Sub-aperture SAR Imaging with Uncertainty Quantification

In the problem of spotlight mode airborne synthetic aperture radar (SAR) image formation, it is well-known that data collected over a wide azimuthal angle violate the isotropic scattering property typically assumed. Many techniques have been proposed to account for this issue, including both full-aperture and sub-aperture methods based on filtering, regularized least squares, and Bayesian methods. A full-aperture method that uses a hierarchical Bayesian prior to incorporate appropriate speckle modeling and reduction was recently introduced to produce samples of the posterior density rather than a single image estimate. This uncertainty quantification information is more robust as it can generate a variety of statistics for the scene. As proposed, the method was not well-suited for large problems, however, as the sampling was inefficient. Moreover, the method was not explicitly designed to mitigate the effects of the faulty isotropic scattering assumption. In this work we therefore propose a new sub-aperture SAR imaging method that uses a sparse Bayesian learning-type algorithm to more efficiently produce approximate posterior densities for each sub-aperture window. These estimates may be useful in and of themselves, or when of interest, the statistics from these distributions can be combined to form a composite image. Furthermore, unlike the often-employed lp-regularized least squares methods, no user-defined parameters are required. Application-specific adjustments are made to reduce the typically burdensome runtime and storage requirements so that appropriately large images can be generated. Finally, this paper focuses on incorporating these techniques into SAR image formation process. That is, for the problem starting with SAR phase history data, so that no additional processing errors are incurred

Bayesian super-resolution with application to radar target recognition

This thesis is concerned with methods to facilitate automatic target recognition using images generated from a group of associated radar systems. Target recognition algorithms require access to a database of previously recorded or synthesized radar images for the targets of interest, or a database of features based on those images. However, the resolution of a new image acquired under non-ideal conditions may not be as good as that of the images used to generate the database. Therefore it is proposed to use super-resolution techniques to match the resolution of new images with the resolution of database images. A comprehensive review of the literature is given for super-resolution when used either on its own, or in conjunction with target recognition. A new superresolution algorithm is developed that is based on numerical Markov chain Monte Carlo Bayesian statistics. This algorithm allows uncertainty in the superresolved image to be taken into account in the target recognition process. It is shown that the Bayesian approach improves the probability of correct target classification over standard super-resolution techniques. The new super-resolution algorithm is demonstrated using a simple synthetically generated data set and is compared to other similar algorithms. A variety of effects that degrade super-resolution performance, such as defocus, are analyzed and techniques to compensate for these are presented. Performance of the super-resolution algorithm is then tested as part of a Bayesian target recognition framework using measured radar data

Novel Methods in Computational Imaging with Applications in Remote Sensing

This dissertation is devoted to novel computational imaging methods with applications in remote sensing. Computational imaging methods are applied to three distinct applications including imaging and detection of buried explosive hazards utilizing array radar, high resolution imaging of satellites in geosynchronous orbit utilizing optical hypertelescope arrays, and characterization of atmospheric turbulence through multi-frame blind deconvolution utilizing conventional optical digital sensors. The first application considered utilizes a radar array employed as a forward looking ground penetrating radar system with applications in explosive hazard detection. A penalized least squares technique with sparsity-inducing regularization is applied to produce imagery, which is consistent with the expectation that objects are sparsely populated but extended with respect to the pixel grid. Additionally, a series of pre-processing steps is demonstrated which result in a greatly reduced data size and computational cost. Demonstrations of the approach are provided using experimental data and results are given in terms of signal to background ratio, image resolution, and relative computation time. The second application involves a sparse-aperture telescope array configured as a hypertelescope with applications in long range imaging. The penalized least squares technique with sparsity-inducing regularization is adapted and applied to this very different imaging modality. A comprehensive study of the algorithm tuning parameters is performed and performance is characterized using the Structure Similarity Metric (SSIM) to maximize image quality. Simulated measurements are used to show that imaging performance achieved using the pro- posed algorithm compares favorably in comparison to conventional Richardson-Lucy deconvolution. The third application involves a multi-frame collection from a conventional digital sensor with the primary objective of characterizing the atmospheric turbulence in the medium of propagation. In this application a joint estimate of the image is obtained along with the Zernike coefficients associated with the atmospheric PSF at each frame, and the Fried parameter r0 of the atmosphere. A pair of constraints are applied to a penalized least squares objective function to enforce the theoretical statistics of the set of PSF estimates as a function of r0. Results of the approach are shown with both simulated and experimental data and demonstrate excellent agreement between the estimated r0 values and the known or measured r0 values respectively

Automatic Target Recognition in Synthetic Aperture Radar Imagery: A State-of-the-Art Review

The purpose of this paper is to survey and assess the state-of-the-art in automatic target recognition for synthetic aperture radar imagery (SAR-ATR). The aim is not to develop an exhaustive survey of the voluminous literature, but rather to capture in one place the various approaches for implementing the SAR-ATR system. This paper is meant to be as self-contained as possible, and it approaches the SAR-ATR problem from a holistic end-to-end perspective. A brief overview for the breadth of the SAR-ATR challenges is conducted. This is couched in terms of a single-channel SAR, and it is extendable to multi-channel SAR systems. Stages pertinent to the basic SAR-ATR system structure are defined, and the motivations of the requirements and constraints on the system constituents are addressed. For each stage in the SAR-ATR processing chain, a taxonomization methodology for surveying the numerous methods published in the open literature is proposed. Carefully selected works from the literature are presented under the taxa proposed. Novel comparisons, discussions, and comments are pinpointed throughout this paper. A two-fold benchmarking scheme for evaluating existing SAR-ATR systems and motivating new system designs is proposed. The scheme is applied to the works surveyed in this paper. Finally, a discussion is presented in which various interrelated issues, such as standard operating conditions, extended operating conditions, and target-model design, are addressed. This paper is a contribution toward fulfilling an objective of end-to-end SAR-ATR system design

Short-Range Millimeter-Wave Sensing and Imaging: Theory, Experiments and Super-Resolution Algorithms

Recent advancements in silicon technology offer the possibility of realizing low-cost and highly integrated radar sensor and imaging systems in mm-wave (between 30 and 300 GHz) and beyond. Such active short-range mm-wave systems have a wide range of applications including medical imaging, security scanning, autonomous vehicle navigation, and human gesture recognition. Moving to higher frequencies provides us with the spectral and spatial degrees of freedom that we need for high resolution imaging and sensing application. Increased bandwidth availability enhances range resolution by increasing the degrees of freedom in the time-frequency domain. Cross-range resolution is enhanced by the increase in the number of spatial degrees of freedom for a constrained form factor. The focus of this thesis is to explore system design and algorithmic development to utilize the available degrees of freedom in mm-wave frequencies in order to realize imaging and sensing capabilities under cost, complexity and form factor constraints. We first consider the fundamental problem of estimating frequencies and gains in a noisy mixture of sinusoids. This problem is ubiquitous in radar sensing applications, including target range and velocity estimation using standard radar waveforms (e.g., chirp or stepped frequency continuous wave), and direction of arrival estimation using an array of antenna elements. We have developed a fast and robust iterative algorithm for super-resolving the frequencies and gains, and have demonstrated near-optimal performance in terms of frequency estimation accuracy by benchmarking against the Cramer Rao Bound in various scenarios.Next, we explore cross-range radar imaging using an array of antenna elements under severe cost, complexity and form factor constraints. We show that we must account for such constraints in a manner that is quite different from that of conventional radar, and introduce new models and algorithms validated by experimental results. In order to relax the synchronization requirements across multiple transceiver elements we have considered the monostatic architecture in which only the co-located elements are synchronized. We investigate the impact of sparse spatial sampling by reducing the number of array antenna elements, and show that ``sparse monostatic'' architecture leads to grating lobe artifact, which introduces ambiguity in the detection/estimation of point targets in the scene. At short ranges, however, targets are ``low-pass'' and contain extended features (consisting of a continuum of points), and are not well-modeled by a small number of point scatterers. We introduce the concept of ``spatial aggregation,'' which provides the flexibility of constructing a dictionary in which each atom corresponds to a collection of point scatterers, and demonstrate its effectiveness in suppressing the grating lobes and preserving the information in the scene.Finally, we take a more fundamental and systematic approach based on singular decomposition of the imaging system, to understand the information capacity and the limits of performance for various geometries. In general, a scene can be described by an infinite number of independent parameters. However, the number of independent parameters that can be measured through an imaging system (also known as the degrees of freedom of the system) is typically finite, and is constrained by the geometry and wavelength. We introduce a measure to predict the number of spatial degrees of freedom of 1D imaging systems for both monostatic and multistatic array architectures. Our analysis reveals that there is no fundamental benefit in multistatic architecture compared to monostatic in terms of achievable degrees of freedom. The real benefit of multistatic architecture from a practical point of view, is in being able to design sparse transmit and receive antenna arrays that are capable of achieving the available degrees of freedom. Moreover, our analytical framework opens up new avenues to investigate image formation techniques that aim to reconstruct the reflectivity function of the scene by solving an inverse scattering problem, and provides crucial insights on the achievable resolution

Image Restoration

This book represents a sample of recent contributions of researchers all around the world in the field of image restoration. The book consists of 15 chapters organized in three main sections (Theory, Applications, Interdisciplinarity). Topics cover some different aspects of the theory of image restoration, but this book is also an occasion to highlight some new topics of research related to the emergence of some original imaging devices. From this arise some real challenging problems related to image reconstruction/restoration that open the way to some new fundamental scientific questions closely related with the world we interact with

Elevation and Deformation Extraction from TomoSAR

3D SAR tomography (TomoSAR) and 4D SAR differential tomography (Diff-TomoSAR) exploit multi-baseline SAR data stacks to provide an essential innovation of SAR Interferometry for many applications, sensing complex scenes with multiple scatterers mapped into the same SAR pixel cell. However, these are still influenced by DEM uncertainty, temporal decorrelation, orbital, tropospheric and ionospheric phase distortion and height blurring. In this thesis, these techniques are explored. As part of this exploration, the systematic procedures for DEM generation, DEM quality assessment, DEM quality improvement and DEM applications are first studied. Besides, this thesis focuses on the whole cycle of systematic methods for 3D & 4D TomoSAR imaging for height and deformation retrieval, from the problem formation phase, through the development of methods to testing on real SAR data. After DEM generation introduction from spaceborne bistatic InSAR (TanDEM-X) and airborne photogrammetry (Bluesky), a new DEM co-registration method with line feature validation (river network line, ridgeline, valley line, crater boundary feature and so on) is developed and demonstrated to assist the study of a wide area DEM data quality. This DEM co-registration method aligns two DEMs irrespective of the linear distortion model, which improves the quality of DEM vertical comparison accuracy significantly and is suitable and helpful for DEM quality assessment. A systematic TomoSAR algorithm and method have been established, tested, analysed and demonstrated for various applications (urban buildings, bridges, dams) to achieve better 3D & 4D tomographic SAR imaging results. These include applying Cosmo-Skymed X band single-polarisation data over the Zipingpu dam, Dujiangyan, Sichuan, China, to map topography; and using ALOS L band data in the San Francisco Bay region to map urban building and bridge. A new ionospheric correction method based on the tile method employing IGS TEC data, a split-spectrum and an ionospheric model via least squares are developed to correct ionospheric distortion to improve the accuracy of 3D & 4D tomographic SAR imaging. Meanwhile, a pixel by pixel orbit baseline estimation method is developed to address the research gaps of baseline estimation for 3D & 4D spaceborne SAR tomography imaging. Moreover, a SAR tomography imaging algorithm and a differential tomography four-dimensional SAR imaging algorithm based on compressive sensing, SAR interferometry phase (InSAR) calibration reference to DEM with DEM error correction, a new phase error calibration and compensation algorithm, based on PS, SVD, PGA, weighted least squares and minimum entropy, are developed to obtain accurate 3D & 4D tomographic SAR imaging results. The new baseline estimation method and consequent TomoSAR processing results showed that an accurate baseline estimation is essential to build up the TomoSAR model. After baseline estimation, phase calibration experiments (via FFT and Capon method) indicate that a phase calibration step is indispensable for TomoSAR imaging, which eventually influences the inversion results. A super-resolution reconstruction CS based study demonstrates X band data with the CS method does not fit for forest reconstruction but works for reconstruction of large civil engineering structures such as dams and urban buildings. Meanwhile, the L band data with FFT, Capon and the CS method are shown to work for the reconstruction of large manmade structures (such as bridges) and urban buildings

Sensor array signal processing : two decades later

Caption title.Includes bibliographical references (p. 55-65).Supported by Army Research Office. DAAL03-92-G-115 Supported by the Air Force Office of Scientific Research. F49620-92-J-2002 Supported by the National Science Foundation. MIP-9015281 Supported by the ONR. N00014-91-J-1967 Supported by the AFOSR. F49620-93-1-0102Hamid Krim, Mats Viberg