Spectral extrapolation of spatially bounded images [MRI application]

Subspace Model-Assisted Deep Learning for Improved Image Reconstruction

Image reconstruction from limited and/or sparse data is known to be an ill-posed problem and a priori information/constraints have played an important role in solving the problem. Early constrained image reconstruction methods utilize image priors based on general image properties such as sparsity, low-rank structures, spatial support bound, etc. Recent deep learning-based reconstruction methods promise to produce even higher quality reconstructions by utilizing more specific image priors learned from training data. However, learning high-dimensional image priors requires huge amounts of training data that are currently not available in medical imaging applications. As a result, deep learning-based reconstructions often suffer from two known practical issues: a) sensitivity to data perturbations (e.g., changes in data sampling scheme), and b) limited generalization capability (e.g., biased reconstruction of lesions). This paper proposes a new method to address these issues. The proposed method synergistically integrates model-based and data-driven learning in three key components. The first component uses the linear vector space framework to capture global dependence of image features; the second exploits a deep network to learn the mapping from a linear vector space to a nonlinear manifold; the third is an unrolling-based deep network that captures local residual features with the aid of a sparsity model. The proposed method has been evaluated with magnetic resonance imaging data, demonstrating improved reconstruction in the presence of data perturbation and/or novel image features. The method may enhance the practical utility of deep learning-based image reconstruction.

Joint calibrationless reconstruction of highly undersampled multicontrast MR datasets using a low-rank Hankel tensor completion framework

PURPOSE

To jointly reconstruct highly undersampled multicontrast two-dimensional (2D) datasets through a low-rank Hankel tensor completion framework.

METHODS

A multicontrast Hankel tensor completion (MC-HTC) framework is proposed to exploit the shareable information in multicontrast datasets with respect to their highly correlated image structure, common spatial support, and shared coil sensitivity for joint reconstruction. This is achieved by first organizing multicontrast k-space datasets into a single block-wise Hankel tensor. Subsequent low-rank tensor approximation via higher-order singular value decomposition (HOSVD) uses the image structural correlation by considering different contrasts as virtual channels. Meanwhile, the HOSVD imposes common spatial support and shared coil sensitivity by treating data from different contrasts as from additional k-space kernels. The missing k-space data are then recovered by iteratively performing such low-rank approximation and enforcing data consistency. This joint reconstruction framework was evaluated using multicontrast multichannel 2D human brain datasets (T₁ -weighted, T₂ -weighted, fluid-attenuated inversion recovery, and T₁ -weighted-inversion recovery) of identical image geometry with random and uniform undersampling schemes.

RESULTS

The proposed method offered high acceleration, exhibiting significantly less residual errors when compared with both single-contrast SAKE (simultaneous autocalibrating and k-space estimation) and multicontrast J-LORAKS (joint parallel-imaging-low-rank matrix modeling of local k-space neighborhoods) low-rank reconstruction. Furthermore, the MC-HTC framework was applied uniquely to Cartesian uniform undersampling by incorporating a novel complementary k-space sampling strategy where the phase-encoding direction among different contrasts is orthogonally alternated.

CONCLUSION

The proposed MC-HTC approach presents an effective tensor completion framework to jointly reconstruct highly undersampled multicontrast 2D datasets without coil-sensitivity calibration.

A minimum-phase Shinnar-Le Roux spectral-spatial excitation RF pulse for simultaneous water and lipid suppression in 1H-MRSI of body extremities

PURPOSE

To develop a spectral-spatial (SPSP) excitation RF pulse for simultaneous water and lipid suppression in proton (1H) magnetic resonance spectroscopic imaging (MRSI) of body extremities.

METHODS

An SPSP excitation pulse is designed to excite Creatine (Cr) and Choline (Cho) metabolite signals while suppressing the overwhelming water and lipid signals. The SPSP pulse is designed using a recently proposed multidimensional Shinnar-Le Roux (SLR) RF pulse design method. A minimum-phase spectral selectivity profile is used to minimize signal loss from T2⁎ decay.

RESULTS

The performance of the SPSP pulse is evaluated via Bloch equation simulations and phantom experiments. The feasibility of the proposed method is demonstrated using three-dimensional, short repetition-time, free induction decay-based 1H-MRSI in the thigh muscle at 3T.

CONCLUSION

The proposed SPSP excitation pulse is useful for simultaneous water and lipid suppression. The proposed method enables new applications of high-resolution 1H-MRSI in body extremities.

LORAKS makes better SENSE: Phase-constrained partial fourier SENSE reconstruction without phase calibration

PURPOSE

Parallel imaging and partial Fourier acquisition are two classical approaches for accelerated MRI. Methods that combine these approaches often rely on prior knowledge of the image phase, but the need to obtain this prior information can place practical restrictions on the data acquisition strategy. In this work, we propose and evaluate SENSE-LORAKS, which enables combined parallel imaging and partial Fourier reconstruction without requiring prior phase information.

THEORY AND METHODS

The proposed formulation is based on combining the classical SENSE model for parallel imaging data with the more recent LORAKS framework for MR image reconstruction using low-rank matrix modeling. Previous LORAKS-based methods have successfully enabled calibrationless partial Fourier parallel MRI reconstruction, but have been most successful with nonuniform sampling strategies that may be hard to implement for certain applications. By combining LORAKS with SENSE, we enable highly accelerated partial Fourier MRI reconstruction for a broader range of sampling trajectories, including widely used calibrationless uniformly undersampled trajectories.

RESULTS

Our empirical results with retrospectively undersampled datasets indicate that when SENSE-LORAKS reconstruction is combined with an appropriate k-space sampling trajectory, it can provide substantially better image quality at high-acceleration rates relative to existing state-of-the-art reconstruction approaches.

CONCLUSION

The SENSE-LORAKS framework provides promising new opportunities for highly accelerated MRI. Magn Reson Med 77:1021-1035, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

Magnetic resonance spectroscopic imaging at superresolution: Overview and perspectives

The notion of non-invasive, high-resolution spatial mapping of metabolite concentrations has long enticed the medical community. While magnetic resonance spectroscopic imaging (MRSI) is capable of achieving the requisite spatio-spectral localization, it has traditionally been encumbered by significant resolution constraints that have thus far undermined its clinical utility. To surpass these obstacles, research efforts have primarily focused on hardware enhancements or the development of accelerated acquisition strategies to improve the experimental sensitivity per unit time. Concomitantly, a number of innovative reconstruction techniques have emerged as alternatives to the standard inverse discrete Fourier transform (DFT). While perhaps lesser known, these latter methods strive to effect commensurate resolution gains by exploiting known properties of the underlying MRSI signal in concert with advanced image and signal processing techniques. This review article aims to aggregate and provide an overview of the past few decades of so-called "superresolution" MRSI reconstruction methodologies, and to introduce readers to current state-of-the-art approaches. A number of perspectives are then offered as to the future of high-resolution MRSI, with a particular focus on translation into clinical settings.

Removal of nuisance signals from limited and sparse 1H MRSI data using a union-of-subspaces model

PURPOSE

To remove nuisance signals (e.g., water and lipid signals) for (1) H MRSI data collected from the brain with limited and/or sparse (k, t)-space coverage.

METHODS

A union-of-subspace model is proposed for removing nuisance signals. The model exploits the partial separability of both the nuisance signals and the metabolite signal, and decomposes an MRSI dataset into several sets of generalized voxels that share the same spectral distributions. This model enables the estimation of the nuisance signals from an MRSI dataset that has limited and/or sparse (k, t)-space coverage.

RESULTS

The proposed method has been evaluated using in vivo MRSI data. For conventional chemical shift imaging data with limited k-space coverage, the proposed method produced "lipid-free" spectra without lipid suppression during data acquisition at 130 ms echo time. For sparse (k, t)-space data acquired with conventional pulses for water and lipid suppression, the proposed method was also able to remove the remaining water and lipid signals with negligible residuals.

CONCLUSION

Nuisance signals in (1) H MRSI data reside in low-dimensional subspaces. This property can be utilized for estimation and removal of nuisance signals from (1) H MRSI data even when they have limited and/or sparse coverage of (k, t)-space. The proposed method should prove useful especially for accelerated high-resolution (1) H MRSI of the brain.

Low-rank modeling of local k-space neighborhoods (LORAKS) for constrained MRI

Recent theoretical results on low-rank matrix reconstruction have inspired significant interest in low-rank modeling of MRI images. Existing approaches have focused on higher-dimensional scenarios with data available from multiple channels, timepoints, or image contrasts. The present work demonstrates that single-channel, single-contrast, single-timepoint k-space data can also be mapped to low-rank matrices when the image has limited spatial support or slowly varying phase. Based on this, we develop a novel and flexible framework for constrained image reconstruction that uses low-rank matrix modeling of local k-space neighborhoods (LORAKS). A new regularization penalty and corresponding algorithm for promoting low-rank are also introduced. The potential of LORAKS is demonstrated with simulated and experimental data for a range of denoising and sparse-sampling applications. LORAKS is also compared against state-of-the-art methods like homodyne reconstruction, l1-norm minimization, and total variation minimization, and is demonstrated to have distinct features and advantages. In addition, while calibration-based support and phase constraints are commonly used in existing methods, the LORAKS framework enables calibrationless use of these constraints.

Hybrid-SPRITE MRI

In a FID based frequency encoding MRI experiment the central part of k-space is not generally accessible due to the probe dead time. This portion of k-space is however crucial for image reconstruction. SPRITE (Single Point Ramped Imaging with T1 Enhancement), SPI with a linearly ramped phase encode gradient, has been employed to image short relaxation time systems for many years with great success. It is a robust imaging method in significant measure because it provides acquisition of high quality k-space origin data. We propose a new sampling scheme, termed hybrid-SPRITE, combining phase and frequency encoding to ensure high quality images with reduced acquisition times, reduced gradient duty cycle and increased sensitivity. In hybrid-SPRITE, numerous time domain points are collected to assist image reconstruction. An Inverse Non-uniform Discrete Fourier Transform (INDFT) is employed in 1D applications. A pseudo-polar grid is exploited in 2D hybrid-SPRITE for rapid and accurate image reconstruction.

Removal of truncation artefacts in magnetic resonance images by recovering missing spectral data

Truncation artefacts are often present in many archived clinical magnetic resonance (MR) images due to the need of shortening the acquisition time by sampling a part of their k-space. This artificial information degrades the quality of the image and may hamper clinical diagnosis. In this paper, we propose a novel method to remove the artefacts by recovering the missing k-space or spectral data. The method consists of four steps: (a) estimating the truncated k-space from the images containing truncations artefacts, (b) computing the parameters of the sparse representation of the difference image of an image from the estimated truncated k-space, (c) recovering the missing spectral data using the parameters computed in (b), and (d) obtaining the artefact-removed image through inverse Fourier transform of the estimated and the recovered spectral data. Experiments on both simulated and real MR images have shown that the proposed method effectively removes truncation artefacts while preserving image quality and outperforms both the conventional Hamming window method and the popular TV method.

Support-assisted optical superresolution of low-resolution image sequences: the one-dimensional problem

We analyze the problem of optical superresolution (OSR) of a one-dimensional (1D) incoherent spatial signal from undersampled data when the support of the signal is known in advance. The present paper corrects and extends our previous work on the calculation of Fisher information (FI) and the associated Cramer-Rao lower bound (CRB) on the minimum error for estimating the signal intensity distribution and its Fourier components at spatial frequencies lying beyond the optical band edge. The faint-signal and bright-signal limits emerge from a unified noise analysis in which we include both additive noise of detection and shot noise of photon counting via an approximate Gaussian statistical distribution. For a large space-bandwidth product, we derive analytical approximations to the exact expressions for FI and CRB in the faint-signal limit and use them to argue why achieving any significant amount o unbiased bandwidth extension in the presence of noise is a uniquely challenging proposition. Unlike previous theoretical work on the subject of support-assisted bandwidth extension, our approach is not restricted to specific forms of the system transfer functions, and provides a unified analysis of both digital and optical superresolution of undersampled data.

Spectroscopy by integration of frequency and time domain information for fast acquisition of high-resolution dark spectra

A simple and effective method, SIFT (spectroscopy by integration of frequency and time domain information), is introduced for processing nonuniformly sampled multidimensional NMR data. Applying the computationally efficient Gerchberg-Papoulis (G-P) algorithm, used previously in picture processing and medical imaging, SIFT supplements data at nonuniform points in the time domain with the information carried by known "dark" points (i.e., empty regions) in the frequency domain. We demonstrate that this rapid integration not only removes the severe pseudonoise characteristic of the Fourier transforms of nonuniformly sampled data, but also provides a robust procedure for using frequency information to replace time measurements. The latter can be used to avoid unnecessary sampling in sampling-limited experiments, and the former can be used to take advantage of the ability of nonuniformly sampled data to minimize trade-offs between the signal-to-noise ratio and the resolution in sensitivity-limited experiments. Processing 2D and 3D data sets takes about 0.1 and 2 min, respectively, on a personal computer. With these several attractive features, SIFT offers a novel, model-independent, flexible, and user-friendly tool for efficient and accurate processing of multidimensional NMR data.

Superresolution parallel magnetic resonance imaging: application to functional and spectroscopic imaging

Standard parallel magnetic resonance imaging (MRI) techniques suffer from residual aliasing artifacts when the coil sensitivities vary within the image voxel. In this work, a parallel MRI approach known as Superresolution SENSE (SURE-SENSE) is presented in which acceleration is performed by acquiring only the central region of k-space instead of increasing the sampling distance over the complete k-space matrix and reconstruction is explicitly based on intra-voxel coil sensitivity variation. In SURE-SENSE, parallel MRI reconstruction is formulated as a superresolution imaging problem where a collection of low resolution images acquired with multiple receiver coils are combined into a single image with higher spatial resolution using coil sensitivities acquired with high spatial resolution. The effective acceleration of conventional gradient encoding is given by the gain in spatial resolution, which is dictated by the degree of variation of the different coil sensitivity profiles within the low resolution image voxel. Since SURE-SENSE is an ill-posed inverse problem, Tikhonov regularization is employed to control noise amplification. Unlike standard SENSE, for which acceleration is constrained to the phase-encoding dimension/s, SURE-SENSE allows acceleration along all encoding directions--for example, two-dimensional acceleration of a 2D echo-planar acquisition. SURE-SENSE is particularly suitable for low spatial resolution imaging modalities such as spectroscopic imaging and functional imaging with high temporal resolution. Application to echo-planar functional and spectroscopic imaging in human brain is presented using two-dimensional acceleration with a 32-channel receiver coil.

Extrapolation and correlation (EXTRACT): a new method for motion compensation in MRI

A postprocessing technique is proposed for the correction of both translational and rotational motion artifacts in magnetic resonance imaging (MRI). The method consists of two steps: 1) k-space extrapolation to generate a motion-free reference, followed by 2) correlation with actual data to estimate motion. In this paper, two different extrapolation methods were investigated for the purpose of motion estimation: edge enhancement and finite-support solution. It was found that finite-support solution performs better near the k-space center, while the edge enhancement method is superior in the outer k-space regions. Therefore, a combination of the two methods was employed to generate a motion-free reference, whose correlations with the acquired data can subsequently determine the object motion. Motion compensation was demonstrated in simulation and in vivo MR experiments. The technique is shown to be robust against noise and various types of motion.

Improved model-based magnetic resonance spectroscopic imaging

Model-based techniques have the potential to reduce the artifacts and improve resolution in magnetic resonance spectroscopic imaging, without sacrificing the signal-to-noise ratio. However, the current approaches have a few drawbacks that limit their performance in practical applications. Specifically, the classical schemes use less flexible image models that lead to model misfit, thus resulting in artifacts. Moreover, the performance of the current approaches is negatively affected by the magnetic field inhomogeneity and spatial mismatch between the anatomical references and spectroscopic imaging data. In this paper, we propose efficient solutions to overcome these problems. We introduce a more flexible image model that represents the signal as a linear combination of compartmental and local basis functions. The former set represents the signal variations within the compartments, while the latter captures the local perturbations resulting from lesions or segmentation errors. Since the combined set is redundant, we obtain the reconstructions using sparsity penalized optimization. To compensate for the artifacts resulting from field inhomogeneity, we estimate the field map using alternate scans and use it in the reconstruction. We model the spatial mismatch as an affine transformation, whose parameters are estimated from the spectroscopy data.

Accelerating dynamic spiral MRI by algebraic reconstruction from undersampled k--t space

The temporal resolution of dynamic magnetic resonance imaging (MRI) can be increased by sampling a fraction of k-space in an interleaved fashion, which introduces spatial and temporal aliasing. We describe algebraically and graphically the aliasing process caused by dynamic undersampled spiral imaging within 3-D xyf space (the Fourier transform of k(x)k(y)t space) and formulate the unaliasing problem as a set of independent linear inversions. Since each linear system is numerically underdetermined, the use of prior knowledge in the form of bounded support regions is proposed. To overcome the excessive memory requirements for handling large matrices, a fast implementation of the conjugate gradient (CG) method is used. Numerical simulation and in vivo experiments using spiral twofold undersampling demonstrate reduced motion artifacts and the improved depiction of fine cardiac structures. The achieved reduction of motion artifacts and motion blur is comparable to simple filtering, which is computationally more efficient, while the proposed algebraic framework offers greater flexibility to incorporate additional algebraic acceleration techniques and to handle arbitrary sampling schemes.

BSLIM: spectral localization by imaging with explicit B0 field inhomogeneity compensation

Magnetic resonance spectroscopy imaging (MRSI) is an attractive tool for medical imaging. However, its practical use is often limited by the intrinsic low spatial resolution and long acquisition time. Spectral localization by imaging (SLIM) has been proposed as a non-Fourier reconstruction algorithm that incorporates spatial a priori information about spectroscopically uniform compartments. Unfortunately, the influence of the magnetic field inhomogeneity--in particular, the susceptibility effects at tissues' boundaries--undermines the validity of the compartmental model. Therefore, we propose BSLIM as an extension of SLIM with field inhomogeneity compensation. A B0-field inhomogeneity map, which can be acquired rapidly and at high resolution, is used by the new algorithm as additional a priori information. We show that the proposed method is distinct from the generalized SLIM (GSLIM) framework. Experimental results of a two-compartment phantom demonstrate the feasibility of the method and the importance of inhomogeneity compensation.

Natural linewidth chemical shift imaging (NL-CSI)

The discrete Fourier transform (FT) is a conventional method for spatial reconstruction of chemical shifting imaging (CSI) data. Due to point spread function (PSF) effects, FT reconstruction leads to intervoxel signal leakage (Gibbs ringing). Spectral localization by imaging (SLIM) reconstruction was previously proposed to overcome this intervoxel signal contamination. However, the existence of magnetic field inhomogeneities creates an additional source of intervoxel signal leakage. It is demonstrated herein that even small field inhomogeneities substantially amplify intervoxel signal leakage in both FT and SLIM reconstruction approaches. A new CSI data acquisition strategy and reconstruction algorithm (natural linewidth (NL) CSI) is presented that eliminates effects of magnetic field inhomogeneity-induced intervoxel signal leakage and intravoxel phase dispersion on acquired data. The approach is based on acquired CSI data, high-resolution images, and magnetic field maps. The data are reconstructed based on the imaged object structure (as in the SLIM approach) and a reconstruction matrix that takes into account the inhomogeneous field distribution inside anatomically homogeneous compartments. Phantom and in vivo results show that the new method allows field inhomogeneity effects from the acquired MR signal to be removed so that the signal decay is determined only by the "natural" R2 relaxation rate constant (hence the term "natural linewidth" CSI).

Spatial localization in nuclear magnetic resonance spectroscopy

The ability to select a discrete region within the body for signal acquisition is a fundamental requirement of in vivo NMR spectroscopy. Ideally, it should be possible to tailor the selected volume to coincide exactly with the lesion or tissue of interest, without loss of signal from within this volume or contamination with extraneous signals. Many techniques have been developed over the past 25 years employing a combination of RF coil properties, static magnetic field gradients and pulse sequence design in an attempt to meet these goals. This review presents a comprehensive survey of these techniques, their various advantages and disadvantages, and implications for clinical applications. Particular emphasis is placed on the reliability of the techniques in terms of signal loss, contamination and the effect of nuclear relaxation and J-coupling. The survey includes techniques based on RF coil and pulse design alone, those using static magnetic field gradients, and magnetic resonance spectroscopic imaging. Although there is an emphasis on techniques currently in widespread use (PRESS, STEAM, ISIS and MRSI), the review also includes earlier techniques, in order to provide historical context, and techniques that are promising for future use in clinical and biomedical applications.

Minimum-norm reconstruction for sensitivity-encoded magnetic resonance spectroscopic imaging

In this work we propose minimum-norm reconstruction as a means to enhance the spatial response behavior in parallel spectroscopic MRI. By directly optimizing the shape of the spatial response function (SRF), the new method accounts for coil sensitivity variation across individual voxels and their side lobes. In this fashion, it mitigates the signal contamination and side-lobe aliasing, to which previous techniques are susceptible at low resolution. Although the computational burden is higher, minimum-norm reconstruction is shown to be feasible using an iterative algorithm. Benefits in terms of SRF shape and artifact suppression are demonstrated.

Missing first points and phase artifact mutually entangled in FT NMR data--noniterative solution

Even moderate distortion at the beginning of the NMR signal contributes significantly to the baseline in the reciprocal domain, when the FID-type experiment is considered. If constant phase artifact is also involved, the net problem cannot be resolved accurately, according to its constituents considered in separation. This issue is particularly severe for powder patterns in solids, featuring complex broadband spectra, which substantially mask the baseline behavior. The complete correction procedure should intrinsically deal with both artifacts, due to the mutual dependency. The aim of this work is to indicate the possibility for the exact treatment of baseline and constant phase artifacts together, providing precise measure whether the correction is successful. We have found the analytical, noniterative solution for this coupled problem in the closed form. In this paper, we introduce the correction efficiency concept in order to have the measure for the correction reliability of the resulting spectrum. Relevant efficiency parameter eta is the subject for quantitative analysis resulting in certain constraints for the measurement. We have determined exemplar trends for this parameter as a function of experimental variables such as signal-to-noise ratio and missing points number. The method is model-free and drawn from the origin of the baseline artifact; therefore has potential to work for a broad range of applications.

A correction algorithm for undersampled images using dynamic segmentation and entropy based focus criterion

A post-processing technique is presented for correcting images undersampled in k-space. The method works by taking advantage of the image's background zeros (dynamically segmented through the application of a threshold) to extrapolate the missing k-space samples. The algorithm can produce good quality images from a small set of k-space frequencies with only a few iterations of simple matrix operations, using the image entropy as the focus criterion. It does not require any special patient preparation, extra pulse sequences, complex gradient programming or specialized hardware. This makes it a good candidate for any application that requires short scan times or where only few frequencies can be sampled.

Extension of finite-support extrapolation using the generalized series model for MR spectroscopic imaging

In magnetic resonance (MR) imaging, limited data sampling in k-space leads to the well-known Fourier truncation artifact, which includes ringing and blurring. This problem is particularly severe for MR spectroscopic imaging, where only 16-24 points are typically acquired along each spatial dimension. Several methods have been proposed to overcome this problem by incorporating prior information in the image reconstruction. These include the generalized series (GS) model and the finite-support extrapolation method. This paper shows the connection between finite-support extrapolation and the GS model. In particular, finite-support extrapolation is a limiting case of the GS model, when the only available prior information is the support region. The support region refers to those image portions with nonzero intensities, and it can be estimated in practice as the nonbackground region of an image. By itself, the support region constitutes a rather weak constraint that may not lead to considerable resolution gain. This situation can be improved by using additional prior information, which can be incorporated systematically with the GS model. Examples of such additional prior information include intensity estimates of anatomical structures inside the support region.

Unifying linear prior-information-driven methods for accelerated image acquisition

In the ongoing quest for faster imaging and higher spatial resolution, several methods have been developed to speed up data acquisition by incorporating prior information about the object being imaged. This study shows that many of these methods can be integrated into a single common equation. The unified framework provides a conceptual link that facilitates comparison among these methods to reveal their strengths and weaknesses. By considering the limitations of existing methods, a new member in this class of methods was developed. The broad-use linear acquisition speed-up technique (BLAST) uses the estimated amount of change within the FOV as prior information. BLAST has the flexibility of incorporating a variable amount of prior information to avoid the misleading appearance of "phantom features," which arise from overconstraining the reconstruction. Examples from dynamic imaging and MR thermometry are shown.

Advances in human cardiac 31P-MR spectroscopy: SLOOP and clinical applications

Phosphorus magnetic resonance spectroscopy (31P-MRS) has revealed a lot about the biochemistry of physiological and pathological processes in the heart. Nevertheless, until today, cardiac 31P-MRS has not had any clinical impact, albeit some pioneering studies demonstrated that 31P-MRS can indeed provide diagnostic information. In this paper, the development of techniques for human cardiac 31P-MRS over the past decade is reviewed, and the requirements for a reliable clinical measurement protocol are discussed. Spatial localization with optimal pointspread function (SLOOP) is a new method to achieve spatial localization and absolute quantitation. Its properties are detailed, and preliminary findings in patients with dilated cardiomyopathy or myocardial infarction are presented.

A filter design method for minimizing ringing in a region of interest in MR spectroscopic images

Magnetic resonance spectroscopic imaging (MRSI) requires a relatively long time to sample k-space (the spatial frequency domain), effectively lowpass filtering the resulting reconstructed image. Ringing is especially problematic when a region of interest (ROI) is close to a bright region outside the ROI, since the bright region tends to create a ringing artifact into the ROI due to the lowpass nature of the data. In this paper, we propose a method that reduces the effect of a stronger signal region on a weaker signal in a nearby ROI by designing a postprocessing filter that steers the strong interference away from the ROI. The proposed method is computationally simple both in the design stage and in applying it to images. We present experiments that illustrate the value of the technique.

Restoration of low resolution metabolic images with a priori anatomic information: 23Na MRI in myocardial infarction

A new iterative extrapolation image reconstruction algorithm is presented, which enhances low resolution metabolic magnetic resonance images (MRI) with information about the bounds of signal sources obtained from a priori anatomic proton ((1)H) MRI. The algorithm ameliorates partial volume and ringing artefacts, leaving unchanged local metabolic heterogeneity that is present in the original dataset but not evident at (1)H MRI. Therefore, it is ideally suited to metabolic studies of ischemia, infarction and other diseases where the extent of the abnormality at (1)H MRI is uncertain. The performance of the algorithm is assessed by simulations, MRI of phantoms, and by surface coil 23Na MRI studies of canine myocardial infarction on a clinical scanner where the injury was not evident at (1)H MRI. The algorithm includes corrections for transverse field inhomogeneity, and for the leakage of intense signals into regions of interest such as 23Na MRI signals from ventricular blood ringing into the myocardium. The simulations showed that the algorithm reduced ringing artefacts by 15%, was stable at low SNR ( approximately 7), but is sensitive to the positioning of the (1)H MRI boundaries. The 23Na MRI showed hyperenhancement of regions identified as infarcted at post-mortem histological staining. The areas of hyperenhancement were measured by five independent observers in four 23Na images of infarction reconstructed with and without the algorithm. The infarct areas were correlated with areas determined by post-mortem histological staining with coefficient 0.85 for the enhanced images, compared to 0.58 with the conventional images. The scatter in the amplitude and in the area measurements of ischemia-associated hyper-enhancement in 23Na MRI was reduced by the algorithm by 1.6-fold and by at least 3-fold, respectively, demonstrating its ability to substantially improve quantification of the extent and intensity of metabolic changes in injured tissue that is not evident by (1)H MRI.

On the optimality of the gridding reconstruction algorithm

Gridding reconstruction is a method to reconstruct data onto a Cartesian grid from a set of nonuniformly sampled measurements. This method is appreciated for being robust and computationally fast. However, it lacks solid analysis and design tools to quantify or minimize the reconstruction error. Least squares reconstruction (LSR), on the other hand, is another method which is optimal in the sense that it minimizes the reconstruction error. This method is computationally intensive and, in many cases, sensitive to measurement noise. Hence, it is rarely used in practice. Despite their seemingly different approaches, the gridding and LSR methods are shown to be closely related. The similarity between these two methods is accentuated when they are properly expressed in a common matrix form. It is shown that the gridding algorithm can be considered an approximation to the least squares method. The optimal gridding parameters are defined as the ones which yield the minimum approximation error. These parameters are calculated by minimizing the norm of an approximation error matrix. This problem is studied and solved in the general form of approximation using linearly structured matrices. This method not only supports more general forms of the gridding algorithm, it can also be used to accelerate the reconstruction techniques from incomplete data. The application of this method to a case of two-dimensional (2-D) spiral magnetic resonance imaging shows a reduction of more than 4 dB in the average reconstruction error.

Partial-FOV reconstruction in dynamic spiral imaging

In many applications of dynamic MR imaging, only a portion of the field-of-view (FOV) exhibits considerable variations in time. In such cases, a prior knowledge of the static part of the image allows a partial-FOV reconstruction of the dynamic section using only a fraction of the raw data. This method of reconstruction generally results in higher temporal resolution, because the scan time for partial-FOV data is shorter. The fidelity of this reconstruction technique depends, among other factors, on the accuracy of the prior information of the static section. This information is usually derived from the reconstructed images at previous time frames. This data, however, is normally corrupted by the motion artifact Because the temporal frequency contents of the motion artifact is very similar to that of the dynamic section, a temporal low-pass filter can efficiently remove this artifact from the static data. The bandwidth of the filter can be obtained from the rate of variations inside and outside the dynamic area. In general, when the temporal bandwidth is not spatially uniform, a bank of low-pass filters can provide a proper suppression of the motion artifact outside the dynamic section. This reconstruction technique is adapted for spiral acquisition and is successfully applied to cardiac fluoroscopy, doubling the temporal resolution.

Transforming NMR data despite missing points

Some NMR experiments produce data with several of the initial points missing. The inverse discrete Fourier transform (IDFT) assumes these points are present so the data cannot be so transformed without artifact-ridden results. This problem is often particularly severe when projection imaging with free-induction decays (FIDs). This paper compares recent methods for obtaining a projection from incomplete data and elaborates on their strengths and limitations. One method is to write the transform that would take the desired projection to the truncated data set, and then solve the matrix equation by singular value decomposition. A second replaces the missing data with zeros, so that an IDFT produces a projection with unwanted artifacts. Then one solves the matrix equation that takes the desired projection to the artifact-ridden projection. A third uses the same artifact-ridden projection, but fits the region outside the bandwidth of the sample with as many sinusoidal functions as there are missing data. The coefficients of these functions are estimates of the missing data, and the projection is obtained by transforming the completed FID or subtracting the extrapolation of the fitted curve from the region containing the object. We show that when all three methods are applicable, they theoretically produce the same result. They differ by ease of implementation and possibly by computational errors. They give a result similar to that of the previous method that iteratively corrects the FID and projection after repeated IDFTs and DFTs. We find that one can obtain a projection despite missing a substantial number of data.

Imaging lungs using inert fluorinated gases

Rat lungs were imaged by 19F projection MRI of hexafluoroethane, mixed with 20% oxygen to form the inhaled gas. The 3D image had 700 microm resolution, and the data took 4.3 h to acquire. Free induction decays were collected in the presence of steady magnetic field gradients in 686 different directions. To take advantage of fast relaxation (T1 = 5.9 +/- 0.2 ms), the repetition time was 5 ms. To eliminate signal loss from magnetic field inhomogeneities, data were collected within 2 ms of spin excitation (from 80 micros to 2 ms after the 42-micros pi/2 pulses). The singular value decomposition of the transform from frequency to time domain was used to obtain projections despite the absence of data during and immediately after the RF pulses. Inert fluorinated gas imaging may be less expensive than polarized noble gas imaging and is appropriate for imaging steady-state rather than transient gas concentrations.

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.

Removal of lipid artifacts in 1H spectroscopic imaging by data extrapolation

Proton MR spectroscopic imaging (MRSI) of human cerebral cortex is complicated by the presence of an intense signal from subcutaneous lipids, which, if not suppressed before Fourier reconstruction, causes ringing and signal contamination throughout the metabolite images as a result of limited k-space sampling. In this article, an improved reconstruction of the lipid region is obtained using the Papoulis-Gerchberg algorithm. This procedure makes use of the narrow-band-limited nature of the subcutaneous lipid signal to extrapolate to higher k-space values without alteration of the metabolite signal region. Using computer simulations and in vivo experimental studies, the implementation and performance of this algorithm were examined. This method was found to permit MRSI brain spectra to be obtained without applying any lipid suppression during data acquisition, at echo times of 50 ms and longer. When applied together with optimized acquisition methods, this provides an effective procedure for imaging metabolite distributions in cerebral cortical surface regions.

MRS imaging using anatomically based k-space sampling and extrapolation

A comprehensive strategy for the acquisition, reconstruction, and postprocessing of MR spectroscopic images is presented. The reconstruction algorithm is the most critical component of this strategy. It is assumes that the desired image is spatially bounded, meaning that the desired image contains an object that is surrounded by a background of zeros. The reconstruction algorithm relies on prior knowledge of the background zeros for k-space extrapolation. This algorithm is a good candidate for proton MR spectroscopic image reconstruction because these images are often spatially bounded and prior knowledge of the zeros is easily obtained from a rapidly acquired high resolution conventional MRI. Although the reconstruction algorithm can be used with the standard 3DFT k-space distribution, a distribution that relies on anatomical features that are likely to occur in the spectroscopic image can produce better results. Prior knowledge of these anatomical features is also obtained from a conventional MRI. Finally, the postprocessing component of this strategy is valuable for reducing subcutaneous lipid contamination. Overall, the comprehensive approach presented here produces images that are better resolved than standard approaches without increasing acquisition time or reducing SNR. Examples using NAA data are provided.