The University of Nebraska-Lincoln has developed an ultra- wideband random noise radar operating over the 1-2 GHz frequency range. The system uses the technique of heterodyne correlation, and is thus phase-coherent. It has therefore been used in applications such as interferometry, polarimetry, and Doppler estimation. Recently, the system has been used for SAR and ISAR imaging of targets and terrain. This work has brought to the forefront various issues, such as the type of images obtained when utilizing a truly stochastic signal as a transmit waveform, and the techniques employed to realize this image. The natural answer to the first question is that the image obtained is based upon the expected value of the return signals, in the probabilistic sense of the word. This leads to answering the second question by determining what sort of estimators one would use to estimate this expected value. In this work, we will discuss the expected value of the image and its properties. We will then examine single look ISAR images collected in anechoic chamber experiments performed at the University of Nebraska-Lincoln.

Under the sponsorship of the U.S. Army's National Ground Intelligence Center (NGIC), researchers at U. Mass. Lowell's Submillimeter-Wave Technology Laboratory (STL) and Center for Electromagnetic Materials and Optical Systems (CEMOS) investigated the feasibility of detecting non-metallic structures embedded in various types of soil using a 1-GHz ground penetrating radar by establishing a 1/10th-scale laboratory environment with two spot-focusing X-band (10- GHz) lens antennae and an HP8510B Network Analyzer. Achieving similitude with the full-scale environment required fabricating replicas that were dimensional and dielectric scale-models of the non-metallic structures of interest (i.e. anti-personnel mines), as well as rocks, and soil with various levels of moisture content. The 1/10th- scale replicas were constructed form models at 10.0-GHz. The monostatic X-band measurements were acquired in an anechoic environment, and digital images of the backscattered radar data from the 1/10th-scale composite scenes were processed using inverse synthetic aperture radar (ISAR) signal processing routines, and also PDFT superresolution imaging techniques. Based on the 1/10th-scale signature measurements performed, the feasibility of detecting a VS-50 anti-personnel mine buried in dry loam at a depth of 11.2mm was established. The full-scale radar cross-section of a VS=50 mine in this configuration was estimated to be -25 dBsm. Radar cross section values were not established for the structures embedded in the wet loam due to a change in the intensity scale (an inherent property of the superresolution algorithm), which changed for each image. However, the embedded objects were detected by the PDFT algorithm, showing promise for the future of this research.

In the framework of ARCHEO, a national research project funded by the Italian Ministry for Universities and Scientific and Technological Research (M.U.R.S.T.), a new ground penetrating radar (GPR) has been developed by the Italian Consortium for Research on Advanced Remote Sensing Systems (CO.RI.S.T.A.). The system has been specially designed to meet archaeological requirements and it will be tested the two archaeological sites of Sinuessa and Cales, in the Southern Italy. An innovative feature of ARCHEO concerns the exploitation of that of a multiview multistatic measurement scheme (at several frequencies) rather than a more common multimonostatic (or multibistatic). In order to reconstruct buried objects starting from the measurement data collected with such an acquisition strategy, it is made use of an inverse scattering technique. With the real project ARCHEO in mind (in particular this scheme of measurement), this paper deals with a theoretical discussion on the features of the class of retrievable profiles by G.P.R. data, within the framework of a linear model for electromagnetic scattering in a two dimensional lossless half space. For a given range of frequencies exploitable, multiview multistatic measurements can be useful in G.P.R. prospecting because they can provide information on low spatial harmonic components of an unknown object not attainable from the multimonostatic scheme exploiting the same frequency range. In particular, we show that, for a given band of work frequencies, the class of the unknowns retrievable by a multiview multistatic multifrequency measurement configuration can be is not much different from that attainable within a multimonostatic configuration with the addition of multiview multistatic data taken at the lowest of the frequencies adopted.

Atmospheric turbulence severely degrades the quality and resolution of images captured by ground based telescopes. Although multiconjugate adaptive optics systems have the potential to compensate over a wide field of view they require characterization of the 3D structure of the atmosphere. Many of the existing remote sensing techniques that analyze scintillation measurements are restricted to binary star measurements, due to the ill-conditioning of the corresponding single star problem. In this paper we discuss the possibility of measuring the turbulent layers in the atmosphere using scintillation measurements made from a single star.

If one replaces the ordinary single receiver of a synthetic- aperture radar (SAR) with a linear array of receivers underneath the wings of an aircraft, one obtains a 3D signal history (to spatial dimensions plus the frequency dimension) that allows the computation of a 3D image (angle-angle- range) of a scene. Because of the limited extent of the wingspan, the cross-track resolution is limited, driving one to use high frequencies, such as 94 GHz, having a wavelength of 3.2 mm. At such short wavelengths, the motion of the wings during the synthetic-aperture integration time will cause large phase errors that will severely blur the image. This paper describes an approach to measuring and correcting these and other phase errors. The approach involves having three transmitters, each at a slightly different monotone frequency. Relative to the first receiver, the second is displaced along the direction of the array of receivers and the third is displaced perpendicular to that direction. The array of receivers can separate the three corresponding signals reflected form the ground from one another. We will show mathematical analysis that allows us to determine the phase errors at each receiver form these three signals. It is required either that the three transmitters experience the same phase errors (so they should be rigidly mounted together) or that the phase errors at the three transmitters are measured. No measurement of phase errors on the receivers is required.

There is currently much interest in deploying large space- based telescopes for various applications including fine- resolution astronomical imaging and earth observing. Often a large primary mirror is synthesized by the precise alignment of several smaller mirror segments. Misalignment or misfigure of these segments results in phase error which degrade the resolution of collected imagery. Phase diversity (PD) is a technique used to infer unknown phase aberrations form image data. It requires the collection of two or more images of the same object, each incorporating a known phase perturbation in addition to the unknown aberrations. Statistical estimation techniques are employed to identify a combination of object and aberrations that is consistent with all of the collected images. The wavefront- sensing performance of PD is evaluated through simulation for a variety of signal and aberration strengths. The aberrations are parameterizes by piston and tilt misalignment of each segment. An unknown extended scene is imaged, complicating the estimation procedure. Since wavefront correction is often an iterative process, moderate estimation errors can be corrected by subsequent estimates. The interpretation of iterative wavefront adjustments as creating new phase-diversity channels suggests a more sophisticated processing approach, called Actuated Phase Diversity. This technique is shown to significantly improve PD wavefront-sensing performance.

Over a wide field of view (e.g., 100 arcsec in optical astronomy) the point spread function due to atmospheric effects is found to be far form position invariant, and appears as a combination of local warping and local blurring. Recently, we discussed a method in which the first step in restoration is to register all points in every frame of a movie sequence to the corresponding points in a prototype image. After registration, each frame is de- warped and summed to form an average, motion-blur corrected result. Previously, we applied a hierarchical, windowed cross correlation process to obtain local x and y registration information, similar to common methods in stereo cartography. We discuss a new approach to image registration for this purpose. Suppose two images to be registered differ mainly in varying random, but spatially coherent warping (such as occurs as one effect of a slowly varying wavefront tip-tilt over a wide field of vies). Imagine that one image, the reference image, is represented by a solid surface corresponding to its intensity distribution. Imagine that the second image is also represented by a surface, but in the form of a flexible, rubber mold. If the two images are identical, then the mold fits the solid like a glove. If one image includes local warping relative to the other, then the mold or glove must be forced to fit though local distortions.

The atmosphere introduces random distortions to propagating wavefronts, resulting in speckled images at ground based telescopes. Blind deconvolution seeks to solve this problem of reconstructing the object and the atmospheric point spread function simultaneously. Due to the ill-posed nature of the problem, the quality of the reconstructions depends strongly on the available a priori information, with a tradeoff between the potential accuracy of the solution and the ease of obtaining it. We investigate the different a priori assumptions that can be made and compare their effectiveness in contrasting the solution.

Global surface wave dispersion maps are useful tools for checking the internal consistency of surface wave data that are used int eh modeling of the 3D elastic heterogeneity within the Earth. This paper describes a variety of data that constrain such maps and outlines the modeling techniques that are used to create them. Some reasons why current maps obtained by different workers may still disagree are discussed.

Turning-point filtering is a method to focus acoustic energy from a vertical line array receiver into an oceanographically meaningful image. The turning-point filter is a simple modification of the linear beamformer which compensates for the sound-speed variation in the water column. Focused peaks in the image (phase-speed, group- speed space) can be regarded as accurate samples of the underlying dispersion curve whenever the WKBJ approximation is valid. Applying this method to real data, still fails to produce a useful observable because of small-scale variations in the ocean. The ocean acoustic waveguide has limited space, time, and frequency coherences which limit the image sharpness. Accounting for this by incoherently combining the limited coherent subspaces generates easily measured observables as demonstrated.

We have performed a series of acoustic phase conjugation (PC0 experiments in shallow water. A time reversal mirror (TRM) was implemented for center frequencies of 450 Hz and 3500 Hz. Very sharp focal regions out to ranges of 30 km were obtained. Analysis, including attenuation effects, indicates that the diffraction limit on the size of the focal region was reached. This has implications for defining the maximum resolution of a matched field processor because the latter is simply a hybrid computational implementation of PC. The fact that a TRM both spatially and temporally refocuses energy with the aid of a probe suggests that ocean self-equalization with respect to communication processing is possible. Indeed, a preliminary demonstration of this self-equalization process was experimentally achieved.

In many experimental observation systems where the goal is to record a 3D observation of an object, or a set of objects, a lower dimensional projection of the intended subject is obtained. In come situations only the statistical properties of such objects is desired: the 3D probability density function. This article demonstrates that under special symmetries this function can be obtained form a 2D probability density function which, has been obtained from the observed, projected data. Standard tomographic theorems can be used to guarantee the uniqueness of this function and a natural basis set can be used in computing the 3D function from the two dimensional projection. Here, the theory of this inversion is explored from a theoretical and numerical point of view with some examples of data functions taken from scientific experiments.

In synthetic aperture sonar, the highest platform speed is limited as a result of the low speed of sound in water and the requirement for adequate sampling in the along-track direction. This can result in slow seafloor mapping. The highest allowable platform speed can be increased by using a linear array of hydrophones. The signal-to-noise can also be improved by using multiple sets of hydrophone arrays. Maximum-likelihood estimation of images using data from sets of hydrophone arrays that each under-sample the underlying signal to different degrees is described. Simulations for synthetic aperture sonar imaging show that this improves the images obtained over those from a single array.

This paper presents a method for constructing couples, one dimensional electrical conductivity models of the Earth from surface geoelectric measurements. The construction of the individual models is a nonlinear inverse problem that can be approached by linearization techniques combined with iterative methods and Tikhonov's regularization. The standard application of these techniques usually leads to smooth models that represent a continuous variation of conductivity with depth. In a previous work, we described how these methods can be modified to incorporate what is known in the Computer Vision as the line process (LP) decoupling technique, which has the ability to include discontinuities in the models. This results in piecewise smooth models which are often more adequate for representing stratified media. In this work, the case of several resistivity soundings located along a line transect is considered. For every sounding site, a one dimensional model is developed, and the models are horizontally coupled in order to include information from neighboring sites. Numerical experiments and application to field data are presented. In both cases, it is assumed that the data are contaminated by static shift effects. The algorithm automatically takes these effects into account. The examples illustrate the performance of the combined LP and Tikhonov's regularization method in the solution of difficult practical problems.

A method for estimating the point spread function of a remotely sensed image is described. The technique developed is based on locating and measuring blurred linear features in the imagery and tomographically reconstructing the point spread function. Image features able to be modeled by a single step function or by a combination of two steps are located. For the latter cases a form of blind deconvolution is applied to extract the estimate of the line spread function (equivalent to the projection of the point spread function in the direction of the feature). The process is unsupervised and requires only that the image contains suitable linear features. Examples are given of the estimation of blur in satellite images.

When imaging the ground from the air, distortions can occur if the imagery was created form an electro-optical line scanner pointing to nadir and mounted on the bottom of an airborne platform. The inability of the aircraft to maintain a perfect trajectory can cause the distortions. In the worst case scenario, camera stabilizers fail, no geographical reference or navigation data is available, and the sensor periodically fails leaving incomplete data for image construction. Motion compensation can restore the images. This paper describes various distortions that can be created for an airborne nadir-aimed line scanner. A motion-compensation technique is introduced that combines multiple cues from geographical reference and navigation data as well as line-scan matched filtering. A semi- automated restoration implementation is introduced followed by the automated line-scan matched filter implementation. These various compensation techniques provide backup for each other thus creating a more efficient motion- compensation system. Even in the worst case scenario, the system continues to attempt motion compensation using an optimal line-scan matched filtering technique. The results of using this automated technique for motion compensation is demonstrated using simulated high-definition imagery and then using actual electro-optical and hyperspectral images that were obtained form the Dynamic Data Base (DDB) program sponsored by the Defense Advanced Research Projects Agency (DARPA).

Recently, a new approach to hyperspectral imaging, relying on the theory of computed tomography, was proposed by researchers at the Air Force Research Laboratory. The approach allows all photons to be recorded and therefore increases robustness of the imaging system to noise and focal plane array non-uniformities. However, as all computed tomography systems, the approach suffers form the limited angle problem, which obstructs reconstruction of the hyperspectral information. In this work we present a direct, one-step algorithm for reconstruction of the unknown information based on a priori knowledge about the hyperspectral image.

High-resolution synthetic aperture radar (SAR) images can be blurred by phase perturbations induced by uncompensated sensor motion and/or unknown propagation effects caused by inhomogeneities in the atmosphere, troposphere, or ionosphere. The inability of the sensor platform to compensate for these effects has driven the development of SAR autofocus algorithms, which are a particular class of blind restoration algorithms. Phase Gradient Autofocus (PGA) was the first robust non- parametric phase estimation and correction algorithm. It has been an enabling technology for high-resolution SARs and is currently being used in a number of operational SAR systems. Most phase errors experienced by SARs defocus the image in one dimension. However, some proposed systems, such as satellite-based UWB foliage penetration (FOPEN) systems will suffer from potentially severe propagation effects through the ionosphere, including Faraday rotation, dispersion, and scintillation. These effects would cause defocus coupled in range and cross-range, degrading the SAR image by a non-separable 2D phase error. In this work, we present the 2D formulation of PGA and some preliminary results. We also describe some of the additional difficulties that may appear in 2D autofocus: phase residues or branch points and a lack of available redundancy.

The concept of linear diffraction tomography is reviewed. Using low coherence tomography as a model we illustrate the importance of gating mechanisms to expand the range of applications, for which linear inverse scattering methods can be used, into the multiple scattering regime. Based on heuristic arguments space-bandwidth product grating (SBPG) is introduced as a generalization of existing gating methods. For turbid media SBPG can be based on geometrical optics and the corresponding phase space representation. First implications to expand the phase space concept to diffractive structures with high permittivity contrast are discussed. Our theoretical investigation is complemented with imaging results originating form numerical simulations.

Quantifying the degree of non linearity with respect to the permittivity profile represents in interesting possibility for quantifying the difficulty of both forward and inverse scattering problems. With reference to the 2D case, in this paper new tools are proposed that allow to determine the degree of non linearity while changing maximum value, dimensions and spatial frequency content of the unknown permittivity profile, as well as polarization of the incident field. As such, the proposed tools allow to identify new solution strategy for the inverse problem and the simpler nature of the TE (vectorial) problem. Numerical examples support the conclusion.

The information content of radiated fields and the achievable resolution limits in the reconstruction of a bounded current distribution are dealt with. The analysis refers to the scalar and one dimensional case of a rectilinear and bounded electric current distribution when data are collected over a segment location in the Fresnel or near zone, orthogonal and centered with respect to the source. In the Fresnel zone, the investigation is carried out by means of the analytical Singular Value Decomposition (SVD) of the radiation operator providing the unknown-data mapping. This has been made possible thanks to the introduction of suitable weighted scalar products both in the unknown and data spaces. In the near zone, a numerical approach based on the SVD of the radiation operator has been followed. The effect of the geometrical parameters of the measurement configuration on depth resolving power is also discussed.

Over the last ten years progress has been made in developing inverse scattering algorithms that go beyond the range of applicability of the first Born and Rytov approximations. Our efforts have focused on a nonlinear filtering technique which appears at first glance to be straightforward to implement and offer the possibility of recovering strongly scattering structures. Upon applying the method to various simulated and real data sets, its performance has been inconsistent. In this paper we discuss the various numerical concerns that have arisen from executing a nonlinear filter on limited sampled noisy data and clarify the potential advantages and limitations of this approach.

We develop a 2D subarray processing technique as an extension of 1D subarray processing to form the image of an inverse synthetic aperture radar (ISAR). By using the 2D processing based on the Capon's spectral estimation method, a high resolution image can be obtained as compared with the conventional Fourier transform and the 1D subarray based method. Our method minimizes the mean output power as much as possible to minimize the interference energy, while the desired scatterer's energy is preserved by using the constraint. Some simulation results are given to demonstrate the performance of the proposed method.

In order to understand at the atomic level how a biological macromolecule functions, a detailed knowledge of its 3D structure is essential. Unlike soluble proteins, integral membrane proteins are usually recalcitrant to the growth of large, well-ordered 3D crystals, which is necessary for high-resolution x-ray crystallographic analyses. An alternative approach is to grown thin, one molecule thick 2D crystals in lipid bilayers and apply electron crystallography to solve the structures. Lipids surround the membrane protein in such a 2D crystal, which allows for a direct assay of function. Another notable advantage of electron crystallography is that phases can be directly obtained form the images unlike in the case of x-ray where phases must be determined indirectly by methods such as isomorphous replacement etc. The availability of the phase information partially compensates for the lack of data at the highest resolution (typically approximately 3.5A and beyond) because of low-contrast in the images. We briefly review the method of recording high-resolution data from many tilted views of a 2D crystal, merging of phase and amplitudes form images and diffraction patterns respectively and the calculation of a 3D density map. The results from such an analysis applied to the human water channel is discussed in the context of its structure/function relationship.

A statistical model for the object and the complete image formation process in cryo electron microscopy of viruses is presented. Using this model, maximum likelihood reconstructions of the 3D structure of viruses are computed using the expectation maximization algorithm and an example based on Cowpea mosaic virus is provided.

A likelihood-based approach to density modification for macromolecular crystallography is presented. The approach can be applied in many cases where some information is available about the electron density at various points in the unit cell. The most important aspect of the method consists of likelihood functions that represent the probability that a particular value of electron density is consistent with prior expectations for the electron density at that point in the unit cell. Such likelihood functions are combined with likelihood functions based on experiment and with any prior knowledge about structure factors to form a combined likelihood function for each structure factor. An approach for maximizing the combined likelihood function that is simple and rapid is developed.

The central problem in the determination of protein structures form x-ray diffraction dada (x-ray crystallography) corresponds to a phase retrieval problem with undersampled amplitude data. Algorithms for this problem that have an increased radius of convergence have the potential for reducing the amount of experimental work, and cost, involved in determining protein structures. We describe such an algorithm. Application of the algorithm to a simulated crystallographic problem shows that it converges to the correct solution, with no initial phase information, where currently used algorithms fail. The results lend support to the possibility of ab initio phasing in protein crystallography.

The M&diaero;bius inversion formula is an interesting theorem from number theory that has application to a number inverse problems, particularly lattice problems. Specific inverse problems, however, often require related M&diaero;bius inversion formulae that can be derived from the fundamental formula. Derivation of such formulae is not easy for the non- specialist, however. Examples of the kinds of inversion formulae that can be derived and their application to inverse lattice problems are described.

An analysis of the spatial resolution and sensitivity of Fourier transform method for fringe detection is carried out. The spatial resolution degradation due to Fourier transform is discussed through a signal processing technique. It is found that the upper-limit of spatial resolution for phase measurement is half the carrier fringe pitch, or half the grid pitch for grid method. The formulation of sensitivity using signal processing and communication theory is also performed and analyzed. The upper limit of the sensitivity for phase measurement is 2(pi) dividing by the number of pixels in a line of the fringe image. Measures to improve the spatial resolution, sensitivity are finally discussed.

Multi-slice helical beam scanning involves cone-beam geometry. The primary advantages for use of divergent cone- beams include reduced data acquisition, improved image resolution and optimized photon utilization. Due to the complexity of 3D cone-beam reconstruction, approximate algorithms have been sought to handle the cone-beam reconstruction. This paper presents a new approximate algorithm termed as oblique surface reconstruction (OSR). Theoretical considerations as well as the reconstruction of simulated phantom data in comparison to the current standard 180 degree(s) LI are presented. OSR is shown to be effective and practical to generate images with diagnostic quality.

During the last few years, OCT has demonstrated considerable promise as a method of high-resolution intravascular imaging. The goal of this study was to apply and to test the applicability of the rotating kernel transformation (RKT) technique to the speckle reduction and enhancement of OCT images. The technique is locally adaptive. It is based on sequential application of directional masks and selection of the maximum of all outputs. This method enhances the image features by emphasizing thin edges while suppressing a noisy background. Qualitatively, the RKT algorithm provides noticeable improvement over the original image. All processed images are smoother and have better-defined borders of media, intima, and plaque. The quantitative evaluation of RKT performance showed that in terms of average contrast-to-noise ratio, there is a significant improvement in image quality between original and enhanced images. The RKT image enhancement technique shows great promise in improving OCT images for superior boundary identification.

Optical diffusion imaging is a new imaging modality that promises great potential in applications such as medical imaging, environmental sensing and nondestructive testing. It presents a difficult nonlinear image reconstruction problem however. An inversion algorithm is formulated in Bayesian framework, and an efficient optimization technique that uses iterative coordinate descent is presented. A general multigrid optimization technique for nonlinear image reconstruction problems is developed and applied to the optical diffusion imaging problem. Numerical results show that this approach improves the quality of reconstructions and dramatically decreases computation times.