Iterative reconstruction of single-shot spiral MRI with off resonance

Selection criteria of image reconstruction algorithms for terahertz short-range imaging applications

Terahertz (THz) imaging has been regarded as cutting-edge technology in a wide range of applications due to its ability to penetrate through opaque materials, non-invasive nature, and its increased bandwidth capacity. Recently, THz imaging has been extensively researched in security, driver assistance technology, non-destructive testing, and medical applications. The objective of this review is to summarize the selection criteria for current state-of-the-art THz image reconstruction algorithms developed for short-range imaging applications over the last two decades. Moreover, we summarize the selected algorithms' performance and their implementation process. This study provides an in-depth understanding of the fundamentals of image reconstruction algorithms related to THz short-range imaging and future aspects of algorithm processing and selection.

A Spatial Off-Resonance Correction in Spirals for Magnetic Resonance Fingerprinting

In MR Fingerprinting (MRF), balanced Steady-State Free Precession (bSSFP) has advantages over unbalanced SSFP because it retains the spin history achieving a higher signal-to-noise ratio (SNR) and scan efficiency. However, bSSFP-MRF is not frequently used because it is sensitive to off-resonance, producing artifacts and blurring, and affecting the parametric map quality. Here we propose a novel Spatial Off-resonance Correction (SOC) approach for reducing these artifacts in bSSFP-MRF with spiral trajectories. SOC-MRF uses each pixel's Point Spread Function to create system matrices that encode both off-resonance and gridding effects. We iteratively compute the inverse of these matrices to reduce the artifacts. We evaluated the proposed method using brain simulations and actual MRF acquisitions of a standardized T1/T2 phantom and five healthy subjects. The results show that the off-resonance distortions in T1/T2 maps were considerably reduced using SOC-MRF. For T2, the Normalized Root Mean Square Error (NRMSE) was reduced from 17.3 to 8.3% (simulations) and from 35.1 to 14.9% (phantom). For T1, the NRMS was reduced from 14.7 to 7.7% (simulations) and from 17.7 to 6.7% (phantom). For in-vivo, the mean and standard deviation in different ROI in white and gray matter were significantly improved. For example, SOC-MRF estimated an average T2 for white matter of 77ms (the ground truth was 74ms) versus 50 ms of MRF. For the same example the standard deviation was reduced from 18 ms to 6ms. The corrections achieved with the proposed SOC-MRF may expand the potential applications of bSSFP-MRF, taking advantage of its better SNR property.

Cardiac real-time MRI using a pre-emphasized spiral acquisition based on the gradient system transfer function

PURPOSE

Segmented Cartesian acquisition in breath hold represents the current gold standard for cardiac functional MRI. However, it is also associated with long imaging times and severe restrictions in arrhythmic or dyspneic patients. Therefore, we introduce a real-time imaging technique based on a spoiled gradient-echo sequence with undersampled spiral k-space trajectories corrected by a gradient pre-emphasis.

METHODS

A fully automatic gradient waveform pre-emphasis based on the gradient system transfer function was implemented to compensate for gradient inaccuracies, to optimize fast double-oblique spiral MRI. The framework was tested in a phantom study and subsequently transferred to compressed sensing-accelerated cardiac functional MRI in real time. Spiral acquisitions during breath hold and free breathing were compared with this reference method for healthy subjects (N = 7) as well as patients (N = 2) diagnosed with heart failure and arrhythmia. Left-ventricular volumes and ejection fractions were determined and analyzed using a Wilcoxon signed-rank test.

RESULTS

The pre-emphasis successfully reduced typical artifacts caused by k-space misregistrations. Dynamic cardiac imaging was possible in real time (temporal resolution < 50 ms) with high spatial resolution (1.34 × 1.34 mm² ), resulting in a total scan time of less than 50 seconds for whole heart coverage. Comparable image quality, as well as similar left-ventricular volumes and ejection fractions, were observed for the accelerated and the reference method.

CONCLUSION

The proposed technique enables high-resolution real-time cardiac MRI with no need for breath holds and electrocardiogram gating, shortening the duration of an entire functional cardiac exam to less than 1 minute.

Ultimate MRI

The basic principles of Magnetic Resonance have been understood for over 70 years and a mainstay of medical imaging for over 40. At this point, it's no longer about simply porting these principles to medical imaging. But we are by no means confined to simply polishing either. Significant innovation and even revolution can come to old technologies. The recent revolution in optical microscopy shattered the resolution constraint imposed by a seemingly fundamental physical law (the diffraction limit) and reinvigorated a 500-year-old modality. Progress comes from re-examining old-ways and sidestepping underlying assumptions. This is already underway for MRI; and is fueled by advances in image reconstruction. Reconstruction increasingly employs sophisticated general models often using subtle and hopefully innocuous prior knowledge about the object. This allows a careful re-examination of some basic prerequisites for MRI such as uniform static fields, linear encoding fields, full Nyquist sampling, or even a stationary object. These powerful reconstruction tools are driving changes in acquisition strategy and basic hardware. The scanner of the future will know more about itself and its patient and his/her biology than ever before. This strategy emboldens relaxed hardware constraints and more specialized scanners, hopefully expanding the reach and value offered by MR imaging.

Calibration-Free B0 Correction of EPI Data Using Structured Low Rank Matrix Recovery

We introduce a structured low rank algorithm for the calibration-free compensation of field inhomogeneity artifacts in echo planar imaging (EPI) MRI data. We acquire the data using two EPI readouts that differ in echo-time. Using time segmentation, we reformulate the field inhomogeneity compensation problem as the recovery of an image time series from highly undersampled Fourier measurements. The temporal profile at each pixel is modeled as a single exponential, which is exploited to fill in the missing entries. We show that the exponential behavior at each pixel, along with the spatial smoothness of the exponential parameters, can be exploited to derive a 3-D annihilation relation in the Fourier domain. This relation translates to a low rank property on a structured multi-fold Toeplitz matrix, whose entries correspond to the measured k-space samples. We introduce a fast two-step algorithm for the completion of the Toeplitz matrix from the available samples. In the first step, we estimate the null space vectors of the Toeplitz matrix using only its fully sampled rows. The null space is then used to estimate the signal subspace, which facilitates the efficient recovery of the time series of images. We finally demonstrate the proposed approach on spherical MR phantom data and human data and show that the artifacts are significantly reduced.

Rapid anatomical brain imaging using spiral acquisition and an expanded signal model

We report the deployment of spiral acquisition for high-resolution structural imaging at 7T. Long spiral readouts are rendered manageable by an expanded signal model including static off-resonance and B₀ dynamics along with k-space trajectories and coil sensitivity maps. Image reconstruction is accomplished by inversion of the signal model using an extension of the iterative non-Cartesian SENSE algorithm. Spiral readouts up to 25 ms are shown to permit whole-brain 2D imaging at 0.5 mm in-plane resolution in less than a minute. A range of options is explored, including proton-density and T₂* contrast, acceleration by parallel imaging, different readout orientations, and the extraction of phase images. Results are shown to exhibit competitive image quality along with high geometric consistency.

Algebraic reconstruction technique for parallel imaging reconstruction of undersampled radial data: application to cardiac cine

PURPOSE

To investigate algebraic reconstruction technique (ART) for parallel imaging reconstruction of radial data, applied to accelerated cardiac cine.

METHODS

A graphics processing unit (GPU)-accelerated ART reconstruction was implemented and applied to simulations, point spread functions and in 12 subjects imaged with radial cardiac cine acquisitions. Cine images were reconstructed with radial ART at multiple undersampling levels (192 Nr × Np  = 96 to 16). Images were qualitatively and quantitatively analyzed for sharpness and artifacts, and compared to filtered back-projection, and conjugate gradient SENSE.

RESULTS

Radial ART provided reduced artifacts and mainly preserved spatial resolution, for both simulations and in vivo data. Artifacts were qualitatively and quantitatively less with ART than filtered back-projection using 48, 32, and 24 Np , although filtered back-projection provided quantitatively sharper images at undersampling levels of 48-24 Np (all P < 0.05). Use of undersampled radial data for generating auto-calibrated coil-sensitivity profiles resulted in slightly reduced quality. ART was comparable to conjugate gradient SENSE. GPU-acceleration increased ART reconstruction speed 15-fold, with little impact on the images.

CONCLUSION

GPU-accelerated ART is an alternative approach to image reconstruction for parallel radial MR imaging, providing reduced artifacts while mainly maintaining sharpness compared to filtered back-projection, as shown by its first application in cardiac studies.

Fast higher-order MR image reconstruction using singular-vector separation

Medical resonance imaging (MRI) conventionally relies on spatially linear gradient fields for image encoding. However, in practice various sources of nonlinear fields can perturb the encoding process and give rise to artifacts unless they are suitably addressed at the reconstruction level. Accounting for field perturbations that are neither linear in space nor constant over time, i.e., dynamic higher-order fields, is particularly challenging. It was previously shown to be feasible with conjugate-gradient iteration. However, so far this approach has been relatively slow due to the need to carry out explicit matrix-vector multiplications in each cycle. In this work, it is proposed to accelerate higher-order reconstruction by expanding the encoding matrix such that fast Fourier transform can be employed for more efficient matrix-vector computation. The underlying principle is to represent the perturbing terms as sums of separable functions of space and time. Compact representations with this property are found by singular-vector analysis of the perturbing matrix. Guidelines for balancing the accuracy and speed of the resulting algorithm are derived by error propagation analysis. The proposed technique is demonstrated for the case of higher-order field perturbations due to eddy currents caused by diffusion weighting. In this example, image reconstruction was accelerated by two orders of magnitude.

Application of k-space energy spectrum analysis for inherent and dynamic B0 mapping and deblurring in spiral imaging

Spiral imaging is vulnerable to spatial and temporal variations of the amplitude of the static magnetic field (B(0)) caused by susceptibility effects, eddy currents, chemical shifts, subject motion, physiological noise, and system instabilities, resulting in image blurring. Here, a novel off-resonance correction method is proposed to address these issues. A k-space energy spectrum analysis algorithm is first applied to inherently and dynamically generate a B(0) map from the k-space data at each time point, without requiring any additional data acquisition, pulse sequence modification, or phase unwrapping. A simulated phase evolution rewinding algorithm and an automatic residual deblurring algorithm are then used to correct for the blurring caused by both spatial and temporal B(0) variations, resulting in a high spatial and temporal fidelity. This method is validated against conventional B(0) mapping and deblurring methods, and its advantages for dynamic MRI applications are demonstrated in functional MRI studies.

High-resolution spiral imaging on a whole-body 7T scanner with minimized image blurring

High-resolution (approximately 0.22 mm) images are preferably acquired on whole-body 7T scanners to visualize minianatomic structures in human brain. They usually need long acquisition time ( approximately 12 min) in three-dimensional scans, even with both parallel imaging and partial Fourier samplings. The combined use of both fast imaging techniques, however, leads to occasionally visible undersampling artifacts. Spiral imaging has an advantage in acquisition efficiency over rectangular sampling, but its implementations are limited due to image blurring caused by a strong off-resonance effect at 7T. This study proposes a solution for minimizing image blurring while keeping spiral efficient. Image blurring at 7T was, first, quantitatively investigated using computer simulations and point-spread functions. A combined use of multishot spirals and ultrashort echo time acquisitions was then employed to minimize off-resonance-induced image blurring. Experiments on phantoms and healthy subjects were performed on a whole-body 7T scanner to show the performance of the proposed method. The three-dimensional brain images of human subjects were obtained at echo time = 1.18 ms, resolution = 0.22 mm (field of view = 220 mm, matrix size = 1024), and in-plane spiral shots = 128, using a home-developed ultrashort echo time sequence (acquisition-weighted stack of spirals). The total acquisition time for 60 partitions at pulse repetition time = 100 ms was 12.8 min without use of parallel imaging and partial Fourier sampling. The blurring in these spiral images was minimized to a level comparable to that in gradient-echo images with rectangular acquisitions, while the spiral acquisition efficiency was maintained at eight. These images showed that spiral imaging at 7T was feasible.

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.

Iterative off-resonance and signal decay estimation and correction for multi-echo MRI

Signal dephasing due to field inhomogeneity and signal decay due to transverse relaxation lead to perturbations of the Fourier encoding commonly applied in magnetic resonance imaging. Hence, images acquired with long readouts suffer from artifacts such as blurring, distortion, and intensity variation. These artifacts can be removed in reconstruction, usually based on separately collected information in form of field and relaxation maps. In this work, a recently proposed gridding-based algorithm for off-resonance correction is extended to also address signal decay. It is integrated into a new fixed-point iteration, which permits the joint estimation of an image and field and relaxation maps from multi-echo acquisitions. This approach is then applied in simulations and in vivo experiments and demonstrated to improve both images and maps. The rapid convergence of the fixed-point iteration in combination with the efficient gridding-based correction promises to render the running time of such a joint estimation acceptable.

Current trends and challenges in MRI acquisitions to investigate brain function

Functional magnetic resonance imaging (fMRI) studies using the blood oxygenation level dependent (BOLD) response have become a widely used tool for noninvasive assessment of functional organization of the brain. Yet the technique is still fairly new, with many significant challenges remaining. Capitalizing on additional contrast mechanisms available with MRI, several other functional imaging techniques have been developed that potentially provide improved quantification or specificity of neuronal function. This article reviews the challenges and the current state of the art in MRI-based methods of imaging cognitive function.

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.

Iterative RF pulse design for multidimensional, small-tip-angle selective excitation

The excitation k-space perspective on small-tip-angle selective excitation has facilitated RF pulse designs in a range of MR applications. In this paper, k-space-based design of multidimensional RF pulses is formulated as a quadratic optimization problem, and solved efficiently by the iterative conjugate-gradient (CG) algorithm. Compared to conventional design approaches, such as the conjugate-phase (CP) method, the new design approach is beneficial in several regards. It generally produces more accurate excitation patterns. The improvement is particularly significant when k-space is undersampled, and it can potentially shorten pulse lengths. A prominent improvement in accuracy is also observed when large off-resonance gradients are present. A further boost in excitation accuracy can be accomplished in regions of interest (ROIs) if they are specified together with "don't-care" regions. The density compensation function (DCF) is no longer required. In addition, regularization techniques allow control over integrated and peak pulse power.

Convergence studies on iterative algorithms for image reconstruction

We introduce a general iterative scheme for image reconstruction based on Landweber's method. In our configuration, a sequential block-iterative (SeqBI) version can be readily formulated from a simultaneous block-iterative (SimBI) version, and vice versa. This provides a mechanism to derive new algorithms from known ones. It is shown that some widely used iterative algorithms, such as the algebraic reconstruction technique (ART), simultaneous ART (SART), Cimmino's, and the recently designed diagonal weighting and component averaging algorithms, are special examples of the general scheme. We prove convergence of the general scheme under conditions more general than assumed in earlier studies, for its SeqBI and SimBI versions in the consistent and inconsistent cases, respectively. Our results suggest automatic relaxation strategies for the SeqBI and SimBI versions and characterize the dependence of the limit image on the initial guess. It is found that in all cases the limit is the sum of the minimum norm solution of a weighted least-squares problem and an oblique projection of the initial image onto the null space of the system matrix.

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.

Reconstruction of MR images from data acquired on a general nonregular grid by pseudoinverse calculation

A minimum-norm least-squares image-reconstruction method for the reconstruction of magnetic resonance images from non-Cartesian sampled data is proposed. The method is based on a general formalism for continuous-to-discrete mapping and pseudoinverse calculation. It does not involve any regridding or interpolation of the data and therefore the methodology differs fundamentally from existing regridding-based methods. Moreover, the method uses a continuous representation of objects in the image domain instead of a discretized representation. Simulations and experiments show the possibilities of the method in both radial and spiral imaging. Simulations revealed that minimum-norm least-squares image reconstruction can result in a drastic decrease of artifacts compared with regridding-based reconstruction. Besides, both in vivo and phantom experiments showed that minimum-norm least-squares image reconstruction leads to contrast improvement and increased signal-to-noise ratio compared with image reconstruction based on regridding. As an appendix, an analytical calculation of the raw data corresponding to the well-known Shepp and Logan software head phantom is presented.