Gregory S. Cunningham

Kernel decomposition of time-frequency distributions

Bilinear time-frequency distributions (TFDs) offer improved time-frequency resolution over linear representations, but suffer from difficult interpretation, higher implementation cost, and the lack of associated low-cost signal synthesis algorithms. In the paper, the authors introduce some new tools for the interpretation and quantitative comparison of high-resolution TFDs. These tools are used in related work to define low-cost high-resolution TFDs and to define linear, low-cost signal synthesis algorithms associated with high-resolution TFDs. First, each real-valued TFD is associated with a self-adjoint linear operator /spl psi/. The spectral representation of /spl psi/ expresses the TFD as a weighted sum of spectrograms (SPs). It is shown that the SP decomposition and Weyl correspondence do not yield useful interpretations for high-resolution TFDs due to the fact that /spl psi/ is not positive. >

Dynamic Radiation Environment Assimilation Model: DREAM

The Dynamic Radiation Environment Assimilation Model (DREAM) is a 3-year effort sponsored by the US Department of Energy to provide global, retrospective, or real-time specification of the natural and potential nuclear radiation environments. The DREAM model uses Kalman filtering techniques that combine the strengths of new physical models of the radiation belts with electron observations from long-term satellite systems such as GPS and geosynchronous systems. DREAM includes a physics model for the production and long-term evolution of artificial radiation belts from high altitude nuclear explosions. DREAM has been validated against satellites in arbitrary orbits and consistently produces more accurate results than existing models. Tools for user-specific applications and graphical displays are in beta testing and a real-time version of DREAM has been in continuous operation since November 2009.

Fast implementations of generalized discrete time-frequency distributions

Cohens class of time-frequency distributions (TFDs) have significant potential for the analysis of complex signals. In order to evaluate the TFD of a signal using its samples, discrete-time TFDs (DTFDs) have been defined as the Fourier transform of a smoothed discrete autocorrelation. Existing algorithms evaluate real-valued DTFDs using FFTs of the conjugate-symmetric autocorrelation. Although the computation required to smooth the autocorrelation is often greater than that for the FFT, there are no widely applicable fast algorithms for this part of the processing. Since the FFT is relatively inexpensive, downsampling is ineffective for reducing computation. If the DTFD needs only to be evaluated at a few frequencies for each time instant, the cost per time-frequency sample can be extremely high. The authors introduce two approaches for reducing the computation time of DTFDs. First, they define approximations to real-valued DTFDs, using spectrograms, that admit fast, space-saving evaluations. Frequency downsampling reduces the computation time of these approximations. Next, they define DTFDs that admit fast evaluations over sparse sets of time-frequency samples. A single short time Fourier transform is calculated in order for DTPD time-frequency samples to be evaluated at an additional, fixed cost per sample. >

Model-based image reconstruction from time-resolved diffusion data

This paper addresses the issue of reconstructing the unknown field of absorption and scattering coefficients from time- resolved measurements of diffused light in a computationally efficient manner. The intended application is optical tomography, which has generated considerable interest in recent times. The inverse problem is posed in the Bayesian framework. The maximum a posteriori (MAP) estimate is used to compute the reconstruction. We use an edge-preserving generalized Gaussian Markov random field to model the unknown image. The diffusion model used for the measurements is solved forward in time using a finite-difference approach known as the alternating-directions implicit method. This method requires the inversion of a tridiagonal matrix at each time step and is therefore of O(N) complexity, where N is the dimensionality of the image. Adjoint differentiation is used to compute the sensitivity of the measurements with respect to the unknown image. The novelty of our method lies in the computation of the sensitivity since we can achieve it in O(N) time as opposed to O(N2) time required by the perturbation approach. We present results using simulated data to show that the proposed method yields superior quality reconstructions with substantial savings in computation.

Global time-dependent chorus maps from low-Earth-orbit electron precipitation and Van Allen Probes data

Substorm injected electrons (several–100 s keV) produce whistler-mode chorus waves that are thought to have a major impact on the radiation belts by causing both energization and loss of relativistic electrons in the outer belt. High-altitude measurements, such as those from the Van Allen Probes, provide detailed wave measurements at a few points in the magnetosphere. But physics-based models of radiation-belt dynamics require knowledge of the global distribution of chorus waves. We demonstrate that time-dependent, global distributions of near-equatorial chorus wave intensities can be inferred from low-Earth-orbit (LEO) measurements of precipitating low-energy electrons. We compare in situ observations of near-equatorial chorus waves with LEO observations of precipitating electrons and derive a heuristic formula that relates, quantitatively, electron precipitation fluxes to chorus wave intensities. Finally, we demonstrate how that formula can be applied to LEO precipitation measurements and in situ Van Allen Probes wave measurements to provide global, data-driven inputs for radiation belt models.

Tomographic reconstruction based on flexible geometric models

When dealing with ill-posed inverse problems in data analysis, the Bayesian approach allows one to use prior information to guide the result toward reasonable solutions. In this work the model consists of an object whose amplitude is constant inside a flexible boundary. The flexibility of the boundary is controlled by through a distortion energy. We present an example of reconstruction of the cross section of a blood vessel from just two projections.<<ETX>>

Object-oriented implementation of a graphical-programming system

Object-oriented (OO) analysis, design, and programming is a powerful paradigm for creating software that is easily understood, modified, and maintained. In this paper we demonstrate how the OO concepts of abstraction, inheritance, encapsulation, polymorphism, and dynamic binding have aided in the design of a graphical-programming tool. The tool that we have developed allows a user to build radiographic system models for computing simulated radiographic data. It will eventually be used to perform Bayesion reconstructions of objects given radiographic data. The models are built by connecting icons that represent physical transformations, such as line integrals, exponentiation, and convolution, on a canvas. We will also briefly discuss ParcPlaces application development environment, VisualWorks, which we have found to be as helpful as the OO paradigm.

Three-dimensional reconstructions from low-count SPECT data using deformable models

We demonstrate the reconstruction of a 3D, time-varying bolus of radiotracer from first-pass data obtained by the dynamic SPECT imager, FASTSPECT, built by the University of Arizona. The object imaged is a CardioWest Total Artificial Heart. The bolus is entirely contained in one ventricle and its associated inlet and outlet tubes. The model for the radiotracer distribution is a time-varying triangulated surface with voxel-to- voxel variations allowed inside the volume defined by the closed surface. The total curvature of the surface as well as the point-to-point variation of the interior voxel values is minimized through the use of weighted priors in the Bayesian framework. MAP estimates for the vertices, voxel values, and background count levels are produced for a subset of the 100 available 50- msec frames. The strengths of the priors (the hyperparameters) are determined by maximizing the evidence for the data over the hyperparameter values under the assumption that the posterior is approximately Gaussian.

UNCERTAINTY ASSESSMENT FOR RECONSTRUCTIONS BASED ON DEFORMABLE GEOMETRY

Deformable geometric models can be used in the context of Bayesian analysis to solve ill‐posed tomographic reconstruction problems. The uncertainties associated with a Bayesian analysis may be assessed by generating a set of random samples from the posterior, which may be accomplished using a Markov Chain Monte Carlo (MCMC) technique. We demonstrate the combination of these techniques for a reconstruction of a two‐dimensional object from two orthogonal noisy projections. The reconstructed object is modeled in terms of a deformable geometrically defined boundary with a uniform interior density yielding a nonlinear reconstruction problem. We show how an MCMC sequence can be used to estimate uncertainties in the location of the edge of the reconstructed object.

Tomographic reconstruction using 3D deformable models

We address the issue of reconstructing the shape of an object with uniform interior activity from a set of projections. We estimate directly from projection data the position of a triangulated surface describing the boundary of the object while incorporating prior knowledge about the unknown shape. This inverse problem is addressed in a Bayesian framework using the maximum a posteriori (MAP) estimate for the reconstruction. The derivatives needed for the gradient-based optimization of the model parameters are obtained using the adjoint differentiation technique. We present results from a numerical simulation of a dynamic cardiac imaging study. A first-pass exam is simulated with a numerical phantom of the right ventricle using the measured system response of the University of Arizona FASTSPECT imager, which consists of 24 detectors. We demonstrate the usefulness of our approach by reconstructing the shape of the ventricle from 10,000 counts. The comparison with an ML-EM result shows the usefulness of the deformable model approach.