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

Why do Large Animals Never Actuate Their Jumps with Latch-Mediated Springs? Because They can Jump Higher Without Them.

As animals get smaller, their ability to generate usable work from muscle contraction is decreased by the muscle's force-velocity properties, thereby reducing their effective jump height. Very small animals use a spring-actuated system, which prevents velocity effects from reducing available energy. Since force-velocity properties reduce the usable work in even larger animals, why don't larger animals use spring-actuated jumping systems as well? We will show that muscle length-tension properties limit spring-actuated systems to generating a maximum one-third of the possible work that a muscle could produce-greatly restricting the jumping height of spring-actuated jumpers. Thus a spring-actuated jumping animal has a jumping height that is one-third of the maximum possible jump height achievable were 100% of the possible muscle work available. Larger animals, which could theoretically use all of the available muscle energy, have a maximum jumping height that asymptotically approaches a value that is about three times higher than that of spring-actuated jumpers. Furthermore, a size related "crossover point" is evident for these two jumping mechanisms: animals smaller than this point can jump higher with a spring-actuated mechanism, while animals larger than this point can jump higher with a muscle-actuated mechanism. We demonstrate how this limit on energy storage is a consequence of the interaction between length-tension properties of muscles and spring stiffness. We indicate where this crossover point occurs based on modeling and then use jumping data from the literature to validate that larger jumping animals generate greater jump heights with muscle-actuated systems than spring-actuated systems

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

Space radiation: The number one risk to astronaut health beyond low earth orbit

Projecting a vision for space radiobiological research necessitates understanding the nature of the space radiation environment and how radiation risks influence mission planning, timelines and operational decisions. Exposure to space radiation increases the risks of astronauts developing cancer, experiencing central nervous system (CNS) decrements, exhibiting degenerative tissue effects or developing acute radiation syndrome. One or more of these deleterious health effects could develop during future multi-year space exploration missions beyond low Earth orbit (LEO). Shielding is an effective countermeasure against solar particle events (SPEs), but is ineffective in protecting crew members from the biological impacts of fast moving, highly-charged galactic cosmic radiation (GCR) nuclei. Astronauts traveling on a protracted voyage to Mars may be exposed to SPE radiation events, overlaid on a more predictable flux of GCR. Therefore, ground-based research studies employing model organisms seeking to accurately mimic the biological effects of the space radiation environment must concatenate exposures to both proton and heavy ion sources. New techniques in genomics, proteomics, metabolomics and other “omics” areas should also be intelligently employed and correlated with phenotypic observations. This approach will more precisely elucidate the effects of space radiation on human physiology and aid in developing personalized radiological countermeasures for astronauts

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

Smart Medical Systems with Application to Nutrition and Fitness in Space

Smart medical systems are being developed to allow medical treatments to address alterations in chemical and physiological status in real time. In a smart medical system sensor arrays assess subject status, which are interpreted by computer processors which analyze multiple inputs and recommend treatment interventions. The response of the subject to the treatment is again assessed by the sensor arrays, closing the loop. An early form of "smart medicine" has been practiced in space to assess nutrition. Nutrient levels are assessed with food frequency questionnaires, which are interpreted by flight surgeons to recommend in-flight alterations in diet. In the future, sensor arrays will directly probe body chemistry. Near infrared spectroscopy can be used to noninvasively measure several blood and tissue parameters which are important in the assessment of nutrition and fitness. In particular, this technology can be used to measure blood hematocrit and interstitial fluid pH. The noninvasive measurement of interstitial pH is discussed as a surrogate for blood lactate measurement for the development and real-time assessment of exercise protocols in space. Earth-based application of these sensors are also described

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

SpaceDock: A Performance Task Platform for Spaceflight Operations

Preliminary evidence during both short- and long-duration spaceflight indicates that perceptual-motor coordination changes occur and persist in-flight. However, there is presently no in-flight method for evaluating astronaut performance on mission-critical tasks such as docking. We present a portable platform we have developed for attempting and evaluating docking, and describe the results of a pilot study wherein flight novices learned the docking task. Methods: A dual-joystick, six degrees of freedom platform-called SpaceDock-was developed to enable portable, adaptable performance testing in a spaceflight operations setting. Upon this platform, a simplified docking task was created, involving a constant rate of approach towards a docking target and requiring the user to correct translation in two dimensions and attitude orientation along one dimension (either pitch or roll). Ten flight naive subjects performed the task over a 45 min period and all joystick inputs and timings were collected, from which we could successfully reconstruct travel paths, input profiles and relative target displacements. Results: Subjects exhibited significant improvements in docking over the course of the experiment. Learning to compensate for roll-alterations was robust, whereas compensation for pitch-alterations was not in evidence in this population and relatively short training period. Conclusion: The SpaceDock platform can provide a novel method for training and testing subjects, on a spaceflight-relevant task, and can be used to examine behavioral learning, strategy use, and has been adapted for use in brain imaging experiments

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