Sensitivity profiles from an array of coils for encoding and reconstruction in parallel (SPACE RIP)

IMJENSE: Scan-Specific Implicit Representation for Joint Coil Sensitivity and Image Estimation in Parallel MRI

Parallel imaging is a commonly used technique to accelerate magnetic resonance imaging (MRI) data acquisition. Mathematically, parallel MRI reconstruction can be formulated as an inverse problem relating the sparsely sampled k-space measurements to the desired MRI image. Despite the success of many existing reconstruction algorithms, it remains a challenge to reliably reconstruct a high-quality image from highly reduced k-space measurements. Recently, implicit neural representation has emerged as a powerful paradigm to exploit the internal information and the physics of partially acquired data to generate the desired object. In this study, we introduced IMJENSE, a scan-specific implicit neural representation-based method for improving parallel MRI reconstruction. Specifically, the underlying MRI image and coil sensitivities were modeled as continuous functions of spatial coordinates, parameterized by neural networks and polynomials, respectively. The weights in the networks and coefficients in the polynomials were simultaneously learned directly from sparsely acquired k-space measurements, without fully sampled ground truth data for training. Benefiting from the powerful continuous representation and joint estimation of the MRI image and coil sensitivities, IMJENSE outperforms conventional image or k-space domain reconstruction algorithms. With extremely limited calibration data, IMJENSE is more stable than supervised calibrationless and calibration-based deep-learning methods. Results show that IMJENSE robustly reconstructs the images acquired at 5× and 6× accelerations with only 4 or 8 calibration lines in 2D Cartesian acquisitions, corresponding to 22.0% and 19.5% undersampling rates. The high-quality results and scanning specificity make the proposed method hold the potential for further accelerating the data acquisition of parallel MRI.

New Theory and Faster Computations for Subspace-Based Sensitivity Map Estimation in Multichannel MRI

Sensitivity map estimation is important in many multichannel MRI applications. Subspace-based sensitivity map estimation methods like ESPIRiT are popular and perform well, though can be computationally expensive and their theoretical principles can be nontrivial to understand. In the first part of this work, we present a novel theoretical derivation of subspace-based sensitivity map estimation based on a linear-predictability/structured low-rank modeling perspective. This results in an estimation approach that is equivalent to ESPIRiT, but with distinct theory that may be more intuitive for some readers. In the second part of this work, we propose and evaluate a set of computational acceleration approaches (collectively known as PISCO) that can enable substantial improvements in computation time (up to  ∼ 100× in the examples we show) and memory for subspace-based sensitivity map estimation.

On Ambiguity in Linear Inverse Problems: Entrywise Bounds on Nearly Data-Consistent Solutions and Entrywise Condition Numbers

Ill-posed linear inverse problems appear frequently in various signal processing applications. It can be very useful to have theoretical characterizations that quantify the level of ill-posedness for a given inverse problem and the degree of ambiguity that may exist about its solution. Traditional measures of ill-posedness, such as the condition number of a matrix, provide characterizations that are global in nature. While such characterizations can be powerful, they can also fail to provide full insight into situations where certain entries of the solution vector are more or less ambiguous than others. In this work, we derive novel theoretical lower- and upper-bounds that apply to individual entries of the solution vector, and are valid for all potential solution vectors that are nearly data-consistent. These bounds are agnostic to the noise statistics and the specific method used to solve the inverse problem, and are also shown to be tight. In addition, our results also lead us to introduce an entrywise version of the traditional condition number, which provides a substantially more nuanced characterization of scenarios where certain elements of the solution vector are less sensitive to perturbations than others. Our results are illustrated in an application to magnetic resonance imaging reconstruction, and we include discussions of practical computation methods for large-scale inverse problems, connections between our new theory and the traditional Cramér-Rao bound under statistical modeling assumptions, and potential extensions to cases involving constraints beyond just data-consistency.

Dual-Domain Reconstruction Network with V-Net and K-Net for Fast MRI

PURPOSE

To introduce a dual-domain reconstruction network with V-Net and K-Net for accurate MR image reconstruction from undersampled k-space data.

METHODS

Most state-of-the-art reconstruction methods apply U-Net or cascaded U-Nets in the image domain and/or k-space domain. Nevertheless, these methods have the following problems: (1) directly applying U-Net in the k-space domain is not optimal for extracting features; (2) classical image-domain-oriented U-Net is heavyweighted and hence inefficient when cascaded many times to yield good reconstruction accuracy; (3) classical image-domain-oriented U-Net does not make full use of information of the encoder network for extracting features in the decoder network; and (4) existing methods are ineffective in simultaneously extracting and fusing features in the image domain and its dual k-space domain. To tackle these problems, we present 3 different methods: (1) V-Net, an image-domain encoder-decoder subnetwork that is more lightweight for cascading and effective in fully utilizing features in the encoder for decoding; (2) K-Net, a k-space domain subnetwork that is more suitable for extracting hierarchical features in the k-space domain, and (3) KV-Net, a dual-domain reconstruction network in which V-Nets and K-Nets are effectively combined and cascaded.

RESULTS

Extensive experimental results on the fastMRI dataset demonstrate that the proposed KV-Net can reconstruct high-quality images and outperform state-of-the-art approaches with fewer parameters.

CONCLUSIONS

To reconstruct images effectively and efficiently from incomplete k-space data, we have presented a dual-domain KV-Net to combine K-Nets and V-Nets. The KV-Net achieves better results with 9% and 5% parameters than comparable methods (XPD-Net and i-RIM).

Parallel MR image reconstruction based on triple cycle optimization

The self-calibration parallel imaging (SC-SENSE) method reconstructs the image by estimating the coil sensitivity matrix. In order to obtain the sensitivity matrix, it is necessary to take a small amount of automatic calibration signal lines (ACSL) in the center of k-space. This method uses the data of the central region to obtain the sensitivity matrix, and then the reconstructed image is obtained. This paper proposed the triple cycle optimization (TCO) method to continuously optimize reconstructed images. The proposed TCO method takes the sensitivity matrix obtained by ACSL and substituted the reconstructed image as the initial data generation into the loop, and estimates the k-space data repeatedly. A new sensitivity matrix is obtained by using k-space data and the reconstructed image, and a stable triple cycle is obtained. In the cycle, all data are optimized to a certain extent, including the reconstructed image. Experimental results show that under the same sampling density, images reconstructed by using the triple cycle optimization method have lower noise and artifacts than those of the traditional method. When combined with the variable density sampling method, the effect is remarkable with a much low sampling rate.

Sliding window reduced FOV reconstruction for real-time cardiac imaging

BACKGROUND

Current functional cardiovascular imaging protocols mostly rely on electrocardiogram (ECG) gating and breathholding. The resulting image quality can substantially suffer from insufficient patient cooperation or severe arrhythmia. Real-time imaging can mitigate these effects but requires highly accelerated techniques, usually relying on non-cartesian trajectories and Compressed Sensing (CS).

METHODS

We investigate a sliding window reduced field of view (FOV) Echo Planar Imaging (EPI) technique for real-time cardiac MRI. Segmented EPI has been combined with a subtraction technique for reducing the FOV in cardiac applications to the region of the beating heart. Residual respiratory motion, potentially impairing the image quality, has been addressed by continuous update of the static image fraction, which is derived from a low-temporal resolution sliding window reconstruction. For further acceleration, the proposed technique was combined with parallel imaging.

RESULTS

The sliding window reduced FOV technique was proven feasible to reconstruct images of diagnostic image quality at a temporal resolution of 36.5ms per image. Semi-quantitative evaluation of image quality showed significant improvement over the existing rFOV method (p=0.039). Derived functional parameters show comparable results as with the BH-CINE reference. However, a trend to a slight underestimation of the largest and smallest in-plane volumes is observed.

CONCLUSION

The proposed technique is feasible of providing real-time cardiac MRI with a temporal resolution better than 40ms without the need of computably complex reconstruction techniques.

KerNL: Kernel-Based Nonlinear Approach to Parallel MRI Reconstruction

The conventional calibration-based parallel imaging method assumes a linear relationship between the acquired multi-channel k-space data and the unacquired missing data, where the linear coefficients are estimated using some auto-calibration data. In this paper, we first analyze the model errors in the conventional calibration-based methods and demonstrate the nonlinear relationship. Then, a much more general nonlinear framework is proposed for auto-calibrated parallel imaging. In this framework, kernel tricks are employed to represent the general nonlinear relationship between acquired and unacquired k-space data without increasing the computational complexity. Identification of the nonlinear relationship is still performed by solving linear equations. Experimental results demonstrate that the proposed method can achieve reconstruction quality superior to GRAPPA and NL-GRAPPA at high net reduction factors.

High-resolution MRI of spinal cords by compressive sensing parallel imaging

Spinal Cord Injury (SCI) is a common injury due to diseases or accidents. Noninvasive imaging methods play a critical role in diagnosing SCI and monitoring the response to therapy. Magnetic Resonance Imaging (MRI), by the virtue of providing excellent soft tissue contrast, is the most promising imaging method for this application. However, spinal cord has a very small cross-section, which needs high-resolution images for better visualization and diagnosis. Acquiring high-resolution spinal cord MRI images requires long acquisition time due to the physical and physiological constraints. Moreover, long acquisition time makes MRI more susceptible to motion artifacts. In this paper, we studied the application of compressive sensing (CS) and parallel imaging to achieve high-resolution imaging from sparsely sampled and reduced k-space data acquired by parallel receive arrays. In particular, the studies are limited to the effects of 2D Cartesian sampling with different subsampling schemes and reduction factors. The results show that compressive sensing parallel MRI has the potential to provide high-resolution images of the spinal cord in 1/3 of the acquisition time required by the conventional methods.

Phase unwinding for dictionary compression with multiple channel transmission in magnetic resonance fingerprinting

PURPOSE

Magnetic Resonance Fingerprinting reconstructions can become computationally intractable with multiple transmit channels, if the B₁⁺ phases are included in the dictionary. We describe a general method that allows to omit the transmit phases. We show that this enables straightforward implementation of dictionary compression to further reduce the problem dimensionality.

METHODS

We merged the raw data of each RF source into a single k-space dataset, extracted the transceiver phases from the corresponding reconstructed images and used them to unwind the phase in each time frame. All phase-unwound time frames were combined in a single set before performing SVD-based compression. We conducted synthetic, phantom and in-vivo experiments to demonstrate the feasibility of SVD-based compression in the case of two-channel transmission.

RESULTS

Unwinding the phases before SVD-based compression yielded artifact-free parameter maps. For fully sampled acquisitions, parameters were accurate with as few as 6 compressed time frames. SVD-based compression performed well in-vivo with highly under-sampled acquisitions using 16 compressed time frames, which reduced reconstruction time from 750 to 25min.

CONCLUSION

Our method reduces the dimensions of the dictionary atoms and enables to implement any fingerprint compression strategy in the case of multiple transmit channels.

Prostate magnetic resonance imaging for brachytherapists: Anatomy and technique

PURPOSE

To present an overview of mp MRI techniques necessary for high-resolution imaging of prostate.

METHODS

We summarize examples from our clinical experience and concepts from the current literature that illustrate normal prostate anatomy on multiparametric MRI (mp MRI).

RESULTS

Our experience regarding optimal mp MRI image acquisition is provided, as well as a summary of prostate and periprostatic anatomy and anatomical variants that pose challenges for BT.

CONCLUSIONS

mp MRI provides unparalleled assessment of the prostate and periprostatic anatomy, making it the most appropriate imaging modality to facilitate prostate BT treatment planning, implantation, and followup. This work provides an introduction to prostate mp MR imaging, anatomy, and anatomical variants essential for successful integration mp MRI into prostate brachytherapy practice.

Hybrid-Space SENSE Reconstruction for Simultaneous Multi-Slice MRI

Simultaneous Multi-Slice (SMS) magnetic resonance imaging (MRI) is a rapidly evolving technique for increasing imaging speed. Controlled aliasing techniques utilize periodic undersampling patterns to help mitigate the loss in signal-to-noise ratio (SNR) in SMS MRI. To evaluate the performance of different undersampling patterns, a quantitative description of the image SNR loss is needed. Additionally, eddy current effects in echo planar imaging (EPI) lead to slice-specific Nyquist ghosting artifacts. These artifacts cannot be accurately corrected for each individual slice before or after slice-unaliasing. In this work, we propose a hybrid-space sensitivity encoding (SENSE) reconstruction framework for SMS MRI by adopting a three-dimensional representation of the SMS acquisition. Analytical SNR loss maps are derived for SMS acquisitions with arbitrary phase encoding undersampling patterns. Moreover, we propose a matrix-decoding correction method that corrects the slice-specific Nyquist ghosting artifacts in SMS EPI acquisitions. Brain images demonstrate that the proposed hybrid-space SENSE reconstruction generates images with comparable quality to commonly used split-slice-generalized autocalibrating partially parallel acquisition reconstruction. The analytical SNR loss maps agree with those calculated by a Monte Carlo based method, but require less computation time for high quality maps. The analytical maps enable a fair comparison between the performances of coherent and incoherent SMS undersampling patterns. Phantom and brain SMS EPI images show that the matrix-decoding method performs better than the single-slice and slice-averaged Nyquist ghosting correction methods under the hybrid-space SENSE reconstruction framework.

Linear Dynamic Sparse Modelling for functional MR imaging

The reconstruction quality of a functional MRI sequence is determined by reconstruction algorithms as well as the information obtained from measurements. In this paper, we propose a Linear Dynamic Sparse Modelling method which is composed of measurement design and reconstruction processes to improve the image quality from both aspects. This method models an fMRI sequence as a linear dynamic sparse model which is based on a key assumption that variations of functional MR images are sparse over time in the wavelet domain. The Hierarchical Bayesian Kalman filter which follows the model is employed to implement the reconstruction process. To accomplish the measurement design process, we propose an Informative Measurement Design (IMD) method. The IMD method addresses the measurement design problem of selecting k feasible measurements such that the mutual information between the unknown image and measurements is maximised, where k is a given budget and the mutual information is extracted from the linear dynamic sparse model. The experimental results demonstrated that our proposed method succeeded in boosting the quality of functional MR images.

Radial k-t SPIRiT: autocalibrated parallel imaging for generalized phase-contrast MRI

PURPOSE

To extend SPIRiT to additionally exploit temporal correlations for highly accelerated generalized phase-contrast MRI and to compare the performance of the proposed radial k-t SPIRiT method relative to frame-by-frame SPIRiT and radial k-t GRAPPA reconstruction for velocity and turbulence mapping in the aortic arch.

THEORY AND METHODS

Free-breathing navigator-gated two-dimensional radial cine imaging with three-directional multi-point velocity encoding was implemented and fully sampled data were obtained in the aortic arch of healthy volunteers. Velocities were encoded with three different first gradient moments per axis to permit quantification of mean velocity and turbulent kinetic energy. Velocity and turbulent kinetic energy maps from up to 14-fold undersampled data were compared for k-t SPIRiT, frame-by-frame SPIRiT, and k-t GRAPPA relative to the fully sampled reference.

RESULTS

Using k-t SPIRiT, improvements in magnitude and velocity reconstruction accuracy were found. Temporally resolved magnitude profiles revealed a reduction in spatial blurring with k-t SPIRiT compared with frame-by-frame SPIRiT and k-t GRAPPA for all velocity encodings, leading to improved estimates of turbulent kinetic energy.

CONCLUSION

k-t SPIRiT offers improved reconstruction accuracy at high radial undersampling factors and hence facilitates the use of generalized phase-contrast MRI for routine use.

Multiparametric MRI of prostate cancer: an update on state-of-the-art techniques and their performance in detecting and localizing prostate cancer

Magnetic resonance (MR) examinations of men with prostate cancer are most commonly performed for detecting, characterizing, and staging the extent of disease to best determine diagnostic or treatment strategies, which range from biopsy guidance to active surveillance to radical prostatectomy. Given both the exam's importance to individual treatment plans and the time constraints present for its operation at most institutions, it is essential to perform the study effectively and efficiently. This article reviews the most commonly employed modern techniques for prostate cancer MR examinations, exploring the relevant signal characteristics from the different methods discussed and relating them to intrinsic prostate tissue properties. Also, a review of recent articles using these methods to enhance clinical interpretation and assess clinical performance is provided. J. Magn. Reson. Imaging 2013;37:1035-1054. © 2013 Wiley Periodicals, Inc.

Robust GRAPPA reconstruction using sparse multi-kernel learning with least squares support vector regression

Accuracy of interpolation coefficients fitting to the auto-calibrating signal data is crucial for k-space-based parallel reconstruction. Both conventional generalized autocalibrating partially parallel acquisitions (GRAPPA) reconstruction that utilizes linear interpolation function and nonlinear GRAPPA (NLGRAPPA) reconstruction with polynomial kernel function are sensitive to interpolation window and often cannot consistently produce good results for overall acceleration factors. In this study, sparse multi-kernel learning is conducted within the framework of least squares support vector regression to fit interpolation coefficients as well as to reconstruct images robustly under different subsampling patterns and coil datasets. The kernel combination weights and interpolation coefficients are adaptively determined by efficient semi-infinite linear programming techniques. Experimental results on phantom and in vivo data indicate that the proposed method can automatically achieve an optimized compromise between noise suppression and residual artifacts for various sampling schemes. Compared with NLGRAPPA, our method is significantly less sensitive to the interpolation window and kernel parameters.

In vivo O-Space imaging with a dedicated 12 cm Z2 insert coil on a human 3T scanner using phase map calibration

Recently, spatial encoding with nonlinear magnetic fields has drawn attention for its potential to achieve faster gradient switching within safety limits, tailored resolution in regions of interest, and improved parallel imaging using encoding fields that complement the sensitivity profiles of radio frequency receive arrays. Proposed methods can broadly be divided into those that use phase encoding (Cartesian-trajectory PatLoc and COGNAC) and those that acquire nonlinear projections (O-Space, Null space imaging, radial PatLoc, and 4D-RIO). Nonlinear projection data are most often reconstructed with iterative algorithms that backproject data using the full encoding matrix. Just like conventional radial sequences that use linear spatial encoding magnetic fields, nonlinear projection methods are more sensitive than phase encoding methods to imperfect calibration of the encoding fields. In this work, voxel-wise phase evolution is mapped at each acquired point in an O-Space trajectory using a variant of chemical shift imaging, capturing all spin dynamics caused by encoding fields, eddy currents, and pulse timing. Phase map calibration is then applied to data acquired from a high-power, 12 cm, Z2 insert coil with an eight-channel radio frequency transmit-receive array on a 3T human scanner. We show the first experimental proof-of-concept O-Space images on in vivo and phantom samples, paving the way for more in-depth exploration of O-Space and similar imaging methods.

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.

Optimal sampling for "Noquist" reduced-data cine magnetic resonance imaging

PURPOSE

To analyze and optimize the signal-to-noise ratio (SNR) for the "Noquist" method for acceleration of cine magnetic resonance imaging in the presence of partially static field of view, designing practical methods for selection of optimal or near-optimal sample sets to allow reliable application of the method for variable image dimensions.

METHODS

To investigate the impact of the Noquist method and its experimental parameters on the SNR in the image reconstructed from reduced data, and to explore optimization of methods for highest SNR stability, three different optimization parameters have been selected: the condition of the forward matrix (R(cond)) as it defines the propagation of noise into the reconstructed image, and the maximum (Φ(maxD)) and the mean (Φ(meanD)) linear noise amplification factor of the dynamic field-of-view (FOV) region. As SNR in a Noquist reconstruction is often not uniform across the FOV and since dynamic regions may contain the part of the image more clinically relevant, primarily these noise levels are targeted for optimization. Using these three optimization parameters, three experiments were conducted: characterization of Noquist SNR properties as a function of important image size parameters; for sufficiently small image dimensions, employment of exhaustive search using lexicographical algorithms to visit all possibilities under the cine imaging constraint that equal numbers of views are acquired at each time point of the sequence; and, departing from an hypothetically optimal pattern, generation and evaluation of SNR characteristics of a series of random variations to that optimal pattern.

RESULTS

The impact of favorable sparse data selection is illustrated, and SNR properties are characterized as a function of relevant acquisition parameters. Optimal data selection is investigated by exhaustive methods for small image sizes, and compared with algorithmic selection patterns. Observations from these experiments are confirmed by further studies on data selection for realistic image dimensions and an optimal selection algorithm is proposed. Sixty-four cases of small image sizes were analyzed through exhaustive search with a total of 527 984 141 matrix inversions called in the process, evaluating several SNR parameters for each case. An algorithm, named "Stairwell," that permits to design image dimensions with optimal SNR characteristics is presented, evaluated and compared with cases analyzed through exhaustive search. In 71.9% of the cases exhaustively studied, the Stairwell algorithm yielded optimal solutions. For no case did the deviation from optimum exceed 3.2% (R(cond)), 1.0% (Φ(meanD)), and 4.9% (Φ(maxD)).

CONCLUSIONS

We have demonstrated SNR-optimality of the "Stairwell" selection algorithm for small image dimensions, and performed additional experiments which all support hypothesized optimality of the algorithm for any image dimensions that satisfy certain symmetry constraints for Noquist reduced-data cine MR imaging. Furthermore, we have presented overall SNR characteristics associated with use of the Noquist method by this algorithm for practical clinical image dimensions. Additionally, observations from our optimization experiments allow us to formulate recommendations for dimensioning Noquist image acquisition parameters which guarantee stable inversion. Moreover, these results allow prediction of the anticipated SNR properties of the reconstruction for given image dimensions (S,D,T), relative to SNR in a conventional full-grid acquisition.

Nonlinear coil sensitivity estimation for parallel magnetic resonance imaging using data-adaptive steering kernel regression method

The parallel magnetic resonance imaging (parallel imaging) technique reduces the MR data acquisition time by using multiple receiver coils. Coil sensitivity estimation is critical for the performance of parallel imaging reconstruction. Currently, most coil sensitivity estimation methods are based on linear interpolation techniques. Such methods may result in Gibbs-ringing artifact or resolution loss, when the resolution of coil sensitivity data is limited. To solve the problem, we proposed a nonlinear coil sensitivity estimation method based on steering kernel regression, which performs a local gradient guided interpolation to the coil sensitivity. The in vivo experimental results demonstrate that this method can effectively suppress Gibbs ringing artifact in coil sensitivity and reduces both noise and residual aliasing artifact level in SENSE reconstruction.

An efficient non-iterative reconstruction algorithm for parallel MRI with arbitrary k-space trajectories

Parallel imaging using multiple receiver coils has emerged as an effective tool to reduce imaging time in various MRI applications. Although several different image reconstruction methods have been developed and demonstrated to be successful for Cartesian k-space trajectories, there is a lack of efficient reconstruction methods for arbitrary trajectories. In this paper, we formulate the reconstruction problem in k-space and propose a novel image reconstruction method that is fast and effective for arbitrary trajectories. To obtain the desired image, the method reconstructs the Nyquist-sampled k-space data of the image on a uniform Cartesian grid from the undersampled multichannel k-space data on an arbitrary grid, followed by inverse Fourier transform. We demonstrate the effectiveness of the proposed fast algorithm using simulations. In particular, we compare the proposed method with the existing iterative method and show that the former is able to achieve similar image quality to the latter but with reduced computational complexity.

Kalman filter techniques for accelerated Cartesian dynamic cardiac imaging

In dynamic MRI, spatial and temporal parallel imaging can be exploited to reduce scan time. Real-time reconstruction enables immediate visualization during the scan. Commonly used view-sharing techniques suffer from limited temporal resolution, and many of the more advanced reconstruction methods are either retrospective, time-consuming, or both. A Kalman filter model capable of real-time reconstruction can be used to increase the spatial and temporal resolution in dynamic MRI reconstruction. The original study describing the use of the Kalman filter in dynamic MRI was limited to non-Cartesian trajectories because of a limitation intrinsic to the dynamic model used in that study. Here the limitation is overcome, and the model is applied to the more commonly used Cartesian trajectory with fast reconstruction. Furthermore, a combination of the Kalman filter model with Cartesian parallel imaging is presented to further increase the spatial and temporal resolution and signal-to-noise ratio. Simulations and experiments were conducted to demonstrate that the Kalman filter model can increase the temporal resolution of the image series compared with view-sharing techniques and decrease the spatial aliasing compared with TGRAPPA. The method requires relatively little computation, and thus is suitable for real-time reconstruction.

SENSE with improved tolerance to inaccuracies in coil sensitivity maps

In this work, an extension of the Cartesian sensitivity encoding (SENSE) parallel imaging framework is proposed. In the well-known SENSE solution, the overdetermined reconstruction inversion problem is optimized to get the highest signal-to-noise ratio in the image. In this extension, the probability of artifacts due to incorrect knowledge of the receiver coil sensitivities is also taken into account. This is realized by assuming an uncertainty in measured receiver coil sensitivities to enable weighting of residual artifact level and signal-to-noise ratio in the inversion problem. This inversion problem can still be solved by a least-squares optimization without the need of any complex iterative scheme. Results in abdominal imaging show that artifact levels can be substantially reduced, at the cost of a signal-to-noise ratio penalty. The size of the signal-to-noise ratio penalty depends on the assumed inaccuracy of the coil sensitivities, sensitivity encoding acceleration factor, and coil configuration.

Nonlinear GRAPPA: a kernel approach to parallel MRI reconstruction

GRAPPA linearly combines the undersampled k-space signals to estimate the missing k-space signals where the coefficients are obtained by fitting to some auto-calibration signals (ACS) sampled with Nyquist rate based on the shift-invariant property. At high acceleration factors, GRAPPA reconstruction can suffer from a high level of noise even with a large number of auto-calibration signals. In this work, we propose a nonlinear method to improve GRAPPA. The method is based on the so-called kernel method which is widely used in machine learning. Specifically, the undersampled k-space signals are mapped through a nonlinear transform to a high-dimensional feature space, and then linearly combined to reconstruct the missing k-space data. The linear combination coefficients are also obtained through fitting to the ACS data but in the new feature space. The procedure is equivalent to adding many virtual channels in reconstruction. A polynomial kernel with explicit mapping functions is investigated in this work. Experimental results using phantom and in vivo data demonstrate that the proposed nonlinear GRAPPA method can significantly improve the reconstruction quality over GRAPPA and its state-of-the-art derivatives.

Parallel reconstruction using null operations

A novel iterative k-space data-driven technique, namely parallel reconstruction using null operations (PRUNO), is presented for parallel imaging reconstruction. In PRUNO, both data calibration and image reconstruction are formulated into linear algebra problems based on a generalized system model. An optimal data calibration strategy is demonstrated by using singular value decomposition, and an iterative conjugate-gradient approach is proposed to efficiently solve missing k-space samples during reconstruction. With its generalized formulation and precise mathematical model, PRUNO reconstruction yields good accuracy, flexibility, and stability. Both computer simulation and in vivo studies have shown that PRUNO produces much better reconstruction quality than generalized autocalibrating partially parallel acquisition (GRAPPA), especially under high accelerating rates. With the aid of PRUNO reconstruction, ultra-high accelerating parallel imaging can be performed with decent image quality. For example, we have done successful PRUNO reconstruction at a reduction factor of 6 (effective factor of 4.44) with eight coils and only a few autocalibration signal lines.

ICE decoupling technique for RF coil array designs

PURPOSE

Parallel magnetic resonance imaging (MRI) requires an array of RF coil elements with different sensitivity distributions and with minimal electromagnetic coupling. The goal of this project was to develop a new method based on induced current compensation or elimination (ICE) for improved coil element decoupling and to investigate its performance in phantom MR images.

METHODS

An electromagnetic decoupling method based on induced current compensation or elimination for nonoverlapping RF coil arrays was developed with the design criteria of high efficiency, easy implementation, and no physical connection to RF array elements. An eigenvalue/eigenvector approach was employed to analyze the decoupling mechanism and condition. A two-channel microstrip array and an eight-channel coil array were built to test the performance of the method. Following workbench tests, MR imaging experiments were performed on a 7T MR scanner.

RESULTS

The bench tests showed that both arrays achieved sufficient decoupling with a S21 less than -25 dB among the coil elements at 298 MHz. The MR phantom images demonstrated well-defined sensitivity distributions from each coil element and the unique decoupling capability of the proposed ICE decoupling technique. B1 distributions of the individual elements were also measured and calculated.

CONCLUSIONS

The theoretical analysis and experiments demonstrated the feasibility of the decoupling method for high field RF coil array designs without overlapping or direct physical connections between coil elements, which provide more flexibility for coil array design and optimization. The method offers a new approach to address the RF array decoupling issue, which is a major challenge in implementing parallel imaging.

Parallel magnetic resonance imaging using localized receive arrays with sinc interpolation (PILARS)

Large arrays with localized coil sensitivity make it possible to use parallel imaging to significantly accelerate MR imaging speed. However, the need for auto calibration signals limits the actual acceleration factors achievable with large arrays. This paper presents a novel method for parallel imaging with large arrays. The method uses Sinc kernels for k-space data interpolation that only requires one phase parameter to be estimated using a small size of calibration signals. Simulations based on synthetic array data and phantom experiments show that the new method can achieve higher actual acceleration factors with comparable reconstruction quality.

SPIRiT: Iterative self-consistent parallel imaging reconstruction from arbitrary k-space

A new approach to autocalibrating, coil-by-coil parallel imaging reconstruction, is presented. It is a generalized reconstruction framework based on self-consistency. The reconstruction problem is formulated as an optimization that yields the most consistent solution with the calibration and acquisition data. The approach is general and can accurately reconstruct images from arbitrary k-space sampling patterns. The formulation can flexibly incorporate additional image priors such as off-resonance correction and regularization terms that appear in compressed sensing. Several iterative strategies to solve the posed reconstruction problem in both image and k-space domain are presented. These are based on a projection over convex sets and conjugate gradient algorithms. Phantom and in vivo studies demonstrate efficient reconstructions from undersampled Cartesian and spiral trajectories. Reconstructions that include off-resonance correction and nonlinear l(1)-wavelet regularization are also demonstrated.

Optimized parallel imaging for dynamic PC-MRI with multidirectional velocity encoding

Phase contrast MRI with multidirectional velocity encoding requires multiple acquisitions of the same k-space lines to encode the underlying velocities, which can considerably lengthen the total scan time. To reduce scan time, parallel imaging is often applied. In dynamic phase contrast MRI using standard generalized autocalibrating partially parallel acquisitions (GRAPPA), several central k-spaces for autocalibration of the reconstruction (autocalibrating signal lines (ACS)) are typically acquired, separately for each velocity direction and each cardiac timeframe, for calculating the reconstruction weights. To further accelerate data acquisition, we developed two methods, which calculated weights with a substantially reduced number of ACSl lines. The effects on image quality and flow quantification were compared to fully sampled data, standard GRAPPA, and time-interleaved sampling scheme in combination with generalized autocalibrating partially parallel acquisitions (TGRAPPA). The results show that the two proposed methods can clearly improve scan efficiency while maintaining image quality and accuracy of measured flow or myocardial tissue velocities. Compared to TGRAPPA, the proposed methods were more accurate in evaluating flow velocity. In conclusion, the proposed reconstruction strategies are promising for dynamic multidirectionally encoded acquisitions and can easily be implemented using the standard GRAPPA reconstruction algorithm.

POCS-enhanced correction of motion artifacts in parallel MRI

A new method for correction of MRI motion artifacts induced by corrupted k-space data, acquired by multiple receiver coils such as phased arrays, is presented. In our approach, a projections onto convex sets (POCS)-based method for reconstruction of sensitivity encoded MRI data (POCSENSE) is employed to identify corrupted k-space samples. After the erroneous data are discarded from the dataset, the artifact-free images are restored from the remaining data using coil sensitivity profiles. The error detection and data restoration are based on informational redundancy of phased-array data and may be applied to full and reduced datasets. An important advantage of the new POCS-based method is that, in addition to multicoil data redundancy, it can use a priori known properties about the imaged object for improved MR image artifact correction. The use of such information was shown to improve significantly k-space error detection and image artifact correction. The method was validated on data corrupted by simulated and real motion such as head motion and pulsatile flow.

Multiple-mouse MRI with multiple arrays of receive coils

Compared to traditional single-animal imaging methods, multiple-mouse MRI has been shown to dramatically improve imaging throughput and reduce the potentially prohibitive cost for instrument access. To date, up to a single radiofrequency coil has been dedicated to each animal being simultaneously scanned, thus limiting the sensitivity, flexibility, and ultimate throughput. The purpose of this study was to investigate the feasibility of multiple-mouse MRI with a phased-array coil dedicated to each animal. A dual-mouse imaging system, consisting of a pair of two-element phased-array coils, was developed and used to achieve acceleration factors greater than the number of animals scanned at once. By simultaneously scanning two mice with a retrospectively gated cardiac cine MRI sequence, a 3-fold acceleration was achieved with signal-to-noise ratio in the heart that is equivalent to that achieved with an unaccelerated scan using a commercial mouse birdcage coil.

Variable-density parallel imaging with partially localized coil sensitivities

Partially parallel imaging with localized sensitivities is a fast parallel image reconstruction method for both Cartesian and non-Cartesian trajectories, but suffers from aliasing artifacts when there are deviations from the assumption of perfect localization. Such reconstructions would normally crop the individual coil images to remove the artifacts prior to combination. However, the sampling densities in variable-density k-space trajectories support different field-of-views for separate regions in k -space. In fact, the higher sampling density of low frequencies can be used to reconstruct a bigger field-of-view without introducing aliasing artifacts and the resulting image signal-to-noise ratio (SNR) can be improved. A novel, fast variable-density parallel imaging method is presented, which reconstructs different field-of-views from separate frequencies according to the local sampling density in k-space. Aliasing-suppressed images can be produced with high SNR-efficiency without the need for accurate estimation of coil sensitivities and complex or iterative computations.

Combining RF encoding with parallel imaging: a simulation study

OBJECT

The aim of this work was to investigate combining spatial encoding by radio frequency (RF) excitation with conventional parallel imaging (PI) methods to determine whether this could improve overall imaging performance.

MATERIALS AND METHODS

A simulation framework was developed to predict imaging performance for regular, central and random under-sampled parallel imaging methods augmented by RF spatial signal modulation. Optimisation methods were used to find the RF modulation patterns that produce optimal image reconstruction using the condition number of the PI encoding matrix as a quality metric. The diverse patterns of raw data sampling produced were compared using a measure of data uniformity across k-space.

RESULTS

Regular under-sampling of k-space provided the best reconstruction quality. When other under-sampling schemes were employed then RF modulation could be used to improve reconstruction, with the optimum achieved by redistributing the signal in k-space to return to regular sub-sampling. For all tested under-sampling patterns, no further improvements in image quality were attained.

CONCLUSION

Using the simulation framework and metrics described the interaction of different spatial encoding approaches could be investigated. Regular sub-sampling provided optimal reconstruction, independent of whether the spatial encoding was achieved by gradients only or a combination of gradient and RF.

Image reconstructions with the rotating RF coil

Recent studies have shown that rotating a single RF transceive coil (RRFC) provides a uniform coverage of the object and brings a number of hardware advantages (i.e. requires only one RF channel, averts coil-coil coupling interactions and facilitates large-scale multi-nuclear imaging). Motion of the RF coil sensitivity profile however violates the standard Fourier Transform definition of a time-invariant signal, and the images reconstructed in this conventional manner can be degraded by ghosting artifacts. To overcome this problem, this paper presents Time Division Multiplexed-Sensitivity Encoding (TDM-SENSE), as a new image reconstruction scheme that exploits the rotation of the RF coil sensitivity profile to facilitate ghost-free image reconstructions and reductions in image acquisition time. A transceive RRFC system for head imaging at 2 Tesla was constructed and applied in a number of in vivo experiments. In this initial study, alias-free head images were obtained in half the usual scan time. It is hoped that new sequences and methods will be developed by taking advantage of coil motion.

K-space reconstruction of magnetic resonance inverse imaging (K-InI) of human visuomotor systems

Using simultaneous measurements from multiple channels of a radio-frequency coil array, magnetic resonance inverse imaging (InI) can achieve ultra-fast dynamic functional imaging of the human with whole-brain coverage and a good spatial resolution. Mathematically, the InI reconstruction is a generalization of parallel MRI (pMRI), which includes image space and k-space reconstructions. Because of the auto-calibration technique, the pMRI k-space reconstruction offers more robust and adaptive reconstructions compared to the image space algorithm. Here we present the k-space InI (K-InI) reconstructions to reconstruct the highly accelerated BOLD-contrast fMRI data of the human brain to achieve 100 ms temporal resolution. Simulations show that K-InI reconstructions can offer 3D image reconstructions at each time frame with reasonable spatial resolution, which cannot be obtained using the previously proposed image space minimum-norm estimates (MNE) or linear constraint minimum variance (LCMV) spatial filtering reconstructions. The InI reconstructions of in vivo BOLD-contrast fMRI data during a visuomotor task show that K-InI offer 3 to 5 fold more sensitive detection of the brain activation than MNE and a comparable detection sensitivity to the LCMV reconstructions. The group average of the high temporal resolution K-InI reconstructions of the hemodynamic response also shows a relative onset timing difference between the visual (first) and somatomotor (second) cortices by 400 ms (600 ms time-to-peak timing difference). This robust and sensitive K-InI reconstruction can be applied to dynamic MRI acquisitions using a large-n coil array to improve the spatiotemporal resolution.

Single echo acquisition MRI using RF encoding

Encoding of spatial information in magnetic resonance imaging is conventionally accomplished by using magnetic field gradients. During gradient encoding, the position in k-space is determined by a time-integral of the gradient field, resulting in a limitation in imaging speed due to either gradient power or secondary effects such as peripheral nerve stimulation. Partial encoding of spatial information through the sensitivity patterns of an array of coils, known as parallel imaging, is widely used to accelerate the imaging, and is complementary to gradient encoding. This paper describes the one-dimensional limit of parallel imaging in which all spatial localization in one dimension is performed through encoding by the radiofrequency (RF) coil. Using a one-dimensional array of long and narrow parallel elements to localize the image information in one direction, an entire image is obtained from a single line of k-space, avoiding rapid or repeated manipulation of gradients. The technique, called single echo acquisition (SEA) imaging, is described, along with the need for a phase compensation gradient pulse to counteract the phase variation contained in the RF coil pattern which would otherwise cause signal cancellation in each imaging voxel. Image reconstruction and resolution enhancement methods compatible with the speed of the technique are discussed. MR movies at frame rates of 125 frames per second are demonstrated, illustrating the ability to monitor the evolution of transverse magnetization to steady state during an MR experiment as well as demonstrating the ability to image rapid motion. Because this technique, like all RF encoding approaches, relies on the inherent spatially varying pattern of the coil and is not a time-integral, it should enable new applications for MRI that were previously inaccessible due to speed constraints, and should be of interest as an approach to extending the limits of detection in MR imaging.