Improving accelerated MRI by deep learning with sparsified complex data.

PURPOSE: To obtain high-quality accelerated MR images with complex-valued reconstruction from undersampled k-space data. METHODS: The MRI scans from human subjects were retrospectively undersampled with a regular pattern using skipped phase encoding, leading to ghosts in zero-filling reconstruction. A complex difference transform along the phase-encoding direction was applied in image domain to yield sparsified complex-valued edge maps. These sparse edge maps were used to train a complex-valued U-type convolutional neural network (SCU-Net) for deghosting. A k-space inverse filtering was performed on the predicted deghosted complex edge maps from SCU-Net to obtain final complex images. The SCU-Net was compared with other algorithms including zero-filling, GRAPPA, RAKI, finite difference complex U-type convolutional neural network (FDCU-Net), and CU-Net, both qualitatively and quantitatively, using such metrics as structural similarity index, peak SNR, and normalized mean square error. RESULTS: The SCU-Net was found to be effective in deghosting aliased edge maps even at high acceleration factors. High-quality complex images were obtained by performing an inverse filtering on deghosted edge maps. The SCU-Net compared favorably with other algorithms. CONCLUSION: Using sparsified complex data, SCU-Net offers higher reconstruction quality for regularly undersampled k-space data. The proposed method is especially useful for phase-sensitive MRI applications.

Motion resilience of the balanced steady-state free precession geometric solution.

PURPOSE: Many MRI sequences are sensitive to motion and its associated artifacts. The linearized geometric solution (LGS), a balanced steady-state free precession (bSSFP) off-resonance signal demodulation technique, is evaluated with respect to motion artifact resilience. THEORY AND METHODS: The mechanism and extent of LGS motion artifact resilience is examined in simulated, flow phantom, and in vivo clinical imaging. Motion artifact correction capabilities are decoupled from susceptibility artifact correction when feasible to permit controlled analysis of motion artifact correction when comparing the LGS with standard and phase-cycle-averaged (complex sum) bSSFP imaging. RESULTS: Simulations reveal that the LGS demonstrates motion artifact reduction capabilities similar to standard clinical bSSFP imaging techniques, with slightly greater resilience in high SNR regions and for shorter-duration motion. Flow phantom experiments assert that the LGS reduces shorter-duration motion artifact error by ∼24%-65% relative to the complex sum, whereas reconstructions exhibit similar error reduction for constant motion. In vivo analysis demonstrates that in the internal auditory canal/orbits, the LGS was deemed to have less artifact in 24%/49% and similar artifact in 76%/51% of radiological assessments relative to the complex sum, and the LGS had less artifact in 97%/81% and similar artifact in 3%/16% of assessments relative to standard bSSFP. Only 2 of 63 assessments deemed the LGS inferior to either complex sum or standard bSSFP in terms of artifact reduction. CONCLUSION: The LGS provides sufficient bSSFP motion artifact resilience to permit robust elimination of susceptibility artifacts, inspiring its use in a wide variety of applications.

A data-driven T2 relaxation analysis approach for myelin water imaging: Spectrum analysis for multiple exponentials via experimental condition oriented simulation (SAME-ECOS).

PURPOSE: The decomposition of multi-exponential decay data into a T2 spectrum poses substantial challenges for conventional fitting algorithms, including non-negative least squares (NNLS). Based on a combination of the resolution limit constraint and machine learning neural network algorithm, a data-driven and highly tailorable analysis method named spectrum analysis for multiple exponentials via experimental condition oriented simulation (SAME-ECOS) was proposed. THEORY AND METHODS: The theory of SAME-ECOS was derived. Then, a paradigm was presented to demonstrate the SAME-ECOS workflow, consisting of a series of calculation, simulation, and model training operations. The performance of the trained SAME-ECOS model was evaluated using simulations and six in vivo brain datasets. The code is available at https://github.com/hanwencat/SAME-ECOS. RESULTS: Using NNLS as the baseline, SAME-ECOS achieved over 15% higher overall cosine similarity scores in producing the T2 spectrum, and more than 10% lower mean absolute error in calculating the myelin water fraction (MWF), as well as demonstrated better robustness to noise in the simulation tests. Applying to in vivo data, MWF from SAME-ECOS and NNLS was highly correlated among all study participants. However, a distinct separation of the myelin water peak and the intra/extra-cellular water peak was only observed in the mean T2 spectra determined using SAME-ECOS. In terms of data processing speed, SAME-ECOS is approximately 30 times faster than NNLS, achieving a whole-brain analysis in 3 min. CONCLUSION: Compared with NNLS, the SAME-ECOS method yields much more reliable T2 spectra in a dramatically shorter time, increasing the feasibility of multi-component T2 decay analysis in clinical settings.

Myelin water imaging data analysis in less than one minute.

PURPOSE: Based on a deep learning neural network (NN) algorithm, a super fast and easy to implement data analysis method was proposed for myelin water imaging (MWI) to calculate the myelin water fraction (MWF). METHODS: A NN was constructed and trained on MWI data acquired by a 32-echo 3D gradient and spin echo (GRASE) sequence. Ground truth labels were created by regularized non-negative least squares (NNLS) with stimulated echo corrections. Voxel-wise GRASE data from 5 brains (4 healthy, 1 multiple sclerosis (MS)) were used for NN training. The trained NN was tested on 2 healthy brains, 1 MS brain with segmented lesions, 1 healthy spinal cord, and 1 healthy brain acquired from a different scanner. RESULTS: Production of whole brain MWF maps in approximately 33 â€‹s can be achieved by a trained NN without graphics card acceleration. For all testing regions, no visual differences between NN and NNLS MWF maps were observed, and no obvious regional biases were found. Quantitatively, all voxels exhibited excellent agreement between NN and NNLS (all R2>0.98, p â€‹< â€‹0.001, mean absolute error <0.01). CONCLUSION: The time for accurate MWF calculation can be dramatically reduced to less than 1 â€‹min by the proposed NN, addressing one of the barriers facing future clinical feasibility of MWI.

Combined geometric and algebraic solutions for removal of bSSFP banding artifacts with performance comparisons.

PURPOSE: Balanced steady state free precession (bSSFP) imaging suffers from off-resonance artifacts such as signal modulation and banding. Solutions for removal of bSSFP off-resonance dependence are described and compared, and an optimal solution is proposed. THEORY AND METHODS: An Algebraic Solution (AS) that complements a previously described Geometric Solution (GS) is derived from four phase-cycled bSSFP datasets. A composite Geometric-Algebraic Solution (GAS) is formed from a noise-variance-weighted average of the AS and GS images. Two simulations test the solutions over a range of parameters, and phantom and in vivo experiments are implemented. Image quality and performance of the GS, AS, and GAS are compared with the complex sum and a numerical parameter estimation algorithm. RESULTS: The parameter estimation algorithm, GS, AS, and GAS remove most banding and signal modulation in bSSFP imaging. The variable performance of the GS and AS on noisy data justifies generation of the GAS, which consistently provides the highest performance. CONCLUSION: The GAS is a robust technique for bSSFP signal demodulation that balances the regional efficacy of the GS and AS to remove banding, a feat not possible with prevalent techniques. Magn Reson Med 77:644-654, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

Improving image quality for skipped phase encoding and edge deghosting (SPEED) by exploiting several sparsifying transforms.

PURPOSE: To improve the image quality of skipped phase encoding and edge deghosting (SPEED) by exploiting several sparsifying transforms. METHODS: The SPEED technique uses a skipped phase encoding (PE) step to accelerate MRI scan. Previously, a difference transform (DT) along PE direction is used to obtain sparse ghosted-edge maps, which were modeled by a double layer ghost model and was then deghosted by a least square error solution. In this work, it is hypothesized that enhanced sparsity, and thus improved image quality may be achievable with other sparsifying transforms, including discrete wavelet transform (DWT), discrete cosine transform (DCT), DWT combined with DT, and DCT combined with DT. RESULTS: For images of human subjects, SPEED with DWT or DCT can yield higher image quality than DT only, especially for those images with low contrast. Reconstruction error can be further reduced if DWT or DCT are combined with DT. CONCLUSION: Image sparsity can be enhanced with more advanced transforms, leading to higher reconstruction quality in SPEED imaging that is desirable for practical MRI applications.

Somatic mosaicism for the p.His1047Arg mutation in PIK3CA in a girl with mesenteric lipomatosis.

We describe a patient who presented with a localized growth of mature fat tissue, which was surgically removed. MRI imaging identified diffuse increase in visceral adipose tissue. Targeted deep sequencing of the resected tissue uncovered a p.H1047R variant in PIK3CA, which was absent in blood. This report expands the phenotypic spectrum of mosaic PIK3CA mutations.

Banding artifact removal for bSSFP imaging with an elliptical signal model.

PURPOSE: Balanced steady-state free precession (bSSFP) imaging has broad clinical applications by virtue of its high time efficiency and desirable contrast. Unfortunately, banding artifact is often seen as a result of signal modulation due to B0 inhomogeneity. This study aims to develop an effective method for banding artifact suppression. METHODS: bSSFP is analyzed with an elliptical signal model. A simple analytical "Geometric-Solution" (GS) is presented to demodulate the signal from B0 inhomogeneity dependence with phase-cycled bSSFP data from both a computer simulation and experiments using phantom and human subjects. RESULTS: The proposed algorithm is able to remove banding artifacts completely. It also compares favorably with the complex sum (CS), which is considered one of the more efficient methods for banding artifact correction. CONCLUSION: Using an elliptical signal model, an analytical solution to the bSSFP banding problem has been found and demonstrated with simulation as well as phantom and in vivo experiments.

Accelerated MRI by SPEED with generalized sampling schemes.

PURPOSE: To enhance the fast imaging technique of skipped phase encoding (PE) and edge deghosting (SPEED) for more general sampling options, and thus more flexibility in implementations and applications. METHODS: SPEED uses skipped PE steps to accelerate MRI scan. Previously, the PE skip size was chosen from prime numbers only. This restriction has been relaxed in this study to allow choice of any integers rather than merely prime numbers. Various sampling patterns were studied under all possible combinations of PE skip size and PE shifts. A criterion based on the rank values of ghost phasor matrices was introduced to evaluate SPEED reconstruction. RESULTS: The reconstruction quality was found to correlate with the rank value of the ghost phasor matrix and the skipped PE size N. A low-rank value indicates a singular matrix that causes failure of the SPEED reconstruction. Composite numbers combined with appropriately chosen PE shifts yielded satisfactory reconstruction results. CONCLUSION: With properly chosen PE shifts, it was found that any integers, including both prime numbers and composite numbers, could be used as PE skip size for SPEED. This finding allows much more flexible data acquisition options that may lead to more freedom in practical implementations and applications.

Accelerating phase contrast MR angiography by simplified skipped phase encoding and edge deghosting with array coil enhancement.

PURPOSE: The aim of this work is to investigate the feasibility of accelerating phase contrast magnetic resonance angiography (PC-MRA) by the fast imaging method of simplified skipped phase encoding and edge deghosting with array coil enhancement (S-SPEED-ACE). METHODS: The parallel imaging method of skipped phase encoding and edge deghosting with array coil enhancement (SPEED-ACE) is simplified for imaging sparse objects like phase contrast MRA. This approach is termed S-SPEED-ACE in which k-space is sparsely sampled with skipped phase encoding at every Nth step using multiple receiver coils simultaneously. The sampled data are then Fourier transformed into a set of ghosted images, each with N-fold aliasing ghosts. Given signal sparseness of MRA, the ghosted images are modeled with a single-layer structure, in which the most dominant ghost within the potentially overlapped ghosts at each pixel is selected to represent the signal of that pixel. The single-layer model is analogous to that used in maximum-intensity-projection (MIP) that selects only the brightest signal even when there are overlapped vessels. With an algorithm based on a least-square-error solution, a deghosted image is obtained, along with a residual map for quality control. In this way, S-SPEED-ACE partially samples k-space using multiple receiver coils in parallel, and yields a deghosted image with an acceleration factor of N. Without full central k-space sampling and differential filtering, S-SPEED-ACE achieves further scan time reduction with a more straightforward reconstruction. In this work, S-SPEED-ACE is demonstrated to accelerate a computer simulated PC-MRA and a real human 3D PC-MRA, which was acquired using a clinical 1.5 T scanner on a healthy volunteer. RESULTS: Images are reconstructed by S-SPEED-ACE to achieve an undersampling factor of up to 8.3 with four receiver coils. The reconstructed images generally have comparable quality as that of the reference images reconstructed from full k-space data. Maximum-intensity-projection images generated from the reconstructed images also demonstrated to be consistent as those from the reference images. CONCLUSIONS: By taking advantage of signal sparsity naturally existing in the data, SPEED-ACE was simplified and its efficiency was improved. The feasibility of the proposed S-SPEED-ACE is demonstrated in this work with simulated sampling of an actual 3D head PC-MRA scan.

Applications of stimulated echo correction to multicomponent T2 analysis.

We propose a multicomponent fitting algorithm for multiecho T(2) data which allows for correction of T(2) distributions in the presence of stimulated echoes. Tracking the population of spins in many coherence pathways via the iterated method of the Extended Phase Graph algorithm allows for accurate quantification of echo magnitudes. The resulting decay curves allow for correction of errors due to nonideal refocusing pulses as a result of inhomogeneities in the B(1) transmit field. Non-Negative Least Squares fitting is used to quantify the magnitude of T(2) components at various T(2) values. This method, allowing calculation of the T(2) distribution with simultaneous extraction of the refocusing pulse flip angle, requires no change to image acquisition procedures and no extra data input. Validation by means of both simulations and in vivo data shows excellent interscan reproducibility while vastly improving the accuracy of extracted T(2) parameters in voxels where poor B(1) homogeneity leads to refocusing pulse flip angles significantly less than 180°. Most notably, myelin water fraction values in these regions are found to have increased consistency and accuracy.

Accelerating non-contrast-enhanced MR angiography with inflow inversion recovery imaging by skipped phase encoding and edge deghosting (SPEED).

PURPOSE: To accelerate non-contrast-enhanced MR angiography (MRA) with inflow inversion recovery (IFIR) with a fast imaging method, Skipped Phase Encoding and Edge Deghosting (SPEED). MATERIALS AND METHODS: IFIR imaging uses a preparatory inversion pulse to reduce signals from static tissue, while leaving inflow arterial blood unaffected, resulting in sparse arterial vasculature on modest tissue background. By taking advantage of vascular sparsity, SPEED can be simplified with a single-layer model to achieve higher efficiency in both scan time reduction and image reconstruction. SPEED can also make use of information available in multiple coils for further acceleration. The techniques are demonstrated with a three-dimensional renal non-contrast-enhanced IFIR MRA study. RESULTS: Images are reconstructed by SPEED based on a single-layer model to achieve an undersampling factor of up to 2.5 using one skipped phase encoding direction. By making use of information available in multiple coils, SPEED can achieve an undersampling factor of up to 8.3 with four receiver coils. The reconstructed images generally have comparable quality as that of the reference images reconstructed from full k-space data. CONCLUSION: As demonstrated with a three-dimensional renal IFIR scan, SPEED based on a single-layer model is able to reduce scan time further and achieve higher computational efficiency than the original SPEED.

Efficient multiple acquisitions by Skipped Phase Encoding and Edge Deghosting (SPEED) using shared spatial information.

The fast MRI method of Skipped Phase Encoding and Edge Deghosting (SPEED) is further developed to accelerate multiple acquisitions. In a single acquisition, SPEED first acquires three sparse ghosted edge maps with an undersampling factor of N/3, which are modeled with a double-layer structure and described by three equations with two unknown ghosts, each with a unique ghost order index. By minimizing least-square-error, a pair of ghost order indexes is determined. Based on them, the two corresponding ghosts are resolved, leading to a deghosted image. In this case, three equations are needed to determine the ghost order index, while only two equations are required to resolve the two ghosts. This shows both inefficiency and potential. Multiple acquisitions often contain similar spatial information. The similarities can be used to improve efficiency by sharing the ghost order index among different acquisitions, leading to acceleration factors greater than that achievable with single acquisition.

Simplified skipped phase encoding and edge deghosting (SPEED) for imaging sparse objects with applications to MRA.

The fast imaging method named skipped phase encoding and edge deghosting (SPEED) has been demonstrated to reduce scan time considerably with typical magnetic resonance imaging data. In this work, SPEED is simplified with improved efficiency to accelerate the scan of sparse objects; we refer to this method as S-SPEED. S-SPEED partially samples k-space into two interleaved data sets, each with the same skip size of N but a different relative shift in phase encoding. The sampled data are then Fourier transformed into two ghosted images with N aliasing ghosts. Given the sparseness of signal distribution, the ghosted images are simply modeled with a single-layer structure, analogous to that used in maximum-intensity projection. With an algorithm based on a least-square-error solution, a deghosted image is solved, and a residual map is output for quality control. S-SPEED can be generalized to include more layers with additional acquisitions for refined results. Without differential filtering and full central k-space sampling, S-SPEED reduces scan time further and achieves more straightforward reconstruction, as compared with SPEED. In this work, S-SPEED is applied to accelerate magnetic resonance angiography (MRA) by taking advantage of the sparse nature of MRA data. With sparse phantom data and in vivo phase contrast MRA data, S-SPEED is demonstrated to achieve satisfactory results with an acceleration factor of 5.5 using a single coil.

Correction for geometric distortion and N/2 ghosting in EPI by phase labeling for additional coordinate encoding (PLACE).

Echo-planar imaging (EPI) is vulnerable to geometric distortion and N/2 ghosting. These artifacts can be analyzed with an intuitive k-t space tool, and here we propose a simple method for their correction. In a slightly modified additional EPI acquisition, we sample the k-t space with a shift in k(y) by adding a small area to the phase-encoding (PE) gradient. Physically, the added gradient area creates a relative phase ramp across the object and directly encodes the undistorted original y-coordinate of each voxel into a phase difference between two distorted complex images, in a method called "phase labeling for additional coordinate encoding" (PLACE). The phase information is then used to map the mismapped signals back to their original locations for geometric and intensity correction. Smoothing of expanded complex data matrix effectively reduces noise in the differential phase map and allows subpixel warping. The two acquired images can also be averaged to effectively suppress the N/2 ghost. Efficient correction for both artifacts can be achieved with three acquisitions. These acquisitions can also serve as reference scans to correct for geometric distortion and/or N/2 ghost artifacts on all images in a time series. The technique was successfully demonstrated in phantom and animal studies.

Highly accelerated MRI by skipped phase encoding and edge deghosting with array coil enhancement (SPEED-ACE).

The fast MRI method of skipped phase encoding and edge deghosting (SPEED) is further developed with array coil enhancement, and thus is termed SPEED-ACE. In SPEED-ACE, k space is sparsely sampled with skipped phase encoding at every Nth step using a set of receiver coils simultaneously, similar to SENSE, leading to sensitivity-weighted images with up to N layers of overlapping aliasing ghosts. The ghosted images are edge enhanced by a differential filter to yield ghosted edge maps, in which the ghost overlapping layers are greatly reduced since the sparseness of edges reduces the chance of ghost overlapping. Typical ghosted edge maps can be adequately modeled with a double-layer structure. By using data from at least three coils through least-square-error minimization, a deghosted edge map is obtained and inverse-filtered into a final deghosted image. In this way, SPEED-ACE partially samples k space with a skip size of N by using multiple receiver coils in parallel, and obtains a fairly good deghosted image with an undersampling factor of N. SPEED-ACE is not limited to the double-layer ghost model, but can be generalized to include more layers of ghosts for more flexible and improved performance. As a new parallel imaging method, SPEED-ACE was tested using in vivo data to demonstrate the possibility of achieving undersampling factors even greater than the number of receiver coils, which is so far not achievable by other parallel imaging methods.

Two-point water-fat imaging with partially-opposed-phase (POP) acquisition: an asymmetric Dixon method.

A novel two-point water-fat imaging method is introduced. In addition to the in-phase acquisition, water and fat magnetization vectors are sampled at partially-opposed-phase (POP) rather than exactly antiparallel as in the original Dixon method. This asymmetric sampling encodes more valuable phase information for identifying water and fat. From the magnitudes of the two complex images, a big and a small chemical component are first robustly obtained pixel by pixel and then used to form two possible error phasor candidates. The true error phasor is extracted from the two error phasor candidates through a simple procedure of regional iterative phasor extraction (RIPE). Finally, least-squares solutions of water and fat are obtained after the extracted error phasor is smoothed and removed from the complex images. For noise behavior, the effective number of signal averages NSA* is typically in the range of 1.87-1.96, very close to the maximum possible value of 2. Compared to earlier approaches, the proposed method is more efficient in data acquisition and straightforward in processing, and the final results are more robust. At both 1.5T and 0.3T, well separated and identified in vivo water and fat images covering a broad range of anatomical regions have been obtained, supporting the clinical utility of the method.

Nonlinear phase correction with an extended statistical algorithm.

This paper presents a new magnetic resonance imaging (MRI) phase correction method. The linear phase correction method using autocorrelation proposed by Ahn and Cho (AC method) is extended to handle nonlinear terms, which are often important for polynomial expansion of phase variation in MRI. The polynomial coefficients are statistically determined from a cascade series of n-pixel-shift rotational differential fields (RDFs). The n-pixel-shift RDF represents local vector rotations of a complex field relative to itself after being shifted by n pixels. We have found that increasing the shift enhances the signal significantly and extends the AC method to handle higher order nonlinear phase error terms. The n-pixel-shift RDF can also be applied to improve other methods such as the weighted least squares phase unwrapping method proposed by Liang. The feasibility of the method has been demonstrated with two-dimensional (2-D) in vivo inversion-recovery MRI data.

Accelerating MRI by skipped phase encoding and edge deghosting (SPEED).

A fast imaging method called skipped phase encoding and edge deghosting (SPEED) is introduced. The k-space is sparsely sampled into three interleaved datasets, each with a skip-size N and a relative shift in phase encoding (PE). These datasets are separately reconstructed by 2DFT and edge-enhanced by a differential filter in the PE direction, resulting in edge maps with phase-shifted aliasing ghosts. The sparseness of edges reduces the chance of ghost overlapping. Typical ghosted-edge maps can be adequately modeled with only two dominating ghost layers that are resolved from a set of three equations using least-square error minimization, yielding N ghost maps of different orders that can be registered and averaged into a single deghosted-edge map for noise and artifact reduction. Finally, the deghosted-edge map is transformed into a deghosted image by an inverse filter. A few central k-space lines are collected without PE skip to aid the inverse filtering. SPEED has been demonstrated by in vivo data to reduce scan time considerably without noticeable artifacts. It has various potential applications, such as MR angiography (MRA), where the signal itself is sparse. As an independent method, SPEED can be combined with other fast imaging methods for further acceleration.

Quantitative evaluation of metal artifact reduction techniques.

PURPOSE: To develop a technique to quantify artifact, and to use it to compare the effectiveness of several approaches to metal artifact reduction, including view angle tilting and increasing the slice select and image bandwidths (BWs), in terms of metal artifact reduction, noise, and blur. MATERIALS AND METHODS: Nonmetallic replicas of two metal implants (stainless steel and titanium/chromium-cobalt femoral prostheses) were fabricated from wax, and MR images were obtained of each component immersed in water. The differences between the images of each metal prosthesis and its wax counterpart were measured. The contributions from noise and blur were isolated, resulting in a measure of the metal artifact. Several off-resonance artifact reduction techniques were assessed in terms of metal artifact reduction capability, as well as signal to noise ratio and blur. RESULTS: Increasing the image BW from +/-16 kHz to +/-64 kHz was found to reduce the artifact by an average of 60%, while employing view angle tilting (VAT) alone was found to reduce the artifact by an average of 63%. The metal artifact reduction sequence (MARS), which combines several susceptibility artifact reduction techniques, resulted in the least amount of image distortion, reducing the artifact by an average of 79%. CONCLUSION: The results indicate that while VAT alone (with an image BW of +/-16 kHz) resulted in the smallest amount of total energy and no reduction in the signal-to-noise ratio compared to a conventional spin-echo pulse sequence, MARS resulted in significantly less artifact and dramatically less blur.