IIR GRAPPA for parallel MR image reconstruction

A dual-interpolator method for improving parallel MRI reconstruction

Autocalibration signal is acquired in the k-space-based parallel MRI reconstruction for estimating interpolation coefficients and reconstructing missing unacquired data. Many ACS lines can suppress aliasing artifacts and noise by covering the low-frequency signal region. However, more ACS lines will delay the data acquisition process and therefore elongate the scan time. Furthermore, a single interpolator is often used for recovering missing k-space data, and model error may exist if the single interpolator size is not selected appropriately. In this work, based on the idea of the disagreement-based semi-supervised learning, a dual-interpolator strategy is proposed to collaboratively reconstruct missing k-space data. Two interpolators with different sizes are alternatively applied to estimate and re-estimate missing data in k-space. The disagreement between two interpolators is converged and real missing values are co-estimated from two views. The experimental results show that the proposed method outperforms GRAPPA, SPIRiT, and Nonlinear GRAPPA methods using relatively low number of ACS data, and reduces aliasing artifacts and noise in reconstructed images.

Group feature selection for enhancing information gain in MRI reconstruction

Magnetic resonance imaging (MRI) has revolutionized the radiology. As a leading medical imaging modality, MRI not only visualizes the structures inside body, but also produces functional imaging. However, due to the slow imaging speed constrained by the MR physics, MRI cost is expensive, and patient may feel not comfortable in a scanner for a long time. Parallel MRI has accelerated the imaging speed through the sub-Nyquist sampling strategy and the missing data are interpolated by the multiple coil data acquired. Kernel learning has been used in the parallel MRI reconstruction to learn the interpolation weights and re-construct the undersampled data. However, noise and aliasing artifacts still exist in the reconstructed image and a large number of auto-calibration signal lines are needed. To further improve the kernel learning-based MRI reconstruction and accelerate the speed, this paper proposes a group feature selection strategy to improve the learning performance and enhance the reconstruction quality. An explicit kernel mapping is used for selecting a subset of features which contribute most to estimate the missing k-space data. The experimental results show that the learning behaviours can be better predicted and therefore the reconstructed image quality is improved.

Improving Nonlinear Interpolation of K-Space Data Using Semi-Supervised Learning and Autoregressive Model

Parallel magnetic resonance imaging (pMRI) accelerates data acquisition by undersampling k-space through an array of receiver coils. Finding accurate relationships between acquired and missing k-space data determines the interpolation performance and reconstruction quality. Autocalibration signals (ACS) are generally used to learn the interpolation coefficients for reconstructing the missing k-space data. Based on the estimation-approximation error analysis in machine learning, increasing training data size can reduce estimation error and therefore enhance generalization ability of the interpolator, but scanning time will be longer if more ACS data are acquired. We propose to augment training data using unacquired and acquired data outside of ACS region through semi-supervised learning idea and autoregressive model. Local neighbor unacquired k-space data can be used for training tasks and reducing the generalization error. Experimental results show that the proposed method outperforms the conventional methods by suppressing noise and aliasing artifacts.

Domain knowledge augmentation of parallel MR image reconstruction using deep learning

A deep learning (DL) method for accelerated magnetic resonance (MR) imaging is presented that incorporates domain knowledge of parallel MR imaging to augment the DL networks for accurate and stable image reconstruction. The proposed DL method employs a novel loss function consisting of a combination of mean absolute error, structural similarity, and sobel edge loss. The DL model takes both original measurements and images reconstructed by the parallel imaging method as inputs to the network. The accuracy of the proposed method was evaluated using two anatomical regions and six MRI contrasts and was compared with state-of-the-art parallel imaging and deep learning methods. The proposed method significantly outperformed the other methods for all the six different contrasts in terms of structural similarity, peak signal to noise ratio, and normalized mean squared error. The out-of-sample performance of the proposed method was assessed for a truly "unseen" case in a volunteer scan. The method produced images without any artificial features, often occurring in the DL image reconstruction methods. A stability analysis was performed by adding perturbations to the input, which demonstrated that the proposed method is robust and stable with respect to small structural changes, and different undersampling ratios. Comprehensive validation on large datasets demonstrated that incorporation of domain knowledge sufficiently regularizes the DL based image reconstruction and produces accurate and stable image enhancement.

Improving GRAPPA reconstruction using joint nonlinear kernel mapped and phase conjugated virtual coils

To improve the reconstruction condition and alleviate the noise amplification of GRAPPA reconstruction by aggregating the phase conjugated and nonlinear kernel mapped coils with the original physical coil. Nonlinear GRAPPA (NL-GRAPPA) is a kernel-based non-iterative approach which can reduce noise-induced error in GRAPPA reconstruction. And virtual conjugate coil (VCC) embeds the conjugate symmetric property of k-space into GRAPPA data synthesis to improve reconstruction condition. This work proposed NL-VCC-GRAPPA to jointly utilize the nonlinear mapped virtual coil and phase conjugated virtual coil to further reduce noise amplification in parallel imaging. In vivo static and dynamic 2D imaging accelerated by uniform undersampling schemes were performed to evaluate the proposed method in terms of visual image quality, root-mean-square-error (RMSE), and geometry factor (g-factor). The effects of acceleration factors, calibration data size and kernel shape on the proposed model were also separately analyzed and discussed. The proposed method illustrated improved visual image quality evidenced by reduced retrospective RMSE and prospective g-factor comparing with conventional GRAPPA and the recently proposed iterative SENSE-LORAKS reconstructions. Although a larger amount of calibration data and smaller kernel size were required to stabilize the calibration of fourfold extended kernel for the proposed method, it was non-iterative and relatively insensitive to parameter adjustment in the applications. The proposed NL-VCC-extension to conventional GRAPPA brings visible improvements for imaging scenarios accelerated by the widely available uniform undersampling schemes in a practically efficient manner without iteration.

Instrument Variables for Reducing Noise in Parallel MRI Reconstruction

Generalized autocalibrating partially parallel acquisition (GRAPPA) has been a widely used parallel MRI technique. However, noise deteriorates the reconstructed image when reduction factor increases or even at low reduction factor for some noisy datasets. Noise, initially generated from scanner, propagates noise-related errors during fitting and interpolation procedures of GRAPPA to distort the final reconstructed image quality. The basic idea we proposed to improve GRAPPA is to remove noise from a system identification perspective. In this paper, we first analyze the GRAPPA noise problem from a noisy input-output system perspective; then, a new framework based on errors-in-variables (EIV) model is developed for analyzing noise generation mechanism in GRAPPA and designing a concrete method-instrument variables (IV) GRAPPA to remove noise. The proposed EIV framework provides possibilities that noiseless GRAPPA reconstruction could be achieved by existing methods that solve EIV problem other than IV method. Experimental results show that the proposed reconstruction algorithm can better remove the noise compared to the conventional GRAPPA, as validated with both of phantom and in vivo brain data.

Improving GRAPPA reconstruction by frequency discrimination in the ACS lines

PURPOSE

GRAPPA is a well-known parallel imaging method that recovers the MR magnitude image from aliasing by using a weighted interpolation of the data in k-space. To estimate the optimal reconstruction weights, GRAPPA uses a band along the center of the k-space where the signal is sampled at the Nyquist rate, the so-called autocalibrated (ACS) lines. However, while the subsampled lines usually belong to the medium- to high-frequency areas of the spectrum, the ACS lines include the low-frequency areas around the DC component. The use for estimation and reconstruction of areas of the k-space with very different features may negatively affect the final reconstruction quality. We propose a simple, yet powerful method to eliminate reconstruction artifacts, based on the discrimination of the low-frequency spectrum.

METHODS

The proposal to improve the estimation of the weights lays on a proper selection of the coefficients within the ACS lines, which advises discarding those points around the DC component. A simple approach is the elimination of a square window in the center of the k-space, although more developed approaches can be used.

RESULTS

The method is tested using real multiple-coil MRI acquisitions. We empirically show this approach achieves great enhancement rates, while keeping the same complexity of the original GRAPPA and reducing the g-factor. The reconstruction is even more accurate when combined with other reconstruction methods. Improvement rates of 35% are achieved for 32 ACS and acceleration rate of 3.

CONCLUSIONS

The method proposed highly improves the accuracy of the GRAPPA coefficients and therefore the final image reconstruction. The method is fully compatible with the original GRAPPA formulation and with other optimization methods proposed in literature, and it can be easily implemented into the commercial scanning software.

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.

Derivative encoding for parallel magnetic resonance imaging

PURPOSE

To introduce a linear shift-invariant relationship between the partial derivatives of k space signals acquired using multichannel receive coils and to demonstrate that k space derivatives can be used for image unwrapping.

METHODS

Fourier transform of k space derivatives contains information on the spatial origins of aliased pixels; therefore, images can be reconstructed by k space derivatives. Fully sampled phantom and brain images acquired at 3 T using a standard eight channel receive coil were used to validate the k space derivatives theorem by unwrapping aliased images.

RESULTS

Derivative encoding leads to new methods for parallel imaging reconstruction in both k space and image domains. Noise amplification in sensitivity encoding image reconstruction, which is considered to produce the optimal SNR, can be further reduced using k space derivative encoding without making any assumptions on the characteristics of the images to be reconstructed.

CONCLUSIONS

This work demonstrated that the partial derivative of the k space signal acquired from one coil with respect to one direction can be expressed as a sum of partial derivatives of signals from multiple coils with respect to the perpendicular k space direction(s). This relationship between the partial derivatives of k space signals is linear and shift-invariant in the Cartesian coordinate system.

Adaptive self-calibrating iterative GRAPPA reconstruction

Parallel magnetic resonance imaging in k-space such as generalized auto-calibrating partially parallel acquisition exploits spatial correlation among neighboring signals over multiple coils in calibration to estimate missing signals in reconstruction. It is often challenging to achieve accurate calibration information due to data corruption with noises and spatially varying correlation. The purpose of this work is to address these problems simultaneously by developing a new, adaptive iterative generalized auto-calibrating partially parallel acquisition with dynamic self-calibration. With increasing iterations, under a framework of the Kalman filter spatial correlation is estimated dynamically updating calibration signals in a measurement model and using fixed-point state transition in a process model while missing signals outside the step-varying calibration region are reconstructed, leading to adaptive self-calibration and reconstruction. Noise statistic is incorporated in the Kalman filter models, yielding coil-weighted de-noising in reconstruction. Numerical and in vivo studies are performed, demonstrating that the proposed method yields highly accurate calibration and thus reduces artifacts and noises even at high acceleration.

Cross-sampled GRAPPA for parallel MRI

As one widely-used parallel-imaging method, Generalized Auto-calibrating Partially Parallel Acquisitions (GRAPPA) technique reconstructs the missing k-space data by a linear combination of the acquired data using a set of weights. These weights are usually derived from auto-calibration signal (ACS) lines that are acquired in parallel to the reduced lines. In this paper, a cross sampling method is proposed to acquire the ACS lines orthogonal to the reduced lines. This cross sampling method increases the amount of calibration data along the direction that the k-space is undersampled and thus improves the calibration accuracy, especially when a small number of ACS lines are acquired. Both phantom and in vivo experiments demonstrate that the proposed method, named cross-sampled GRAPPA (CS-GRAPPA), can effectively reduce the aliasing artifacts of GRAPPA when high acceleration is desired.

An electromagnetic reverse method of coil sensitivity mapping for parallel MRI - theoretical framework

In this paper, a novel sensitivity mapping method is proposed for the image domain parallel MRI (pMRI) technique. Instead of refining raw sensitivity maps by means of conventional image processing operations such as polynomial fitting, the presented method determines coil sensitivity profiles through an iterative optimization process. During the algorithm implementation the optimization cost function is defined as the difference between the raw sensitivity profile and the desired profile. The minimization is governed by the physics of low-frequency electromagnetic and reciprocity theories. The performance of the method was theoretically investigated and compared with that of a traditional polynomial fitting, against a range of system noise levels. It was found that, the new method produces high-fidelity sensitivity profiles with noise amplitudes, measured as root mean square deviation an order of magnitude less than that of the polynomial fitting method. Using the sensitivity profiles generated by our method, SENSE (sensitivity encoding) reconstructions produce significantly less image artefacts than conventional methods. The successful implementation of this method has far-reaching implications that accurate sensitivity mapping is not only important for parallel reconstruction, but also essential for its transmission analogy, such as Transmit SENSE.