Nonuniform Fast Fourier Transforms Using Min-Max Interpolation

The fast Fourier transform (FFT) is used widely in signal processing for efficient computation of the FT of finite-length signals over a set of uniformly spaced frequency locations. However, in many applications, one requires nonuniform sampling in the frequency domain, i.e., a nonuniform FT. Several papers have described fast approximations for the nonuniform FT based on interpolating an oversampled FFT. This paper presents an interpolation method for the nonuniform FT that is optimal in the min-max sense of minimizing the worst-case approximation error over all signals of unit norm. The proposed method easily generalizes to multidimensional signals. Numerical results show that the min-max approach provides substantially lower approximation errors than conventional interpolation methods. The min-max criterion is also useful for optimizing the parameters of interpolation kernels such as the Kaiser-Bessel function.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85840/1/Fessler70.pd

Fast, Iterative, Field-Corrected Image Reconstruction for MRI

Magnetic field inhomogeneities cause distortions in the reconstructed images for non-cartesian k-space MRI (using spirals, for example). Several noniterative methods are currently used to compensate for the off-resonance during the reconstruction, but these methods rely on the assumption of a smoothly varying field map. Recently, iterative methods have been proposed that do not rely on this assumption and have the potential to estimate undistorted field maps, but suffer from prohibitively long computation times. In this abstract we present a min-max derived, time-segmented approximation to the signal equation for MRI that, when combined with the nonuniform fast Fourier transform, provides a fast, accurate field-corrected image reconstruction.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/86011/1/Fessler175.pd

Conjugate Phase MRI Reconstruction With Spatially Variant Sample Density Correction

A new image reconstruction method to correct for the effects of magnetic field inhomogeneity in non-Cartesian sampled magnetic resonance imaging (MRI) is proposed. The conjugate phase reconstruction method, which corrects for phase accumulation due to applied gradients and magnetic field inhomogeneity, has been commonly used for this case. This can lead to incomplete correction, in part, due to the presence of gradients in the field inhomogeneity function. Based on local distortions to the k-space trajectory from these gradients, a spatially variant sample density compensation function is introduced as part of the conjugate phase reconstruction. This method was applied to both simulated and experimental spiral imaging data and shown to produce more accurate image reconstructions. Two approaches for fast implementation that allow the use of fast Fourier transforms are also described. The proposed method is shown to produce fast and accurate image reconstructions for spiral sampled MRI.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85978/1/Fessler52.pd

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 transform (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.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/86010/1/Fessler69.pd

Dynamic field map estimation using a spiral-in/spiral-out acquisition

The long readout times of single-shot acquisitions and the high field strengths desired for functional MRI (fMRI) using blood oxygenation level-dependent (BOLD) contrast make functional scans sensitive to magnetic field inhomogeneity. If it is not corrected during image reconstruction, field inhomogeneity can cause geometric distortions in the images when Cartesian k -space trajectories are used or blurring with spiral acquisitions. Many traditional methods to correct for field inhomogeneity distortions rely on a static field map measured with the use of images that are themselves distorted. In this work, we employ a regularized least-squares approach to jointly estimate both the undistorted image and field map at each acquisition using a spiral-in/spiral-out pulse sequence. Simulation and phantom studies show that this method is accurate and stable over a time series. Human functional studies show that the jointly estimated field map may be more accurate than standard field map estimates in the presence of respiration-induced phase oscillations, leading to better detection of functional activation. The proposed method measures a dynamic field map that accurately tracks magnetic field drift and respiration-induced phase oscillations during the course of a functional study. Magn Reson Med 51:1194–1204, 2004. © 2004 Wiley-Liss, Inc.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/34930/1/20079_ftp.pd

Associations of functional connectivity and walking performance in multiple sclerosis

Background Persons with multiple sclerosis (MS) often demonstrate impaired walking performance, and neuroimaging methods such as resting state functional connectivity (RSFC) may support a link between central nervous system damage and disruptions in walking. Objectives This study examined associations between RSFC in cortical networks and walking performance in persons with MS. Methods 29 persons with MS underwent 3-T brain magnetic resonance imaging (MRI) and we computed RSFC among 68 Gy matter regions of interest in the brain. Participants completed the Timed 25-foot Walk as a measure of walking performance. We examined associations using partial Pearson product-moment correlation analyses (r), controlling for age. Results There were eight cortical brain regions that were significantly associated with the T25FW, including the left parahippocampal gyrus and transverse temporal gyrus, and the right fusiform gyrus, inferior temporal gyrus, lingual gyrus, pericalcarine cortex, superior temporal gyrus, and transverse temporal gyrus. Conclusions We provide novel evidence that RSFC can be a valuable tool to monitor the motor and non-motor networks impacted in MS that relate to declines in motor impairment. RSFC may identify critical nodes involved in a range of motor tasks such as walking that can be more sensitive to disruption by MS

Comparing aging and fitness effects on brain anatomy

Recent studies suggest that cardiorespiratory fitness (CRF) mitigates the brain’s atrophy typically associated with aging, via a variety of beneficial mechanisms. One could argue that if CRF is generally counteracting the negative effects of aging, the same regions that display the greatest age-related volumetric loss should also show the largest beneficial effects of fitness. To test this hypothesis we examined structural MRI data from 54 healthy older adults (ages 55–87), to determine the overlap, across brain regions, of the profiles of age and fitness effects. Results showed that lower fitness and older age are associated with atrophy in several brain regions, replicating past studies. However, when the profiles of age and fitness effects were compared using a number of statistical approaches, the effects were not entirely overlapping. Interestingly, some of the regions that were most influenced by age were among those not influenced by fitness. Presumably, the age-related atrophy occurring in these regions is due to factors that are more impervious to the beneficial effects of fitness. Possible mechanisms supporting regional heterogeneity may include differential involvement in motor function, the presence of adult neurogenesis, and differential sensitivity to cerebrovascular, neurotrophic and metabolic factors