A homogeneity correction method for magnetic resonance imaging with time-varying gradients

When time-varying gradients are used for imaging, the off-resonance behavior does not just cause geometric distortion as is the case with spin-warp imaging, but changes the shape of the impulse response and causes blurring. This effect is well known for projection reconstruction and spiral k-space scanning sequences. The authors introduce a reconstruction and homogeneity correction method to correct for the zeroth order effects of inhomogeneity using prior knowledge of the inhomogeneity. In this method, the data are segmented according to collection time, reconstructed using some fast, linear algorithm, correlated for inhomogeneity, and then superimposed to yield a homogeneity corrected image. This segmented method is compared to a conjugate phase reconstruction in terms of degree of correction and execution time. The authors apply this method to in vivo images using projection-reconstruction and spiral-scan sequences.     

A New Distortion Model for Strong Inhomogeneity Problems in Echo-Planar MRI

This paper proposes a new distortion model for strong inhomogeneity problems in echo planar imaging (EPI). Fast imaging sequences in magnetic resonance imaging (MRI), such as EPI, are very important in applications where temporal resolution or short total acquisition time is essential. Unfortunately, fast imaging sequences are very sensitive to variations in the homogeneity of the main magnetic field. The inhomogeneity leads to geometrical distortions and intensity changes in the image reconstructed via fast Fourier transform. Also, under strong inhomogeneity, the accelerated intravoxel dephase may overly attenuate signals coming from regions with higher inhomogeneity variations. Moreover, coarse discretization schemes for the inhomogeneity are not able to cope with this problem, producing discretization artifacts when large inhomogeneity variations occur. Most of the existing models do not attempt to solve this problem. In this paper, we propose a modification of the discrete distortion model to incorporate the effects of the intravoxel inhomogeneity and to minimize the discretization artifacts. As a result, these problems are significantly reduced. Extensive experiments are shown to demonstrate the achieved improvements. Also, the performance of the new model is evaluated for conjugate phase, least squares method (minimized iteratively using conjugated gradients), and regularized methods (using a total variation penalty).      

Off-resonance correction of MR images

In magnetic resonance imaging (MRI), the spatial inhomogeneity of the static magnetic field can cause degraded images if the reconstruction is based on inverse Fourier transformation. This paper presents and discusses a range of fast reconstruction algorithms that attempt to avoid such degradation by taking the field inhomogeneity into account. Some of these algorithms are new, others are modified versions of known algorithms. Speed and accuracy of all these algorithms are demonstrated using spiral MRI.     

Reconstruction by weighted correlation for MRI with time-varying gradients

A general reconstruction algorithm for magnetic resonance imaging (MRI) with gradients having arbitrary time dependence is presented. This method estimates spin density by calculating the weighted correlation of the observed free induction decay signal and the phase modulation function at each point. A theorem which states that this method can be derived from the conditions of linearity and shift invariance is presented. Since these conditions are general, most of the MRI reconstruction algorithms proposed so far are equivalent to the weighted correlation method. An explicit representation of the point spread function (PSF) in the weighted correlation method is given. By using this representation, a method to control the PSF and the static field inhomogeneity effects is studied. A correction method for the inhomogeneity is proposed, and a limitation is clarified. Some simulation results are presented.     

Inhomogeneity and multiple dimension considerations in magnetic resonance imaging with time-varying gradients

The inhomogeneity of the main magnetic field is a significant factor limiting the performance and increasing the cost of commercial magnetic resonance imaging (MRI) and spectroscopy machines. This is particularly true where shielding is employed to limit fringing fields. In this paper, we investigate the performance of a recently introduced MRI technique using time-varying gradients in the presence of such inhomogeneity. It is shown that the time-varying gradient imaging system can accommodate considerable inhomogeneities (1000 ppm in typical imaging application). The problem of selection of the gradient frequencies for simultaneous multiple dimension imaging in the presence of inhomogeneity is formulated and solved.     

Iterative reconstruction of single-shot spiral MRI with offresonance

A variety of applications and research directions in magnetic resonance imaging which require fast scan times have recently become popular. In order to satisfy many of the requirements of these applications, snapshot imaging methods, which acquire an entire image in one excitation, are often used. These snapshot techniques are relatively insensitive to motion and can allow rapidly occurring processes to be imaged. However, snapshot imaging techniques acquire data over a relatively long period, during which off-resonance phase can accumulate, leading to image degradation. This degradation often limits the usefulness of the images. Presented here is a method to iteratively reconstruct an image acquired by a spiral snapshot technique and to remove image degradation due to off resonance. This iterative method does not assume that the inhomogeneity is slowly varying within the image, allowing better results than with deblurring techniques which do not take abrupt changes into account. Although presented here with a spiral imaging technique, the iterative algorithm is general enough to be applied to a variety of snapshot imaging techniques.     

Joint Estimation and Correction of Geometric Distortions for EPI Functional MRI Using Harmonic Retrieval

Magnetic resonance imaging (MRI) uses applied spatial variations in the magnetic field to encode spatial position. Therefore, nonuniformities in the main magnetic field can cause image distortions. In order to correct the image distortions, it is desirable to simultaneously acquire data with a field map in registration. We propose a joint estimation (JE) framework with a fast, noniterative approach using harmonic retrieval (HR) methods, combined with a multi-echo echo-planar imaging (EPI) acquisition. The connection with HR establishes an elegant framework to solve the JE problem through a sequence of 1-D HR problems in which efficient solutions are available. We also derive the condition on the smoothness of the field map in order for HR techniques to recover the image with high signal-to-noise ratio. Compared to other dynamic field mapping methods, this method is not constrained by the absolute level of the field inhomogeneity over the slice, but relies on a generous pixel-to-pixel smoothness. Moreover, this method can recover image, field map, and T2* map simultaneously.      

Regularized field map estimation in MRI

In fast magnetic resonance (MR) imaging with long readout times, such as echo-planar imaging (EPI) and spiral scans, it is important to correct for the effects of field inhomogeneity to reduce image distortion and blurring. Such corrections require an accurate field map, a map of the off-resonance frequency at each voxel. Standard field map estimation methods yield noisy field maps, particularly in image regions with low spin density. This paper describes regularized methods for field map estimation from two or more MR scans having different echo times. These methods exploit the fact that field maps are generally smooth functions. The methods use algorithms that decrease monotonically a regularized least-squares cost function, even though the problem is highly nonlinear. Results show that the proposed regularized methods significantly improve the quality of field map estimates relative to conventional unregularized methods.      

Field inhomogeneity correction based on gridding reconstruction for magnetic resonance imaging

Spatial variations of the main field give rise to artifacts in magnetic resonance images if disregarded in reconstruction. With non-Cartesian k-space sampling, they often lead to unacceptable blurring. Data from such acquisitions are usually reconstructed with gridding methods and optionally restored with various correction methods. Both types of methods essentially face the same basic problem of adequately approximating an exponential function to enable an efficient processing with fast Fourier transforms. Nevertheless, they have commonly addressed it differently so far. In the present work, a unified approach is pursued. The principle behind gridding methods is first generalized to nonequispaced sampling in both domains and then applied to field inhomogeneity correction. Three new algorithms, which are compatible with a direct conjugate phase and an iterative algebraic reconstruction, are derived in this way from a straightforward embedding of the data into a higher dimensional space. Their evaluation in simulations and phantom experiments with spiral k-space sampling shows that one of them promises to provide a favorable compromise between fidelity and complexity compared with existing algorithms. Moreover, it allows a simple choice of key parameters involved in approximating an exponential function and a balance between the accuracy of reconstruction and correction.     

Real-time image reconstruction for spiral MRI using fixed-point calculation

Because spiral magnetic resonance imaging (MRI) is more robust to motion artifacts than echo planar imaging (EPI), spiral imaging method is more suitable in real-time imaging applications where dynamic processes are to be observed. The major hurdle to use spiral imaging method in real-time applications is its slow reconstruction speed. Since spiral trajectories do not sample data on rectilinear grids, raw data must be regridded before inverse fast Fourier transform (FFT). At present, the computational cost for the spiral reconstruction algorithm is still too high and it is not fast enough to achieve the minimum speed requirement of 20 frames/s for real-time imaging applications. In this paper, we propose to replace floating-point calculations with fixed-point calculations in the reconstruction algorithm to remove the computational bottlenecks. To overcome the quantization and round-off errors introduced by fixed-point calculations, we devise a method to find the optimal precision for the fixed-point representation. Adding with a highly efficient vector-radix two-dimensional (2-D) FFT algorithm and modifications to speed up the gridding convolution, we have cut the reconstruction time by 42% and achieved real-time reconstruction at 30 frames/s for 128 x 128 matrices on low-cost PC's.     

A technique for accurate magnetic resonance imaging in the presence of field inhomogeneities

A technique for producing geometrically accurate magnetic resonance images (MRIs) with undistorted intensity in the face of high levels of static field inhomogeneity arising from either source is presented. The technique requires the acquisition of two images of the same object with altered gradients. On the basis of a knowledge of these gradients it employs an automatic postprocessing step that exploits some invariant characteristics of the distortions to produce a rectified image from the two acquired images. No phantom imaging is involved and no operator interaction is required. The technique is theoretically justified and compared to other techniques, and experimental results that show that the technique works are presented. The improved accuracy in geometry and intensity may improve reliability of stereotactic surgery, may enhance the feasibility of both clinical and industrial imaging via external fields, and may increase the resolution of microscopic imaging.     

Augmented Lagrangian based reconstruction of non-uniformly sub-Nyquist sampled MRI data

MRI has recently been identified as a promising application for compressed-sensing-like regularization because of its potential to speed up the acquisition while maintaining the image quality. Thereby non-uniform k-space trajectories, such as random or spiral trajectories, are becoming more and more important, because they are well suited to be used within the compressed-sensing (CS) acquisition framework. In this paper, we propose a new reconstruction technique for non-uniformly sub-Nyquist sampled k-space data. Several parts make up this technique, such as the non-uniform Fourier transform (NUFT), the discrete shearlet transform and a augmented Lagrangian based optimization algorithm. Because MRI images are real-valued, we introduce a new imaginary value suppressing prior, which attenuates imaginary components of MRI images during reconstruction, resulting in a better overall image quality. Further, a preconditioning based on the Voronoi cell size of each NUFT data point speeds up the conjugate gradient optimization used as part of the optimization algorithm. The resulting algorithm converges in a relatively small number of iterations and guarantees solutions that fully comply to the imposed constraints. The results show that the algorithm is applicable not only to sub-Nyquist sampled k-space reconstruction, but also to MR image fusion and/or resolution enhancement.     

Improved reconstruction for MR spectroscopic imaging

Sensitivity limitations of in vivo magnetic resonance spectroscopic imaging (MRSI) require that the extent of spatial-frequency (k-space) sampling be limited, thereby reducing spatial resolution and increasing the effects of Gibbs ringing that is associated with the use of Fourier transform reconstruction. Additional problems occur in the spectral dimension, where quantitation of individual spectral components is made more difficult by the typically low signal-to-noise ratios, variable lineshapes, and baseline distortions, particularly in areas of significant magnetic field inhomogeneity. Given the potential of in vivo MRSI measurements for a number of clinical and biomedical research applications, there is considerable interest in improving the quality of the metabolite image reconstructions. In this report, a reconstruction method is described that makes use of parametric modeling and MRI-derived tissue distribution functions to enhance the MRSI spatial reconstruction. Additional preprocessing steps are also proposed to avoid difficulties associated with image regions containing spectra of inadequate quality, which are commonly present in the in vivo MRSI data     

Compressed sensing with wavelet domain dependencies for coronary MRI: a retrospective study

Coronary magnetic resonance imaging (MRI) is a noninvasive imaging modality for diagnosis of coronary artery disease. One of the limitations of coronary MRI is its long acquisition time due to the need of imaging with high spatial resolution and constraints on respiratory and cardiac motions. Compressed sensing (CS) has been recently utilized to accelerate image acquisition in MRI. In this paper, we develop an improved CS reconstruction method, Bayesian least squares-Gaussian scale mixture (BLS-GSM), that uses dependencies of wavelet domain coefficients to reduce the observed blurring and reconstruction artifacts in coronary MRI using traditional l(1) regularization. Images of left and right coronary MRI was acquired in 7 healthy subjects with fully-sampled k-space data. The data was retrospectively undersampled using acceleration rates of 2, 4, 6, and 8 and reconstructed using l(1) thresholding, l(1) minimization and BLS-GSM thresholding. Reconstructed right and left coronary images were compared with fully-sampled reconstructions in vessel sharpness and subjective image quality (1-4 for poor-excellent). Mean square error (MSE) was also calculated for each reconstruction. There were no significant differences between the fully sampled image score versus rate 2, 4, or 6 for BLS-GSM for both right and left coronaries (=N.S.). However, for l(1) thresholding significant differences were observed for rates higher than 2 and 4 for right and left coronaries respectively. l(1) minimization also yields images with lower scores compared to the reference for rates higher than 4 for both coronaries. These results were consistent with the quantitative vessel sharpness readings. BLS-GSM allows acceleration of coronary MRI with acceleration rates beyond what can be achieved with l(1) regularization.     

Multishot rosette trajectories for spectrally selective MR imaging

In nuclear magnetic resonance, different spectral components often correspond to different chemical species and as such, spectral selectivity can be a valuable tool for diagnostic imaging. In the work presented here, a multishot image acquisition method based upon rosette k-space trajectories has been developed and implemented for spectrally selective magnetic resonance imaging (MRI). Parametric forms for the gradient waveforms and design constraints are derived, and an example multishot gradient design is presented. The spectral behaviour for this imaging method is analyzed in a simulation model. For frequencies that are near to the resonant frequency, this method results in a lower intensity, but undistorted image, while for frequencies that are off-resonance by a large amount, the object is incoherently dephased into noise. A method by which acquisitions are delayed by small amounts is introduced to further reduce the residual intensity for off-resonant signals. An image reconstruction method based on convolution gridding, including a correction method for small amounts of magnetic field inhomogeneity, is implemented. Finally, the spectral selectivity is demonstrated in vivo in a study in which both water and lipid images are generated from a single imaging data set     

Motion-compensated and gated cone beam filtered back-projection for 3-D rotational X-ray angiography

This paper presents a method to reconstruct moving objects from cone beam X-ray projections acquired during a single rotational run using a given motion vector field. The method is applicable to voxel driven cone-beam filtered back-projection reconstruction approaches. Here, a formulation based on the algorithm of Feldkamp, Davis, and Kress (FDK) is presented. The motion correction is applied during the back-projection step by shifting the voxel to be reconstructed according to the motion vector field. The method is applied to three-dimensional (3-D) rotational X-ray angiography. Projections from a beating coronary heart phantom are simulated. Motion-compensated reconstructions with varying accuracy of the applied motion field are carried out for a late diastolic heart phase and compared to the reconstruction obtained with the standard FDK-method from projections of the corresponding motion-free model in the same heart phase. Furthermore, gated reconstructions are calculated by weighting the projections according to their cardiac phase without using a motion vector field. Different gating window widths are applied, and the reconstructions are compared. Using the correct motion field with the motion-compensated reconstruction, the image quality of the standard reconstruction from the corresponding motion-free coronary model can almost be recovered. The reconstructed image quality stays acceptable if the accuracy of the motion field sampling points is better than 1 mm. The gated reconstructions with a window width of 15%-20% of the cardiac cycle lead to superior results compared to nearest neighbor gating, especially for histogram based visualization and analysis. The motion-compensated reconstructions provide sharp images of the coronaries far surpassing the image quality of gated reconstructions.     

Magnetic resonance electrical impedance tomography (MREIT): simulation study of J-substitution algorithm

We developed a new image reconstruction algorithm for magnetic resonance electrical impedance tomography (MREIT). MREIT is a new EIT imaging technique integrated into magnetic resonance imaging (MRI) system. Based on the assumption that internal current density distribution is obtained using magnetic resonance imaging (MRI) technique, the new image reconstruction algorithm called J-substitution algorithm produces cross-sectional static images of resistivity (or conductivity) distributions. Computer simulations show that the spatial resolution of resistivity image is comparable to that of MRI. MREIT provides accurate high-resolution cross-sectional resistivity images making resistivity values of various human tissues available for many biomedical applications.     

Constrained reconstruction applied to 2-D chemical shift imaging

The method of constrained reconstruction, previously applied to magnetic resonance imaging (MRI), is extended to magnetic resonance spectroscopy. This method assumes a model for the MR signal. The model parameters are estimated directly from the phase encoded data. This process obviates the need for the fast Fourier transform (FFT) (which often exhibits limited resolution and ringing artifact). The technique is tested on simulated data, phantom data, and data acquired from human liver in vivo. In each case, constrained reconstruction offers spatial resolution superior to that obtained with the FFT     

A Practical Acceleration Algorithm for Real-Time Imaging

A practical acceleration algorithm for real-time magnetic resonance imaging (MRI) is presented. Neither separate training scans nor embedded training samples are used. The Kalman filter based algorithm provides a fast and causal reconstruction of dynamic MRI acquisitions with arbitrary readout trajectories. The algorithm is tested against abrupt changes in the imaging conditions and offline reconstructions of in vivo cardiac MRI experiments are presented.      

Fast,iterative image reconstruction for MRI in the presence of field inhomogeneities

In magnetic resonance imaging, magnetic field inhomogeneities cause distortions in images that are reconstructed by conventional fast Fourier trasform (FFT) methods. Several noniterative image reconstruction methods are used currently to compensate for field inhomogeneities, but these methods assume that the field map that characterizes the off-resonance frequencies is spatially smooth. Recently, iterative methods have been proposed that can circumvent this assumption and provide improved compensation for off-resonance effects. However, straightforward implementations of such iterative methods suffer from inconveniently long computation times. This paper describes a tool for accelerating iterative reconstruction of field-corrected MR images: a novel time-segmented approximation to the MR signal equation. We use a min-max formulation to derive the temporal interpolator. Speedups of around 60 were achieved by combining this temporal interpolator with a nonuniform fast Fourier transform with normalized root mean squared approximation errors of 0.07%. The proposed method provides fast, accurate, field-corrected image reconstruction even when the field map is not smooth.