This work introduces a method to select linear functional measurements of a vector-valued time series optimized for forecasting distant time-horizons. By formulating and solving the problem of sequential linear measurement design as an infinite-horizon problem with the time-averaged trace of the Cramér-Rao lower bound (CRLB) for forecasting as the cost, the most informative data can be collected irrespective of the eventual forecasting algorithm. By introducing theoretical results regarding measurements under additive noise from natural exponential families, we construct an equivalent problem from which a local dimensionality reduction can be derived. This alternative formulation is based on the future collapse of dimensionality inherent in the limiting behavior of many differential equations and can be directly observed in the low-rank structure of the CRLB for forecasting. Implementations of both an approximate dynamic programming formulation and the proposed alternative are illustrated using an extended Kalman filter for state estimation, with results on simulated systems with limit cycles and chaotic behavior demonstrating a linear improvement in the CRLB as a function of the number of collapsing dimensions of the system.

We present a registration algorithm which jointly estimates motion and the ground truth image from a set of noisy frames under rigid, constant translation. The algorithm is non-iterative and needs no hyperparameter tuning. It requires a fixed number of FFT, multiplication, and downsampling operations for a given input size, enabling fast implementation on embedded platforms like cubesats where on-board image fusion can greatly save on limited downlink bandwidth. The algorithm is optimal in the maximum likelihood sense for additive white Gaussian noise and non-stationary Gaussian approximations of Poisson noise. Accurate registration is achieved for very low SNR, even when visible features are below the noise floor.

The computation required for a switching Kalman Filter (SKF) increases exponentially with the number of system operation modes. In this paper, a computationally tractable graph representation is proposed for a switching linear dynamic system (SLDS) along with the solution of a minimum-sum optimization problem for clustering to reduce the switching mode cardinality offline, before collecting measurements. It is shown that upon perfect mode detection, the induced error caused by mode clustering can be quantified exactly in terms of the dissimilarity measures in the proposed graph structure. Numerical results verify that clustering based on the proposed framework effectively reduces model complexity given uncertain mode detection and that the induced error can be well approximated if the underlying assumptions are satisfied.

Switching Kalman Filters (SKF) are well known for solving switching linear dynamic system (SLDS), i.e., piece-wise linear estimation problems. Practical SKFs are heuristic, approximate filters and require more computational resources than a single-mode Kalman filter (KF). On the other hand, applying a single-mode mismatched KF to an SLDS results in erroneous estimation. This paper quantifies the average error an SKF can eliminate compared to a mismatched, single-mode KF before collecting measurements. Derivations of the first and second moments of the estimators errors are provided and compared. One can use these derivations to quantify the average performance of filters beforehand and decide which filter to run in operation to have the best performance in terms of estimation error and computation complexity. We further provide simulation results that verify our mathematical derivations.

For linear space-invariant temporal systems, we provide a lower bound on the penalty incurred by approximating system dynamics in a Kalman filter by a random walk model, a common model when dynamics are unknown. We then present a computationally tractable algorithm for system identification of high-dimensional linear space-invariant dynamical systems, whereby the circulant structure of the state transition operator yields an estimate of the governing dynamics from a small number of temporal steps. By completing all operations in the frequency domain, we efficiently provide an estimate of the system dynamics and the state of the system. The estimation of system dynamics greatly improves the state estimation over the random walk model, suggesting classical estimators may remain applicable in modern imaging tasks.

Diffractive lenses have recently been applied to the domain of multispectral imaging in the X-ray and UV regimes where they can achieve very high resolution as compared to reflective and refractive optics. Conventionally, spectral components are reconstructed by taking measurements at the focal planes. However, the reconstruction quality can be improved by optimizing the measurement configuration. In this work, we adapt a sequential backward selection algorithm to search for a configuration which minimizes expected reconstruction error. By approximating the forward system as a circular convolution and making assumptions on the source and noise, we greatly reduce the complexity of the algorithm. Numerical results show that the configuration found by the algorithm significantly improves the reconstruction performance compared to a standard configuration.

We propose a computationally efficient estimator for multi-dimensional linear space-invariant system dynamics with periodic boundary conditions that attains low mean squared error from very few temporal steps. By exploiting the inherent redundancy found in many real-world spatiotemporal systems, the estimator performance improves with the dimensionality of the system. This paper provides a detailed analysis of maximum likelihood estimation of the state transition operator in linear space-invariant systems driven by Gaussian noise. The key result of this work is that, by incorporating the space-invariance prior, the mean squared error of a estimator normalized to the number of parameters is upper bounded by N-1M-1+ O(N-1M-2), where N is the number of spatial points, and M is the number of observed timesteps after the initial value.

In this paper, we address the problem of estimating a noisy, incomplete time series of a dynamical system with an unknown state evolution. The technique that we will present is transformed spiked covariance completion (TSCC), a matrix completion method for signal estimation. This method exploits the spiked covariance model of the underlying signal to develop a linear estimator that is resilient to noise. We discuss the conditions in the signal model for which this technique is applicable and compare this method against other state-of-the-art time series estimation techniques with a numerical example. Our algorithm gives estimates that are more robust to noise in comparison to the current state-of-the-art techniques that address this same estimation problem.

Knowledge of the three-dimensional spatial structure of Earth's uppermost atmosphere is necessary both to understand its role as a dynamic buffer against the solar-driven environment of interplanetary space as well as to assess the rate of its permanent escape from Earth's gravity through evaporation. The only available means of inferring atmospheric structure at these altitudes is through space-based remote sensing of solar radiation that is resonantly scattered or fluoresced by the ambient atoms. In this paper, the resultant tomographic image formation problem is formulated as an edge-preserving reconstruction algorithm based on the framework originally proposed by Mumford & Shah. Statistical interpretation of this reconstruction solution is formulated in the context of MAP estimation. The numerical results illustrate that the proposed reconstruction algorithm is capable of obtaining physically meaningful solutions that are superior to previous results formulated based on parametric assumptions on the unknown density.

Spectral imaging is a fundamental diagnostic technique in physical sciences with widespread application. Conventionally, spectral imaging techniques rely on a scanning process, which renders them unsuitable for dynamic scenes. Here we study the problem of estimating the physical parameters of interest from the measurements of a non-scanning spectral imager based on a parametric model. This inverse problem, which can be viewed as a multi-frame deblurring problem, is formulated as a maximum a posteriori (MAP) estimation problem. The global optimum of the nonlinear MAP problem is found using an efficient dynamic programming algorithm. Lastly, the method is illustrated for an application in solar spectral imaging. Numerical results suggest that estimation accuracy is comparable to the conventional slit spectroscopy, but with the added benefit of a two-dimensional fleld-of-view.

Current sensory array systems do not fully exploit tactile sensing strategies widely used by vibrissal sensing animals to explore their surroundings. We develop a new tactile fluid-flow imaging technique, which relates rat's whisker movements to tomographic imaging to extract fluid-flow characteristics with a robotic whisker array. At high Reynolds numbers, the drag force on a whisker segment is proportional to the relative velocity squared, and acts as a distributed load along the whisker length. Therefore, we propose that it is possible to map out the 2-D cross-sectional mean fluid-flow velocity field with a robotic whisker array by measuring the moment sensed at each whisker base from different directions for tomographic reconstruction. The associated inverse problem for the tomographic image formation is formulated as a MAP estimation problem and solved computationally. The experimental results demonstrate that this new approach offers a fundamentally novel sensor technology for flow-field measurements.

Photon sieves, modifications of Fresnel zone plates, are a new class of diffractive image forming devices that open up new possibilities for high resolution imaging and spectroscopy, especially at UV and x-ray regime. In this paper, we develop a novel computational photon sieve imaging modality that enables high-resolution spectral imaging. For the spatially incoherent illumination, we study the problem of recovering the individual spectral images from the superimposed and blurred measurements of the proposed photon sieve system. This inverse problem, which can be viewed as a multi frame deconvolution problem involving multiple objects, is formulated as a maximum posterior estimation problem, and solved using a fixed-point algorithm. The performance of the proposed technique is illustrated for EUV spectral imaging through numerical simulations. The results suggest that higher spatial and spectral resolution can be achieved as compared to conventional spectral imagers.

Spectroscopy is a fundamental diagnostic technique in physical sciences with widespread application. Multi-order slitless imaging spectroscopy has been recently proposed to overcome the limitations of traditional spectrographs, in particular their small instantaneous field of view. Since an inversion is required to infer the physical parameters of interest from slitless spectroscopic measurements, a rigorous theory is essential for quantitative characterization of their performance. In this paper we develop such a theory using the Cramer-Rao lower bounds for the physical parameters of interest, which are derived in terms of important instrument design considerations including the spectral orders to measure, dispersion scale, signal-to-noise ratio, and number of pixels. Our treatment provides a framework for exploring the optimal choices of these design considerations. We illustrate these concepts for an application in EUV solar spectroscopy.

A photon sieve, modification of a Fresnel zone plate, has been recently proposed to achieve higher resolution imaging and spectroscopy at UV and x-ray wavelengths. In this paper, we present Fresnel imaging formulas that relate the output of a photon sieve imaging system to its input, originating from either a coherent or incoherent extended source. By using a well-known model for the zone plate, we also provide approximations to these imaging formulas, which are more efficient to compute. These imaging relations for both photon sieve and the approximate model are crucial for effectively analyzing and solving the inverse problems that arise from the new imaging modalities enabled by photon sieves. We illustrate this by formulating the forward model of the image formation process for an application in polychromatic imaging.

Classical tomographic reconstruction methods fail for problems in which there is extreme temporal and spatial sparsity in the measured data.Reconstruction of coronal mass ejections (CMEs), a space weather phenomenon with potential negative effects on the Earth, is one such problem.However, the topological complexity of CMEs renders recent limited data reconstruction methods inapplicable.We propose an energy function, based on a phase field level set framework, for the joint segmentation and tomographic reconstruction of CMEs from measurements acquired by coronagraphs, a type of solar telescope.Our phase field model deals easily with complex topologies, and is more robust than classical methods when the data are very sparse.We use a fast variational algorithm that combines the finite element method with a trust region variant of Newton's method to minimize the energy.We compare the results obtained with our model to classical regularized tomography for synthetic CME-like images. Motivation and BackgroundOur knowledge of the physical processes that drive the sun is far from complete.Phenomena such as active regions, solar flares, coronal mass ejections (CMEs), and solar wind, all of which contribute to geoeffective events, collectively referred to as space weather, are c 2012.The copyright of this document resides with its authors.

Dynamic tomography is concerned with the image formation of a temporally changing object from its line integral projections. The problem remains challenging because of its high dimensionality. In this paper, we identify a sufficient class of dynamic tomography problems that can be solved by a state estimator that requires only linear shift-invariant filtering operations. This class includes rigid-body motion, common in biomedical imaging scenarios. The new state estimator is far less computationally demanding than classic methods such as the Kalman filter. Whereas the Kalman filter requires O(N2) memory storage and O(N3) processing for anN-dimensional problem, the state estimator derived in this work requires only O(N) storage and O(N logN) processing.

This paper describes the methodology to estimate the intrinsic parameters of atmospheric gravity waves from multiple ground-based observations of a single mesospheric airglow emission. In this configuration, several spectroscopic imagers are placed on the ground to achieve multiple perspectives of the emission as it is perturbed by gravity waves. The classical way to analyze this data is to use a tomographic approach to estimate the wave parameters. In this paper, a strategy is developed to estimate the wave parameters directly from the data without using tomography. This approach is then demonstrated with a simulation.

A tomographic forward and inverse model is presented for deriving 3-D images of ionospheric electron density from ground-based dual-frequency Global Positioning System (GPS) measurements and ionosonde data. The GPS observation geometry is discretely modeled, and a linear algebraic relationship is derived between the integrated electron density measurements and the ionospheric electron density. Because the inverse problem is ill conditioned, regularization is used to stabilize the solution in the presence of noise. In this paper, we regularize the inverse problem by incorporating neighborhood smoothness and continuity constraints applicable to general ionospheric conditions. To avoid oversmoothing of edges, nonconvex regularizing functionals are used to capture potential localized ionospheric density structures. A deterministic relaxation technique is used to minimize the proposed cost function. The specific formulation of the reconstruction geometry is directly related to the sparseness and the nonuniform distribution of the GPS ray paths. The grid boundaries, the regularization parameters, the model order, and the grid placement are selected in conjunction with available remote sensing data and appropriate optimality criteria. The algorithm is tested using simulations of ionospheric structures with actual GPS observation geometry. These simulations demonstrate the effectiveness in detecting and reconstructing ionospheric height and density fluctuations, and illustrate the statistical performance and bounds of the inversion technique.

We address the image formation of a dynamic object from projections by formulating it as a state estimation problem. The problem is solved with the ensemble Kalman filter (EnKF), a Monte Carlo algorithm that is computationally tractable when the state dimension is large. In this paper, we first rigorously address the convergence of the EnKF. Then, the effectiveness of the EnKF is demonstrated in a numerical experiment where a highly variable object is reconstructed from its projections, an imaging modality not yet explored with the EnKF. The results show that the EnKF can yield estimates of almost equal quality as the optimal Kalman filter but at a fraction of the computational effort. Further experiments explore the rate of convergence of the EnKF, its performance relative to an idealized particle filter, and implications of modeling the system dynamics as a random walk.

This paper formally addresses the asymptotic convergence of the ensemble Kalman filter (EnKF), a state estimation procedure that, when combined with a technique called localization, provides computationally tractable solutions to large-dimensional state estimation problems. The proof presented in this paper shows that the estimates given by the EnKF converge to the optimal estimates given by the Kalman filter (KF) and provides a formal justification for the use of the EnKF in dynamic remote sensing image formation. The implications of the proof are twofold: it shows that the EnKF converges to a well-defined limit and provides a formal argument that the EnKF is in fact a Monte Carlo algorithm that converges to the KF.

Determination of optimal sensor configuration is an important issue in many remote imaging modalities, such as tomographic and interferometric imaging. In this paper, a statistical optimality criterion is defined and a search is performed over the space of candidate sensor locations to determine the configuration that optimizes the criterion over all candidates. To make the search process computationally feasible, a modified version of a previously proposed suboptimal backward greedy algorithm is used. A statistical framework is developed which allows for inclusion of several widely used image constraints. Computational complexity of the proposed algorithm is discussed and a fast implementation is described. Furthermore, upper bounds on the sum of the squared error of the proposed algorithm are derived. Connections of the method to the deterministic backward greedy algorithm for the subset selection problem are presented, and two application examples are described. Five compelling optimality criteria are considered, and their performance is investigated through numerical experiments for a tomographic imaging scenario. In all cases, it is verified that the configuration designed by the proposed algorithm performs better than wisely chosen alternatives.

An attractive property of wavelet bases is their ability to sparsely represent piecewise polynomial signals. The sparsity of a wavelet-domain representation depends on several factors such as the mother wavelet, the number of decomposition levels, and the structure of the original signal. We consider the problem of selecting an overcomplete or dyadic wavelet basis that can sparsely represent a sparse piecewise polynomial signal. Most existing applications that apply wavelet-domain processing techniques to signals that are inherently sparse have not considered the sparsity of underlying signal when selecting a wavelet basis. By accounting for the initial sparseness of a signal, the maximum wavelet filter length and number of decomposition levels can be computed. Selecting a wavelet basis that satisfies these maximum values guarantees that the resulting wavelet-domain representation will be at least as sparse as the original signal. This criteria for wavelet basis selection is of use in applications having sparse source signals.

We address the reconstruction of a physically evolving unknown from tomographic measurements by formulating it as a state estimation problem. The approach presented in this paper is the localized ensemble Kalman filter (LEnKF); a Monte Carlo state estimation procedure that is computationally tractable when the state dimension is large. We establish the conditions under which the LEnKF is equivalent to the Gaussian particle filter. The performance of the LEnKF is evaluated in a numerical example and is shown to give state estimates of almost equal quality as the optimal Kalman filter but at a 95% reduction in computation.

We present a novel scheme for blind suppression of noise from a sequence of optical coherence tomography (OCT) images, such as those collected on a real-time OCT imaging system. In contrast to virtually all existing approaches to OCT denoising, our technique is specifically aimed at collections of images and is able to exploit the correlations among those images. The proposed method approximates the optimal linear denoising operator for log-transformed data using a 2-D discrete wavelet transform (DWT) to decorrelate in space and the discrete Fourier transform (DFT), or an estimated transform, to decorrelate in time. Decorrelated coefficients are then denoised and converted back to the image domain to produce denoised OCT images. Real-time OCT data processed with this technique shows significant reduction in noise

We present motivation for performing the filtering step of FBP in a non-Radon domain. Specifically, we show that for penalized-likelihood regularization, with a shift-invariant penalty function, filtering noisy projection data in a domain for which the true projection data is sparse yields filtered data that is more faithful to the ideal filtered data than directly filtering the Radon-domain data. In contrast to simply penalizing across angles, the proposed method exploits correlation in the angle dimension. This allows for simple penalty matrices to be constructed, enables penalty coefficient to be calculated in a straightforward manner, and results in easily an computed, closed-form solution for the regularizing filters. Reconstructions employing this transform-domain filtering are superior to their Radon-domain filtered counterparts.

Optimal estimation of a two-dimensional (2-D) multichannel signal ideally decorrelates the data in both channel and space and weights the resulting coefficients according to their SNR. Many scenarios exist where the required second-order signal and noise statistics are not known in which the decorrelation is difficult or expensive to calculate. An asymptotically optimal estimation scheme proposed here uses a 2-D discrete wavelet transform to approximately decorrelate the signal in space and the discrete Fourier transform to decorrelate between channels. The coefficient weighting is replaced with a wavelet-domain thresholding operation to result in an efficient estimation scheme for both stationary and nonstationary signals. In contrast to optimal estimation, this new scheme does not require second-order signal statistics, making it well suited to many applications. In addition to providing vastly improved visual quality, the new estimator typically yields signal-to-noise ratio gains 12 dB or higher for hyperspectral imagery and functional magnetic resonance images.

An inverse-theoretic approach to ultrasonic pulse-echo imaging based on nonquadratic regularization is presented, and its effectiveness is investigated computationally by: 1) evaluating the quality of the reconstruction of speckle-based images as a function of the transmit-receive bandwidth and focal number of the transducer; 2) comparing the reconstructed images with those obtained by using conventional B-mode imaging. The L-curve and the generalized cross-validation methods were evaluated as automatic regularization parameter selection techniques. The inversion using regularization produced better results than conventional B-mode imaging for high signal-to-noise ratios (SNRs). A lower bound of 30 dB for the SNR was found for this study, below which several of the image features were lost during the reconstruction process in order to control the distortion due to the noise.

Optimal detection of a known FSK-modulated binary signal in additive white Gaussian noise using a matched filter receiver requires knowledge of second-order noise statistics. The dependence on noise statistics causes the probability of detection to be sensitive to errors in the noise variance value. This makes the optimal scheme of limited use in situations where the noise statistics are unknown and cannot be estimated reliably. We propose an alternative approach, which has a more easily calculated test statistic than the optimal method and yields a constant false detection rate, regardless of noise statistics. While this approach has sub-optimal detection probability, it is significantly advantageous in applications where a primary interest is to limit false detections strictly. In addition, it allows one to determine easily the required detection length (in symbols) to achieve a desired performance level.

A robust method for tomographic image reconstruction from limited-angle noisy measurements is proposed which builds upon a combination of regularization theory and the method of projections onto convex sets (POCS). Two specific formulations of the proposed method, namely, Tikhonov-POCS and TV-POCS, are introduced and investigated. A statistical framework is developed that provides insight into the behavior of the two algorithms. The inclusion of a reference image is approached by either a coarse reconstruction or a model generated background image. The method is validated in the context of simulations for the reconstruction of highly structured images from partial projections. Results demonstrate significant improvement over conventional regularization methods in situations where the conventional techniques are inadequate.

Determination of optimal sensor configuration is an important issue in many remote imaging modalities such as tomographic and interferometric imaging. In this paper, a statistical optimality criterion is defined and a search is performed over the space of candidate sensor locations to determine the configuration that optimizes the criterion over all candidates. To make the search process computationally feasible, a modified version of a previously proposed sub-optimal backward greedy algorithm is used. Connections of the method to the deterministic backward greedy algorithm for the subset selection problem are presented and a conjecture on the optimality of the proposed method is suggested. Three compelling optimality criteria are introduced and their performance is investigated through numerical experiments for a tomographic imaging scenario. In all cases, it is verified that the chosen configuration by the proposed algorithm performs better than wisely chosen alternatives.

We describe a method for extracting atmospheric gravity wave motion from spectroscopic airglow images using two-dimensional spectral analysis. This method detects quasi-monochromatic wave components and estimates wavelengths, wave propagation directions, and phase speeds from the cross periodogram of two consecutive time-differenced images. Monte Carlo simulations have been used to validate the phase-difference technique for motion estimation and to compare its performance with a translational block-motion extraction method, which represents the conventional approach. The new technique is shown to be more precise than its predecessor. We have also applied the two techniques to real airglow images for both statistical and case studies. The variances of the phase speeds generated by both methods are insignificant relative to the geophysical variation of the gravity wave phase speeds. An individual wave study illustrates that the phase-difference method provides more stable estimation of phase speeds than the block-motion method.

Atmospheric gravity waves play a significant role in the dynamics and thermal balance of the upper atmosphere. In this paper, we present a novel technique for automated and robust calculation of momentum flux of high-frequency quasi-monochromatic wave components from spectroscopic imaging and horizontal radar wind measurements. Our approach uses the two-dimensional (2-D) cross periodogram of two consecutive Doppler-shifted time-differenced (TD) images to identify wave components and estimate intrinsic wave parameters. Besides estimating the average perturbation of dominant waves in the whole field of view, this technique applies 2-D short-space Fourier transform to the TD images to identify localized wave events. With the wave parameters acquired, the momentum flux carried by all vertically propagating wave components is calculated using an analytical model relating the measured intensity perturbation to the wave amplitude. This model is tested by comparing wave perturbation amplitudes inferred from spectroscopic images with those from sodium lidar temperature measurements. The proposed technique enables characterization of the variations in the direction and strength of gravity waves with high temporal resolution for each clear data-taking night. The nightly results provide statistical information for investigating seasonal and geographical variations in momentum flux of gravity waves.

Imaging resolution in optical coherence tomography (OCT) is a key determinant for acquiring clinically useful optical biopsies of tissues. In contrast to light or confocal microscopy, the axial and transverse resolutions in OCT are independent and each can be analyzed individually. A method for mitigating transverse blurring and the apparent loss of transverse resolution in OCT by means of Gaussian beam deconvolution is presented. Such a method provides better representation of a specimen by using known physical parameters of a lens. To implement this method, deconvolution algorithms based on a focal-dependent kernel are investigated. First, the direct inverse problem is investigated using two types of regularization, truncated singular value decomposition, and Tikhonov. Second, an iterative expectation maximization algorithm, the Richardson-Lucy algorithm, with a beam-width-dependent iteration scheme is developed. A dynamically iterative Richardson-Lucy algorithm can reduce transverse blurring by providing an improvement in the transverse point-spread-function for sparse scattering samples in regions up to two times larger than the confocal region of the lens. These deblurring improvements inside and outside of the confocal region, which are validated experimentally, are possible without introducing new optical imaging hardware or acquiring multiple images of the same specimen. Implementation of this method in sparse scattering specimens, such as engineered tissues, has the potential to improve cellular detection and categorization.

In this paper, we present a new wavelet-based estimator for 2-D multichannel signals. Estimation of a 2-D multichannel signal relies on the ability to decorrelate the signal in both space and channel. The new estimator we present uses a 2-D discrete wavelet transform to approximately decorrelate the signal in space, allowing for efficient estimation of both stationary and nonstationary signals. When channel correlation is unknown, but depends only on channel separation, the DFT may be utilized to decorrelate the channel efficiently. In contrast to the optimal estimation scheme, our new estimator does not require second-order signal statistics, making it well suited to many applications. In addition to providing vastly improved visual quality, the new estimator typically yields signal-to-noise ratio gains of over 12 dB.

In this paper, we present a novel DFT- and wavelet-based estimation scheme for hyperspectral imagery. Optimal hyperspectral image estimation relies on the ability to decorrelate the signal in both space and channel at the cost of requiring second-order signal statistics. This statistical requirement is removed by the proposed estimator, which approximately decorrelates the signal in space using a 2D discrete wavelet transform and in channel using a discrete Fourier transform. In addition to allowing extremely efficient estimation, the proposed estimator vastly improves visual quality and yields typical signal-to-noise ratio gains of over 14 dB.

Atmospheric gravity waves play a significant role in the dynamics and thermal balance of the upper atmosphere. The vertical fluxes of horizontal momentum characterizing the cross-correlation between the wave-induced vertical wind perturbations and the associated horizontal wind have proved to be difficult to measure. In this paper, we develop a novel technique for calculating momentum fluxes of monochromatic wave components from spectroscopic imaging and meteor radar wind measurement. Our approach uses the two-dimensional (2-D) cross-periodogram of two consecutive Doppler-shifted time differenced (TD) images to identify a dominant wave component and extract the wave parameters. Besides estimating the average perturbation of the dominant wave in the whole field of view (FOV), 2-D short-time Fourier transform is applied to the TD images to obtain the strongest perturbation of this wave in a portion of the FOV. With the wave parameters acquired, we calculate the momentum flux of the dominant wave component. The alternation of the direction and strength of dominant waves can be tracked for each clear night. Nightly averages provide information for investigating seasonal and geographical variation in momentum flux of gravity waves.

Spectroscopic images of atmospheric chemiluminescent airglow contain fundamental diagnostic information about the structure and dynamics of the upper atmosphere. However, westward movement of stars causes non-negligible contamination in the two-dimensional horizontal wavenumber spectra extracted from all-sky airglow images. The conventional star-removing scheme is not effective in attenuating the star artifacts in the spectra of emission intensities of gravity wave perturbation, hindering the subsequent calculation of the angular spectra and the momentum fluxes of the profiles. To address this problem, a gradient-based edge detection algorithm for locating and attenuating the undesired star signal is developed. Comparatively, this algorithm is more effective than the conventional star-removing methods. The algorithm is validated in the context of experimentally obtained spectra.

This paper presents a novel technique for wide field hyperspectral imaging using a tomographic approach which yields superior throughput over conventional schemes, an attribute that is highly desirable in spectral imaging of low signal-to-noise ratio sources. This technique is capable of simultaneous multi-object spectroscopy on point sources and imaging spectroscopy of faint diffuse emissions, and consequently has applications in astrophysical and space remote imaging at ultraviolet (UV) and optical wavelengths. Unlike conventional hyperspectral imaging techniques which raster the scene through a slit spectrograph over some time, this method encodes three dimensions of data (two spatial and one spectral) into a two-dimensional signal, using an optical system where photons from the entire scene are collected at all times. Inversion of this data back into the three-dimensional space is accomplished by formulating a tomographic reconstruction problem. Intrinsic presence of noise, however, poses difficulties on conventional inversion methods such as the filtered back-projection (FBP) or the minimum norm least squares methods such that they often produce unacceptable results. This limitation is overcome by the incorporation of regularization schemes, minimizing appropriate l/sub 1/ and l/sub 2/ norm functionals. Through simulations, the performance of this technique is demonstrated quantitatively in comparison with conventional spectral imaging techniques.

We apply a natural pixel (NP) decomposition to the problem of computerized ionospheric tomography (CIT). For tomography from very few angles, the NP approach provides some distinct advantages over standard basis expansions. The NP solution requires no prior assumption and as such embeds into the solution the natural spatial resolution supported by the data. For the uniquely constrained CIT geometry, however, NP estimated fields will contain significant negative values. We propose a method of improving the NP estimates by enforcing positivity through an entropy regularization algorithm. These techniques are demonstrated in an example.