normalized by their respective values at T₁=100ms. The two vertical reference lines indicate the assumed T1 values for WM (800ms) and GM (1600ms). Note that T₁WE signal curve is non-monotonic.

Figure 2. Reconstructed 3D T1 and M0 maps of whole cerebrum for 1 healthy subject. Image quality was similar between SUPER-SENSE and SUPER-CAIPIRINHA and between retrospective and prospective reconstruction. Image fine details were truthfully preserved even for 5-fold acceleration. SUPER-SENSE and SUPER-CAIPIRINHA reduced the scan time from 6:11 minutes to 2:09 minutes and 1:29 minutes, respectively.

Figure 1. Acceleration pipeline of SUPER-CAIPIRINHA for 5-fold acceleration. Column 1 shows k-Space undersampling pattern of SUPER-CAIPIRINHA, black blocks represent points to be sampled while white blocks represent undersampled points in k-space. Severe aliasing was caused by high undersampling rate (column 2&3). Parametric maps without aliasing artifact were reconstructed by blockwise curve-fitting method of SUPER (column 4).

Figure 3 - Example of EAP reconstruction with MAP MRI of a single fiber population voxel of one subject from the HCP dataset. (A) 3D of the EAP reconstruction. (B) A 2D slice of the EAP. The black axis represents the orientation of the fiber population in the voxel (fixel). (C) Graph of the EAP profile computed from the angles of the fixels’ orientation at different radii in mm starting at 0mm to 0.020mm in this example.

Figure 4 - Columns: EAP profiles of the three bundles depending on the database (HCP and Penthera 3T). Rows: EAP profiles depending on the region of interest (left or right).

Figure 3: Comparison of uniformity between 7T brain MP2RAGE MRI images with and without UNICORN (L1-based) normalization. UNICORN results for both the inversion volumes from the 4D MP2RAGE data are shown. Images before and after normalization have the same window-width (WW) and window-level (WL). It can be observed that UNICORN reduced the hyper-intensity near the surface of the brain and improved the conspicuity of the inferior regions of the brain.

Figure 2: Comparison of 7T brain dark-fluid TSE MRI images without normalization, with UNICORN normalization, and N4 normalization. UNICORN results from both SVD- and L1-based optimal coil combination are shown. Same window-width (WW) and window-level (WL) were used for all the images. It can be observed that both UNICORN options reduced the hyper-intensity near the surface of the brain. Improved intensity and uniformity in the interior regions of the brain (relatively better than the N4 normalization method) can also be observed.

Figure 1. The estimation framework used in QTI+.

Figure 5. Maps of parameters estimated through all conventional (top two rows) and QTI+ methods. Red voxels in $$$\mu$$$FA depict complex values.

Fig. 1. (A): High-resolution ground truth image; (B): Single image vector extraction; (C): Temporal phase expansion; (E-F): Forming low-resolution dynamic images; (G): Adding Gaussian noise, extracting local ROI; (H): Forming a denoised local ROI multi-band-low-resolution dynamic images; (I): Coil sensitivities; (J): Separating multi-band and concatenating with the noise-free non-ROI low-resolution dynamic images to form low-resolution local ROI dynamic images; (K): The reconstruction matrix.

Fig. 2. Simulation results on through-plane susceptibility effect on a single voxel. (AB): Demonstration of the geometry of single voxel; ((a1), (b1)): Signal intensity with T2* decay without the present of susceptibility gradient; Linear (a2) and nonlinear (b2) susceptibility gradients along the slice selection direction; ((a3), (b3)): Signal intensity with both T2* decay and susceptibility gradient; ((a4), (b4)): Dephasing effect vs echo time; ((a5), (b5)): Dephasing effect vs slice thickness.

Figure 4. The estimated T_1ρ parameter maps for selected cartilage ROIs with axial view overlaid on the reconstructed T1ρ-weighted images at TSL=5 ms with 6x accelerated Possion sampling pattern ((b) and (c)) and with 7.6x accelerated uniform sampling pattern ((d) and (e)). Visually, as can be seen from the direction of the arrow, our proposed method is more accurate in estimating the T1ρ parameter maps than SCOPE.

Figure 2. The framework of the proposed k-space interpolation network. It consists of several stages and each stage is a component of three modules: learned k-space interpolation module, data consistency module and learned joint TV module (from left to right in red box).

Figure 1: RMSD values for all subsampling factors and subsampling strategies. Blue: full k-space, orange: 1D alternated subsampling, grey: 1D random subsampling. Higher subsampling factors lead to a larger error, but for all factors 1D alternated subsampling performs best, indicating the enhanced performance of subsampling in q-space and 2 k-space dimensions.

Figure 2: Normalized reconstruction error of a single slice for b0 (top, left) and all 60 diffusion direction, for the best case results, using 1/3 of the original data by using 40 q-space coordinates and 1d alternated subsampling. Most errors are near the ears, whereas in the brain errors are very small.

Figure 4: Illustrating the comparison of reference non-SMS ERASE images, SMS-ERASE images with no CAIPI, and SMS-ERASE images with CAIPI. (a) Two slices of non-SMS ERASE, (b) Unfolded images of SMS-ERASE with no CAIPI, (c) Unfolded images of SMS-ERASE with CAIPI, (d) Error maps obtained by subtracting SMS-ERASE images with no CAIPI from non-SMS ERASE images, (e) Error maps obtained by subtracting SMS-ERASE images with CAIPI from non-SMS ERASE images.

Figure 1: (a) Pulse sequence diagram of the original non-SMS ERASE, (b) Schematic representation of CAIPI in case of two-banded SMS ERASE, (c) Aliased images of SMS-ERASE with reduction of aliased regions by CAIPI.

Figure 1 Proposed reconstruction scheme used in this study. To remove the background phase, two acquisitions with opposite RF phase increments are acquired. T1w and T2w images were calculated through the addition and subtraction of these images.

Figure 4 T1w and T2w images produced using the proposed method, compared with T1w and T2w FSE. Both images using the proposed method showed similar contrast to those using FSE imaging. The proposed method exhibited slightly weaker gray-white matter T1w contrast and slightly weaker T2w contrast in the basal ganglia. Mild flow-related artifacts were also observed in the CSF (arrow). Scan time for the proposed method was 1:02 min, compared to 2:23 min for T1w and T2w FSE.

Figure 2. Comparison of XD-GRASP (left) and proposed XD-NET (right) on a healthy volunteer. a) Images for 3 motion states (end-expiration, center, end-inspiration). B) Corresponding correlation curve and coefficient (r), SSIM and PSNR.

Figure 3. Comparison of XD-GRASP (left) and proposed XD-NET (right) on a patient with liver metastasis. a) Images for 3 motion states (end-expiration, center, end-inspiration). B) Corresponding correlation curve and coefficient (r), SSIM and PSNR.

Figure 2. Reconstructed parametric maps (D, f and D*) of IVIM model using proposed method, least square and Bayesian algorithm. (a) A 59-year-old man with pathologically confirmed oligodendroglioma. The lesion hardly enhanced on postcontrast T₁ weighted image. (b) A 57-year-old man with pathologically confirmed IDH wild-type astrocytoma. The lesion shows remarkable enhancement on postcontrast T₁ weighted image. (c) A 49-year-old man with pathologically confirmed IDH-mutated astrocytoma. The lesion hardly enhanced on postcontrast T₁ weighted image.

Figure 4. RMSE of the estimated IVIM parameters (D, f and D*) for proposed method, least square (LS), and Bayesian algorithm (BP) under SNR from 10 to 80 dB.

Figure 1. Complex domain pipeline for mouse-brain extraction. Raw data is used to generate real and imaginary components for k-space data, which was used to train the complex Residual Attention U-Net network. Model output was compared to ground truth mouse-brain masks.

Figure 2. Sample complex network Residual Attention U-Net architecture. This network shows the architecture of one of the complex networks trained for the mouse-brain extraction task. The network consists of 4 encoding layers and 4 decoding layers. Spatial dimension decreases by 2 and channel dimension increases by 2 as the data propagates through the encoding layers while the reverse happens along the decoding layers. A similar structure is used for networks with 3, 5, and 6 layers.

Figure 2: Images of 1 NEX without DLR, 1 NEX with DLR-a to DLR-d, and 5 NEX of a 50-year-old healthy female. (a) the SN (yellow arrows) and (b) LC (pink arrows). DLR reduces image noise while preserving the contrast of the SN and LC against background areas.

Figure 4: Images of the SN (yellow arrows) and LC (pink arrows) of a 50-year-old female healthy volunteer and a 54-year-old female patient with PD. Images of 1 NEX without DLR and 1 NEX with DLR-c are shown. The images with DLR can visualize the SN and LC more clearly than without DLR. The patient with PD shows decreased contrast of the SN and LC compared to the HC.

(Left) original MR image of a knee. (Center-left) Daubechies Wavelet transform of the knee. (Center-right) Daubechies Wavelet transform of the knee with $4$ levels of recursion. (Right) Zoom in of lowest-frequency portion shows a lack of sparsity.

Zoom in to reconstructions of MRI data of knee from 8% of the data. (a) shows the original image; (b) shows the reconstruction using BPD; and (c) shows reconstruction with MSBPD. The red arrows point to regions in the imagery where the improvement in quality of MSBPD over the other algorithms is very apparent. Furthermore, one notes that the variations in the bone marrow are significantly less in the MSBPD reconstruction than in the BPD result, as expected.

Figure 2: Modulation transfer functions in the phase encoding direction are shown for acceleration factors R = 1 and R = 2 on CS-reconstructed HiSS MRI data. At k = 0.625 1/mm (corresponding to in-plane resolution of 0.8 mm), the value of MTF at R = 1 is 0.0053. For R = 2, this MTF value corresponds to k = 0.48 (see inset), or an equivalent resolution of 1.05 mm.

Figure 4: The spatial resolution in the readout (left), and phase encoding (right) direction is shown as a function of the compressed sensing (CS) acceleration factor R, with nominal resolution at R =1 set to 0.8 mm in-plane. There is no noticeable degradation of spatial resolution in the readout direction, even at very high acceleration factors. The spatial resolution in the phase encoding direction is adversely affected for acceleration factors R ≥ 6.

Figure 1: The illustration of our feedback mechanism. Similar to RNN, the output of the network is used as an input to the network in the next fold.

Figure 2: An illustration of our feedback block. In the figure, green thick arrows represents $$$1 \times 1$$$ convolutional layers; Blue thick arrows denote $$$3 \times 3$$$ convolutional layers, each of them is followed by a normalization layer and a nonlinear activation layer; Red and yellow thick arrows represent the pooling layers and unpooling layers respectively; The skip connections are represented by the green thin arrows; The black thin arrows are the input/output for the feedback block, while the red thin arrows represent the input/output for the feedback connections.

Figure 5: Comparison of the execution times for inverse NUFFT using FNUFFT and CUNFFT with increasing grid size, total variation and varying number of iterations for both kernels.

Figure 2: Comparison of the adjoint execution times for the CUNFFT and FNUFFT algorithms for differing grid sizes. The kernel width was 2 for the convolution. The k-space data were reconstructed with 32-channels for both in (a) and with 32 channels for FNUFFT and one channel for CUNNFT in (b)

Left-to-right and then top down: images of a two-dimensional slice of a heart separated by approximately 2 seconds reconstructed with the proposed algorithm. Intensity values are shown in decibels to accentuate differences in low values.

Left-to-right and then top down: images of a two-dimensional slice of a heart separated by approximately 2 seconds reconstructed with the gridding algorithm. Intensity values are shown in decibels to accentuate differences in low values.

Figure 2. Example images from the reconstructions. The columns show the results of different sampling masks VPD or the proposed optimised method. The rows show different sampling density. The left block shows slice 2 of the data set, and the right block slice 3 of the data set. The fully sampled slices are shown at the bottom.

Figure 4. Image quality metric score as a function of density for the RMSE image quality metric, closer to zero is better. The VDP and optimised sampling patterns for 14%, 25%, and 34% are show for both sampling methods. The fully sampled test-retest level is shown in green. In most cases the optimised sampling gives better scores than the VDP.

Signal intensity as a function of T1 and T2 for the sum of squares (SoS) bGRE signal and configuration states M0, M1 and M-1. For the configuration states a logarithmic scale is used, each isocontour represents the same amplitude of signal change. Please note, that proton density and receive sensitivity also modulate image signal intensity, and are not accounted for in this analysis.

Phase cycled bGRE scans of the male pelvis, shown as: sum of squares (SoS) bGRE signal and first three configuration states M0, M1 and M-1.

Figure 2 Original phase map (a) after N=100 diffusive iterations. It contains smoothly varying background phase error as well as the large phase loop, both to be removed from the original phase map in Fig.1(b). Clean phase map (b) with only desired local susceptibility tissue contrast after phase in Fig.2(a) is removed from that of Fig.1(b).

Figure 3 Compared with Fig.2, (a) is the phase of original complex image after smoothed in real and imaginary parts by a 3x3 sliding window N=100 times. The circled pole was slightly shifted to another location which may cause artifact when this phase map is subtracted from the original. (b) Result after phase in Fig.3(a) was removed from that of Fig.1(b). A phase dipole was created in the circle, which may cause “cusp artifact” after subsequent minimum or maximum intensity projections. The result was also unstable in regions where the background phase changed rapidly (arrows).

Figure 1. Schematic of parallelized blind image denoising (ParBID). The first step is the linear combination of adjacent images with given weights $$$a$$$. The second step is the blind DnCNN of the combined images. The third step is the separation of linearly combined images by solving linear equations.

Figure 3. Denoised image with ParBID in BDnCNN. Original image is shown in (a), and target noisy image is (c). The linear combination of adjacent images (b), (d) is shown in image (e). Subimages (e) through (h) show the denoised images using single-slice BDnCNN and the 2- and 3-slice ParBID using BDnCNN. Subimages (i) through (n) are the enlarged images.

Figure 2. Waveforms of the optimized adiabatic pulses. (A) Waveform of HS pulse. (B) Waveform of HSExp pulse. (C) Waveform of tanh/tan pulse.

Figure 3. The Mz trajectories for optimized pulses and the variance distribution for HSExp pulse. (A) Trajectory for HS pulse. (B) Trajectory for HSExp pulse. (C) Trajectory for tanh/tan pulse. (D) Variance distribution over μ and Twindow for HSExp pulse.

Spectrogram (top left) and local field potential (middle left) during and immediately after EPI scan. The EPI scan period (up to 467.6 s) is indicated by blue shading in the time-domain plots. Neuronal spike signal during the same period (bottom left). The SVD shrinkage approach uncovers excellent quality LFP recordings when compared to post-scan time periods in the spectrogram and time domain. The mean EPI images acquired during the recording are presented on the right.

Schematic of artifact removal approach. Artifact contaminated data is aligned by TR and the first difference is computed, followed by mean waveform separation, and SVD-based shrinkage on residuals to further separate artifacts from neural signals. Separated artifact and neural signal contributions are reconstructed and integrated (cumulative summation) to form artifact and clean neural signal estimates. Data acquired from rat cortex in vivo during echo planar imaging at 16.4T.

Figure 1. The original ZTE image (A) is bias corrected with N4ITK (ZTE_N4; B) and histogram-based methods ( ZTE_hist; C). PCA is applied to the Dixon images (D-G) to extract the first two principal components. These are input into a five-class k-means cluster (H) together with the normalised ZTE_N4 image to obtain a lung segmentation (I). A hybrid bias field (L) is created by replacing the lung region values in the ZTE_N4 bias field (J) with those from the ZTE_hist bias field (K). After smoothing the lung edges, a bias-corrected ZTE image (M) is calculated by dividing (A) by the hybrid bias field (L).

Figure 3. Boxplot showing the coefficient of variation for the body, tissue and lung regions (n = 9 patients). Subplot D illustrates the corresponding coefficient of joint variation for tissue and lung.

Fig. 1: Comparison of different coil combinations in a kidney cancer patient acquired with an 8-channel receive coil (average of time steps 3 to 10; slice 3 out of 5 slices).

Fig. 2: Sensitivity maps in the same kidney cancer patient as in Fig. 1 (real part only) acquired with eight ¹³C receive channels: raw receive sensitivities after SVD calculation are shown in the top row (“bare SVD”) and the sensitivities after polynomial smoothing and channel normalisation in the bottom row (“SVD+”).

Figure 3: Relative contributions for each modality to the linked component associated with scanner noise.