A predictor-corrector phase unwrapping algorithm for temporally undersampled gradient-echo MRI.

PURPOSE: To develop a method for unwrapping temporally undersampled and nonlinear gradient recalled echo (GRE) phase. THEORY AND METHODS: Temporal unwrapping is performed as a sequential one step prediction of the echo phase, followed by a correction to the nearest integer wrap-count. A spatio-temporal extension of the 1D predictor corrector unwrapping (PCU) algorithm improves the prediction accuracy, and thereby maintains spatial continuity. The proposed method is evaluated using numerical phantom, physical phantom, and in vivo brain data at both 3 T and 9.4 T. The unwrapping performance is compared with the state-of-the-art temporal and spatial unwrapping algorithms, and the spatio-temporal iterative virtual-echo based Nyquist sampled (iVENyS) algorithm. RESULTS: Simulation results showed significant reduction in unwrapping errors at higher echoes compared with the state-of-the-art algorithms. Similar to the iVENyS algorithm, the PCU algorithm was able to generate spatially smooth phase images for in vivo data acquired at 3 T and 9.4 T, bypassing the use of additional spatial unwrapping step. A key advantage over iVENyS algorithm is the superior performance of PCU algorithm at higher echoes. CONCLUSION: PCU algorithm serves as a robust phase unwrapping method for temporally undersampled and nonlinear GRE phase, particularly in the presence of high field gradients.

Compressed sensing MRI using an interpolation-free nonlinear diffusion model.

PURPOSE: Constraints in extended neighborhood system demand the use of a large number of interpolations in directionality-guided compressed-sensing nonlinear diffusion MR image reconstruction technique. This limits its practical application in terms of computational complexity. The proposed method aims at multifold improvement in its runtime without compromising the image quality. THEORY AND METHODS: Conventional approach to extended neighborhood computation requires 108 linear interpolations per pixel for 10 sets of neighborhoods. We propose a neighborhood stretching technique that systematically extends the location of neighboring pixels such that 66% to 100% fewer interpolations are required to compute the gradients along multiple directions. A spatial frequency-based deviation measure is then used to choose the most reliable edges from the set of images generated by diffusion along different directions. RESULTS: The semi-interpolated and interpolation-free diffusion techniques proposed in this paper are compared with the fully interpolated diffusion-based reconstruction by reconstruing multiple multichannel in vivo datasets, undersampled using different sampling patterns at various sampling rates. Results indicate a two- to fivefold increase in reconstruction speed with a potential to generate 1 to 2 dB improvement in peak SNR measure. CONCLUSION: The proposed method outperforms the state-of-the-art fully interpolated diffusion model and generates high-quality reconstructions for different sampling patterns and acceleration factors with a two- to fivefold increment in reconstruction speed. This makes it the most suitable candidate for edge-preserving penalties used in the compressed sensing MRI reconstruction methods.

Multi-echo gradient-recalled-echo phase unwrapping using a Nyquist sampled virtual echo train in the presence of high-field gradients.

PURPOSE: To develop a spatio-temporal approach to accurately unwrap multi-echo gradient-recalled echo phase in the presence of high-field gradients. THEORY AND METHODS: Using the virtual echo-based Nyquist sampled (VENyS) algorithm, the temporal unwrapping procedure is modified by introduction of one or more virtual echoes between the first lower and the immediate higher echo, so as to reinstate the Nyquist condition at locations with high-field gradients. An iterative extension of the VENyS algorithm maintains spatial continuity by adjusting the phase rotations to make the neighborhood phase differences less than π. The algorithm is evaluated using simulated data, Gadolinium contrast-doped phantom, and in vivo brain, abdomen, and chest data sets acquired at 3 T and 9.4 T. The unwrapping performance is compared with the standard temporal unwrapping algorithm used in the morphology-enabled dipole inversion-QSM pipeline as a benchmark for validation. RESULTS: Quantitative evaluation using numerical phantom showed significant reduction in unwrapping errors in regions of large field gradients, and the unwrapped phase revealed an exact match with the linear concentration profile of vials in a gadolinium contrast-doped phantom data acquired at 9.4 T. Without the need for additional spatial unwrapping, the iterative VENyS algorithm was able to generate spatially continuous phase images. Application to in vivo data resulted in better unwrapping performance, especially in regions with large susceptibility changes such as the air/tissue interface. CONCLUSION: The iterative VENyS algorithm serves as a robust unwrapping method for multi-echo gradient-recalled echo phase in the presence of high-field gradients.

Directionality guided non linear diffusion compressed sensing MR image reconstruction.

PURPOSE: Address the shortcomings of edge-preserving filters to preserve the complex nature of edges, by adapting the direction of diffusion to the local variations in intensity function on a subpixel level, thereby achieving a reconstruction accuracy superior to that of data-driven learning-based approaches. THEORY AND METHODS: Rate of diffusion for edges is found to vary in accordance with their gradient direction. Therefore, the edge preservation is strongly dependent on the direction in which the gradient is computed. Since the directionality of edges varies at different regions of the image, the proposed technique computes the gradients in all possible angular directions and uses a spatial-frequency-based deviation measure to choose the most reliable edges from the images diffused along different directions. RESULTS: The proposed method is compared with the state-of-the-art data-driven learning-based techniques of block matching and 3D filtering (BM3D), patch-based nonlocal operator (PANO), and dictionary learning MRI (DLMRI). Best results are obtained when directionality of edges is estimated from a prior optimized k-space and shows an improvement in peak signal-to-noise ratio (PSNR) measures by a factor of 2.36 dB, 1.92 dB, and 1.59 dB over BM3D, PANO, and dictionary learning MRI, respectively. CONCLUSION: The proposed technique prevents the emphasis of false edges and better captures the structural details by a locally varying directionality-guided diffusion to make the error lower than that of the state-of-the-art reconstruction techniques. In addition, a highly parallelizable form of the proposed model promises a significant gain in the reconstruction speed for practical implementations.

A mixed-order nonlinear diffusion compressed sensing MR image reconstruction.

PURPOSE: Avoid formation of staircase artifacts in nonlinear diffusion-based MR image reconstruction without compromising computational speed. METHODS: Whereas second-order diffusion encourages the evolution of pixel neighborhood with uniform intensities, fourth-order diffusion considers smooth region to be not necessarily a uniform intensity region but also a planar region. Therefore, a controlled application of fourth-order diffusivity function is used to encourage second-order diffusion to reconstruct the smooth regions of the image as a plane rather than a group of blocks, while not being strong enough to introduce the undesirable speckle effect. RESULTS: Proposed method is compared with second- and fourth-order nonlinear diffusion reconstruction, total variation (TV), total generalized variation, and higher degree TV using in vivo data sets for different undersampling levels with application to dictionary learning-based reconstruction. It is observed that the proposed technique preserves sharp boundaries in the image while preventing the formation of staircase artifacts in the regions of smoothly varying pixel intensities. It also shows reduced error measures compared with second-order nonlinear diffusion reconstruction or TV and converges faster than TV-based methods. CONCLUSION: Because nonlinear diffusion is known to be an effective alternative to TV for edge-preserving reconstruction, the crucial aspect of staircase artifact removal is addressed. Reconstruction is found to be stable for the experimentally determined range of fourth-order regularization parameter, and therefore not does not introduce a parameter search. Hence, the computational simplicity of second-order diffusion is retained.

Multichannel compressed sensing MR image reconstruction using statistically optimized nonlinear diffusion.

PURPOSE: Eliminate the need for parametric tuning in total variation (TV) based multichannel compressed-sensing image reconstruction using statistically optimized nonlinear diffusion without compromising image quality. THEORY AND METHODS: Nonlinear diffusion controls the denoising process using a contrast parameter that separates the gradients corresponding to noise and true edges in the image. This parameter is statistically estimated from the variance of combined image gradient to yield minimum steady-state reconstruction error. In addition, it uses acquired k-space data to bias the diffusion process toward an optimal solution. RESULTS: The proposed method is compared with TV using a set of noisy spine and brain data sets for three, four, and five-fold undersampling. It is observed that the choice of regularization parameter (step size) of TV-based methods requires prior tuning based on an extensive search procedure. In contrast, statistical estimation of contrast parameter removes this need for tuning by adapting to the changes in data sets and undersampling levels. CONCLUSIONS: Although an a-priori tuned TV-based reconstruction can provide a comparable image quality to that of controlled nonlinear diffusion, there are practical limitations with regard to its time complexity for ad-hoc applications to multicoil compressed-sensing reconstruction. Magn Reson Med 78:754-762, 2017. © 2017 International Society for Magnetic Resonance in Medicine.

Adaptive continuation based smooth l0-norm approximation for compressed sensing MR image reconstruction.

Purpose: There are a number of algorithms for smooth l0-norm (SL0) approximation. In most of the cases, sparsity level of the reconstructed signal is controlled by using a decreasing sequence of the modulation parameter values. However, predefined decreasing sequences of the modulation parameter values cannot produce optimal sparsity or best reconstruction performance, because the best choice of the parameter values is often data-dependent and dynamically changes in each iteration. Approach: We propose an adaptive compressed sensing magnetic resonance image reconstruction using the SL0 approximation method. The SL0 approach typically involves one-step gradient descent of the SL0 approximating function parameterized with a modulation parameter, followed by a projection step onto the feasible solution set. Since the best choice of the parameter values is often data-dependent and dynamically changes in each iteration, it is preferable to adaptively control the rate of decrease of the parameter values. In order to achieve this, we solve two subproblems in an alternating manner. One is a sparse regularization-based subproblem, which is solved with a precomputed value of the parameter, and the second subproblem is the estimation of the parameter itself using a root finding technique. Results: The advantage of this approach in terms of speed and accuracy is illustrated using a compressed sensing magnetic resonance image reconstruction problem and compared with constant scale factor continuation based SL0-norm and adaptive continuation based l1-norm minimization approaches. The proposed adaptive estimation is found to be at least twofold faster than automated parameter estimation based iterative shrinkage-thresholding algorithm in terms of CPU time, on an average improvement of reconstruction performance 15% in terms of normalized mean squared error. Conclusions: An adaptive continuation-based SL0 algorithm is presented, with a potential application to compressed sensing (CS)-based MR image reconstruction. It is a data-dependent adaptive continuation method and eliminates the problem of searching for appropriate constant scale factor values to be used in the CS reconstruction of different types of MRI data.

Unveiling metabolic patterns in dementia: Insights from high-resolution quantitative blood-oxygenation-level-dependent MRI.

BACKGROUND: Oxygen extraction fraction (OEF) and deoxyhemoglobin (DoHb) levels reflect variations in cerebral oxygen metabolism in demented patients. PURPOSE: Delineating the metabolic profiles evident throughout different phases of dementia necessitates an integrated analysis of OEF and DoHb levels. This is enabled by leveraging high-resolution quantitative blood oxygenation level dependent (qBOLD) analysis of magnitude images obtained from a multi-echo gradient-echo MRI (mGRE) scan performed on a 3.0 Tesla scanner. METHODS: Achieving superior spatial resolution in qBOLD necessitates the utilization of an mGRE scan with only four echoes, which in turn limits the number of measurements compared to the parameters within the qBOLD model. Consequently, it becomes imperative to discard non-essential parameters to facilitate further analysis. This process entails transforming the qBOLD model into a format suitable for fitting the log-magnitude difference (L-MDif) profiles of the four echo magnitudes present in each brain voxel. In order to bolster spatial specificity, the log-difference qBOLD model undergoes refinement into a representative form, termed as r-qBOLD, particularly when applied to class-averaged L-MDif signals derived through k-means clustering of L-MDif signals from all brain voxels into a predetermined number of clusters. The agreement between parameters estimated using r-qBOLD for different cluster sizes is validated using Bland-Altman analysis, and the model's goodness-of-fit is evaluated using a χ 2 ${\chi ^2}$ -test. Retrospective MRI data of Alzheimer's disease (AD), mild cognitive impairment (MCI), and non-demented patients without neuropathological disorders, pacemakers, other implants, or psychiatric disorders, who completed a minimum of three visits prior to MRI enrolment, are utilized for the study. RESULTS: Utilizing a cohort comprising 30 demented patients aged 65-83 years in stages 4-6 representing mild, moderate, and severe stages according to the clinical dementia rating (CDR), matched with an age-matched non-demented control group of 18 individuals, we conducted joint observations of OEF and DoHb levels estimated using r-qBOLD. The observations elucidate metabolic signatures in dementia based on OEF and DoHb levels in each voxel. Our principal findings highlight the significance of spatial patterns of metabolic profiles (metabolic patterns) within two distinct regimes: OEF levels exceeding the normal range (S1-regime), and OEF levels below the normal range (S2-regime). The S1-regime, accompanied by low DoHb levels, predominantly manifests in fronto-parietal and perivascular regions with increase in dementia severity. Conversely, the S2-regime, accompanied by low DoHb levels, is observed in medial temporal (MTL) regions. Other regions with abnormal metabolic patterns included the orbitofrontal cortex (OFC), medial-orbital prefrontal cortex (MOPFC), hypothalamus, ventro-medial prefrontal cortex (VMPFC), and retrosplenial cortex (RSP). Dysfunction in the OFC and MOPFC indicated cognitive and emotional impairment, while hypothalamic involvement potentially indicated preclinical dementia. Reduced metabolic activity in the RSP suggested early-stage AD related functional abnormalities. CONCLUSIONS: Integrated analysis of OEF and DoHb levels using r-qBOLD reveals distinct metabolic signatures across dementia phases, highlighting regions susceptible to neuronal loss, vascular involvement, and preclinical indicators.

SWI processing using a local phase difference modulated venous enhancement filter with noise compensation.

Susceptibility weighted imaging (SWI) involves post-processing of gradient echo images which are sensitive to the spatial variations in magnetic susceptibility. The aim of this study is to develop an automated filtering scheme to enhance the contrast-to-noise ratio (CNR) and blooming on SWI. Here, the high-pass filtering for SWI processing is designed by applying a weighting function to the neighboring phase differences to enhance the susceptibility-related (SuR) contrast. This is accomplished by summing the neighboring phase differences, weighted with a scaled and shifted error function of the phase difference. Besides using the filter weights of this weighted high-pass (WHP) filter to minimize the filtering artefacts using a filter scale parameter, the CNR is further increased by introduction of the neighborhood-based noise compensation weights into the filtering process. These weights are deduced from the channel phase distribution, conditioned on the channel magnitude and noise variance. Using in vivo SWI data acquired at 1.5 T (16 nos.) and 3.0 T (30 nos.), the magnitude SWI processed using the noise compensated WHP (WHPC) filter is shown to provide an average CNR improvement of 68.40% over that of a homodyne high-pass (HHP) filter. Two tailed t-tests performed separately for different field strengths, show significant differences (p < 0.001) between mean separations of phase masks generated from the WHPC and HHP filtered phase images. In conclusion, the WHPC filter, tuned by the mean separation of the phase mask, enhances the SuR contrast of magnitude SWI for evaluation of mild cognitive impairments, brain tumor and hemorrhagic stroke.

Improved image reconstruction of low-resolution multichannel phase contrast angiography.

In low-resolution phase contrast magnetic resonance angiography, the maximum intensity projected channel images will be blurred with consequent loss of vascular details. The channel images are enhanced using a stabilized deblurring filter, applied to each channel prior to combining the individual channel images. The stabilized deblurring is obtained by the addition of a nonlocal regularization term to the reverse heat equation, referred to as nonlocally stabilized reverse diffusion filter. Unlike reverse diffusion filter, which is highly unstable and blows up noise, nonlocal stabilization enhances intensity projected parallel images uniformly. Application to multichannel vessel enhancement is illustrated using both volunteer data and simulated multichannel angiograms. Robustness of the filter applied to volunteer datasets is shown using statistically validated improvement in flow quantification. Improved performance in terms of preserving vascular structures and phased array reconstruction in both simulated and real data is demonstrated using structureness measure and contrast ratio.

A higher dimensional homodyne filter for phase sensitive partial Fourier reconstruction of magnetic resonance imaging.

The aim of this paper is to introduce procedural steps for extension of the 1D homodyne phase correction for k-space truncation in all gradient encoding directions. Compared to the existing method applied to 2D partial k-space, signal losses introduced by the phase correction filter are observed to be minimal for the modified approach. In addition, the modified form of phase correction retains the inherent property of homodyne filtering for elimination of incidental phase artifacts due to truncation. In parallel imaging, this new form of homodyne filtering is shown to be effective for minimizing the signal losses, when each of the channel k-spaces is truncated along both phase and frequency-encode directions. This is illustrated with 2D partial k-space for flow compensated multichannel susceptibility weighted imaging. Extension of this method to 3D partial k-space shows improved reconstruction of flow information in phase contrast magnetic resonance angiography with reduced blur and enhanced background suppression.

Texture-based segmentation of diffuse lesions of the brain's white matter.

Diffuse lesions of the white matter of the human brain are common pathological findings in magnetic resonance images of elderly subjects. These lesions are typically caused by small vessel diseases (e.g., due to hypertension, diabetes), and related to cognitive decline. Because these lesions are inhomogeneous, unsharp, and faint, but show an intensity pattern that is different from the adjacent healthy tissue, a segmentation based on texture properties is proposed here. This method was successfully applied to a set of 116 image data sets of elderly subjects. Quantitative measures for the lesion load are derived that compare well with results from experts that visually rated lesions on a semiquantitative scale. Texture-based segmentation can be considered as a general method for lesion segmentation, and an outline for adapting this method to similar problems is presented.

Noncanonical spike-related BOLD responses in focal epilepsy.

Till now, most studies of the Blood Oxygen Level-Dependent (BOLD) response to interictal epileptic discharges (IED) have assumed that its time course matches closely to that of brief physiological stimuli, commonly called the canonical event-related haemodynamic response function (canonical HRF). Analyses based on that assumption have produced significant response patterns that are generally concordant with prior electroclinical data. In this work, we used a more flexible model of the event-related response, a Fourier basis set, to investigate the presence of other responses in relation to individual IED in 30 experiments in patients with focal epilepsy. We found significant responses that had a noncanonical time course in 37% of cases, compared with 40% for the conventional, canonical HRF-based approach. In two cases, the Fourier analysis suggested activations where the conventional model did not. The noncanonical activations were almost always remote from the presumed generator of epileptiform activity. In the majority of cases with noncanonical responses, the noncanonical responses in single-voxel clusters were suggestive of artifacts. We did not find evidence for IED-related noncanonical HRFs arising from areas of pathology, suggesting that the BOLD response to IED is primarily canonical. Noncanonical responses may represent a number of phenomena, including artefacts and propagated epileptiform activity.