W. Scott Hoge

Statistical noise analysis in GRAPPA using a parametrized noncentral Chi approximation model

The characterization of the distribution of noise in the magnitude MR image is a very important problem within image processing algorithms. The Rician noise assumed in single‐coil acquisitions has been the keystone for signal‐to‐noise ratio estimation, image filtering, or diffusion tensor estimation for years. With the advent of parallel protocols such as sensitivity encoding or Generalized Autocalibrated Partially Parallel Acquisitions that allow accelerated acquisitions, this noise model no longer holds. Since Generalized Autocalibrated Partially Parallel Acquisitions reconstructions yield the combination of the squared signals recovered at each receiving coil, noncentral Chi statistics have been previously proposed to model the distribution of noise. However, we prove in this article that this is a weak model due to several artifacts in the acquisition scheme, mainly the correlation existing between the signals obtained at each coil. Alternatively, we propose to model such correlations with a reduction in the number of degrees of freedom of the signal, which translates in an equivalent nonaccelerated system with a minor number of independent receiving coils and, consequently, a lower signal‐to‐noise ratio. With this model, a noncentral Chi distribution can be assumed for all pixels in the image, whose effective number of coils and effective variance of noise can be explicitly computed in a closed form from the Generalized Autocalibrated Partially Parallel Acquisitions interpolation coefficients. Extensive experiments over both synthetic and in vivo data sets have been performed to show the goodness of fit of out model. Magn Reson Med, 2010.

Robust EPI Nyquist ghost elimination via spatial and temporal encoding.

Nyquist ghosts are an inherent artifact in echo planar imaging acquisitions. An approach to robustly eliminate Nyquist ghosts is presented that integrates two previous Nyquist ghost correction techniques: temporal domain encoding (phase labeling for additional coordinate encoding: PLACE and spatial domain encoding (phased array ghost elimination: PAGE). Temporal encoding modulates the echo planar imaging acquisition trajectory from frame to frame, enabling one to interleave data to remove inconsistencies that occur between sampling on positive and negative gradient readouts. With PLACE, one can coherently combine the interleaved data to cancel residual Nyquist ghosts. If the level of ghosting varies significantly from image to image, however, the signal cancellation that occurs with PLACE can adversely affect SNR‐sensitive applications such as perfusion imaging with arterial spin labeling. This work proposes integrating PLACE into a PAGE‐based reconstruction process to yield significantly better Nyquist ghost correction that is more robust than PLACE or PAGE alone. The robustness of this method is demonstrated in the presence of magnetic field drift with an in‐vivo arterial spin labeling perfusion experiment. Magn Reson Med, 2010.

Collateral nerve fibers in human spinal cord: visualization with magnetic resonance diffusion tensor imaging.

Diffusion tensor magnetic resonance imaging provides structural information about nerve fiber tissue. The first eigenvector of the diffusion tensor is aligned with the nerve fibers, i.e., longitudinally in the spinal cord. The underlying hypothesis of this study is that the presence of collateral nerve fibers running orthogonal to the longitudinal fibers results in an orderly arrangement of the second eigenvectors. Magnetic resonance diffusion tensor scans were performed with line scan diffusion imaging on a clinical MR scanner. Axial sections were scanned in a human cervical spinal cord specimen at 625 microm resolution and the cervical spinal cord of four normal volunteers at 1250 microm resolution. The spinal cord specimen was fixed and stained for later light microscopy of the collateral fiber architecture at 0.53 microm resolution. Diffusion measured by MR was found to be anisotropic for both white and gray matter areas of the spinal cord specimen; the average fractional anisotropy (FA) was 0.63 +/- 0.09 (diffusion eigenvalues lambda1 0.38 +/- 0.05 micros/mm2, lambda2 0.14 +/- 0.03 micros/mm2, lambda3 0.10 +/- 0.03 micros/mm2) in white matter and 0.27 +/- 0.04 (lambda1 0.36 +/- 0.04 micros/mm2, lambda2 0.28 +/- 0.03 micros/mm2, lambda3 0.21 +/- 0.04 micros/mm2 in gray matter. The normal-volunteer FA values were similar, i.e., 0.66 +/- 0.04 (lambda1 1.66 +/- 0.14 micros/mm2, lambda2 0.55 +/- 0.02 micros/mm2, lambda3 0.40 +/- 0.01 micros/mm2) in white matter and 0.35 +/- 0.03 (lambda1 1.14 +/- 0.07 micros/mm2, lambda2 0.70 +/- 0.03 micros/mm2, lambda3 0.58 +/- 0.02 micros/mm2) in gray matter. The first eigenvector pointed, as expected, in the longitudinal direction. The second eigenvector directions exhibited a striking arrangement, consistent with the distribution of interconnecting collateral nerve fibers discerned on the histology section. This finding was confirmed for the specimen by quantitative pixel-wise comparison of second eigenvector directions and collateral fiber directions assessed on light microscopy image data. Diffusion tensor MRI can reveal non-invasively and in great detail the intricate fiber architecture of the human spinal cord.

3D GRASE PROPELLER: improved image acquisition technique for arterial spin labeling perfusion imaging.

Arterial spin labeling is a noninvasive technique that can quantitatively measure cerebral blood flow. While traditionally arterial spin labeling employs 2D echo planar imaging or spiral acquisition trajectories, single‐shot 3D gradient echo and spin echo (GRASE) is gaining popularity in arterial spin labeling due to inherent signal‐to‐noise ratio advantage and spatial coverage. However, a major limitation of 3D GRASE is through‐plane blurring caused by T2 decay. A novel technique combining 3D GRASE and a periodically rotated overlapping parallel lines with enhanced reconstruction trajectory (PROPELLER) is presented to minimize through‐plane blurring without sacrificing perfusion sensitivity or increasing total scan time. Full brain perfusion images were acquired at a 3 × 3 × 5 mm3 nominal voxel size with pulsed arterial spin labeling preparation sequence. Data from five healthy subjects was acquired on a GE 1.5T scanner in less than 4 minutes per subject. While showing good agreement in cerebral blood flow quantification with 3D gradient echo and spin echo, 3D GRASE PROPELLER demonstrated reduced through‐plane blurring, improved anatomical details, high repeatability and robustness against motion, making it suitable for routine clinical use. Magn Reson Med, 2011.

Fast regularized reconstruction of non-uniformly subsampled parallel MRI data

Parallel MR imaging is an effective approach to reduce MR image acquisition time. Non-uniform subsampling allows one to tailor the subsampling scheme for improved image quality at high acceleration factors. However, non-uniform subsampling precludes fast reconstruction schemes such as SENSE, and is more likely to require a regularized solution than reconstruction of uniformly subsampled data demands. This means that one needs to choose a good regularization parameter, typically requiring multiple expensive system solves. Here, we present an efficient LSQR-Hybrid algorithm which simultaneously addresses the need for rapid regularization parameter selection and fast reconstruction. This algorithm can reconstruct non-uniformly subsampled parallel MRI data, with automatic regularization and good image quality, in a time competitive with Cartesian SENSE

A 2D MTF approach to evaluate and guide dynamic imaging developments

As the number and complexity of partially sampled dynamic imaging methods continue to increase, reliable strategies to evaluate performance may prove most useful. In the present work, an analytical framework to evaluate given reconstruction methods is presented. A perturbation algorithm allows the proposed evaluation scheme to perform robustly without requiring knowledge about the inner workings of the method being evaluated. A main output of the evaluation process consists of a two‐dimensional modulation transfer function, an easy‐to‐interpret visual rendering of a methods ability to capture all combinations of spatial and temporal frequencies. Approaches to evaluate noise properties and artifact content at all spatial and temporal frequencies are also proposed. One fully sampled phantom and three fully sampled cardiac cine datasets were subsampled (R = 4 and 8) and reconstructed with the different methods tested here. A hybrid method, which combines the main advantageous features observed in our assessments, was proposed and tested in a cardiac cine application, with acceleration factors of 3.5 and 6.3 (skip factors of 4 and 8, respectively). This approach combines features from methods such as k‐t sensitivity encoding, unaliasing by Fourier encoding the overlaps in the temporal dimension‐sensitivity encoding, generalized autocalibrating partially parallel acquisition, sensitivity profiles from an array of coils for encoding and reconstruction in parallel, self, hybrid referencing with unaliasing by Fourier encoding the overlaps in the temporal dimension and generalized autocalibrating partially parallel acquisition, and generalized autocalibrating partially parallel acquisition–enhanced sensitivity maps for sensitivity encoding reconstructions. Magn Reson Med, 2010.

Non-Fourier-encoded parallel MRI using multiple receiver coils.

This paper describes a general theoretical framework that combines non‐Fourier (NF) spatially‐encoded MRI with multichannel acquisition parallel MRI. The two spatial‐encoding mechanisms are physically and analytically separable, which allows NF encoding to be expressed as complementary to the inherent encoding imposed by RF receiver coil sensitivities. Consequently, the number of NF spatial‐encoding steps necessary to fully encode an FOV is reduced. Furthermore, by casting the FOV reduction of parallel imaging techniques as a dimensionality reduction of the k‐space that is NF‐encoded, one can obtain a speed‐up of each digital NF spatial excitation in addition to accelerated imaging. Images acquired at speed‐up factors of 2× to 8× with a four‐element RF receiver coil array demonstrate the utility of this framework and the efficiency afforded by it. Magn Reson Med 52:321–328, 2004.

Motion Information in the Phase Domain

Analysis and fusion of information in video data usually require estimating the motion between two or more adjacent frames in the sequence. This process, which is commonly referred to as registration, has been widely studied in the literature for different applications such as remote sensing, robotics, and bio-medical imaging [5, 25]. Registration techniques typically assume that motion can be modeled using a given family of transformations such as rigid, affine, or Euclidean. Registration is performed by looking for a particular transformation within the family that optimizes some similarity or redundancy criterion, e.g. correlation coefficients or mutual entropy. Herein, we are interested in investigating the motion information contained in the phase domain. We are particularly motivated by applications that require registration at sub-pixel accuracy. Examples of such applications include super-resolution from multiple views [11, 12, 20, 30] or examination of same-patient MRI data in a clinical setting [6, 15]

Dual‐polarity GRAPPA for simultaneous reconstruction and ghost correction of echo planar imaging data

The purpose of this study was to seek improved image quality from accelerated echo planar imaging (EPI) data, particularly at ultrahigh fields. Certain artifacts in EPI reconstructions can be attributed to nonlinear phase differences between data acquired using frequency‐encoding gradients of alternating polarity. These errors appear near regions of local susceptibility gradients and typically cannot be corrected with conventional Nyquist ghost correction (NGC) methods.

Rapid full-brain fMRI with an accelerated multi shot 3D EPI sequence using both UNFOLD and GRAPPA

The desire to understand complex mental processes using functional MRI drives development of imaging techniques that scan the whole human brain at a high spatial and temporal resolution. In this work, an accelerated multishot three‐dimensional echo‐planar imaging sequence is proposed to increase the temporal resolution of these studies. A combination of two modern acceleration techniques, UNFOLD and GRAPPA is used in the secondary phase encoding direction to reduce the scan time effectively. The sequence (repetition time of 1.02 s) was compared with standard two‐dimensional echo‐planar imaging (3 s) and multishot three‐dimensional echo‐planar imaging (3 s) sequences with both block design and event‐related functional MRI paradigms. With the same experimental setup and imaging time, the temporal resolution improvement with our sequence yields similar activation regions in the block design functional MRI paradigm with slightly increased t‐scores. Moreover, additional information on the timing of rapid dynamic changes was extracted from accelerated images for the case of the event related complex mental paradigm. Magn Reson Med, 2012.