Autofocused Spotlight SAR Image Reconstruction of Off-Grid Sparse Scenes

Synthetic aperture radar (SAR) has significant role in remote sensing. Phase errors due to uncompensated platform motion, measurement model mismatch, and measurement noise can cause degradations in SAR image reconstruction. For efficient processing of the measurements, image plane is discretized and autofocusing algorithms on this discrete grid are employed. However, in addition to the platform motion errors, the reflectors, which are not exactly on the reconstruction grid, also degrade the image quality. This is called the off-grid target problem. In this paper, a sparsity-based technique is developed for autofocused spotlight SAR image reconstruction that can correct phase errors due to uncompensated platform motion and provide robust images in the presence of off-grid targets. The proposed orthogonal matching pursuit-based reconstruction technique uses gradient descent parameter updates with built in autofocus. The technique can reconstruct high-quality images by using sub Nyquist rate of sampling on the reflected signals at the receiver. The results obtained using both simulated and real SAR system data show that the proposed technique provides higher quality reconstructions over alternative techniques in terms of commonly used performance metrics. © 2017 IEEE

SAR image reconstruction by expectation maximization based matching pursuit

Cataloged from PDF version of article.Synthetic Aperture Radar (SAR) provides high resolution images of terrain and target reflectivity. SAR systems are indispensable in many remote sensing applications. Phase errors due to uncompensated platform motion degrade resolution in reconstructed images. A multitude of autofocusing techniques has been proposed to estimate and correct phase errors in SAR images. Some autofocus techniques work as a post-processor on reconstructed images and some are integrated into the image reconstruction algorithms. Compressed Sensing (CS), as a relatively new theory, can be applied to sparse SAR image reconstruction especially in detection of strong targets. Autofocus can also be integrated into CS based SAR image reconstruction techniques. However, due to their high computational complexity, CS based techniques are not commonly used in practice. To improve efficiency of image reconstruction we propose a novel CS based SAR imaging technique which utilizes recently proposed Expectation Maximization based Matching Pursuit (EMMP) algorithm. EMMP algorithm is greedy and computationally less complex enabling fast SAR image reconstructions. The proposed EMMP based SAR image reconstruction technique also performs autofocus and image reconstruction simultaneously. Based on a variety of metrics, performance of the proposed EMMP based SAR image reconstruction technique is investigated. The obtained results show that the proposed technique provides high resolution images of sparse target scenes while performing highly accurate motion compensation. (C) 2014 Elsevier Inc. All rights reserved

An Efficient Solution to the Factorized Geometrical Autofocus Problem

This paper describes a new search strategy within the scope of factorized geometrical autofocus (FGA) and synthetic-aperture-radar processing. The FGA algorithm is a fast factorized back-projection formulation with six adjustable geometry parameters. By tuning the flight track step by step and maximizing focus quality by means of an object function, a sharp image is formed. We propose an efficient two-stage approach for the geometrical variation. The first stage is a low-order (few parameters) parallel search procedure involving small image areas. The second stage then combines the local hypotheses into one global autofocus solution, without the use of images. This method has been applied successfully on ultrawideband CARABAS II data. Errors due to a constant acceleration are superposed on the measured track prior to processing, giving a 6-D autofocus problem. Image results, including resolution, peak-to-sidelobe ratio and magnitude values for point-like targets, finally confirm the validity of the strategy. The results also verify the prediction that there are several satisfying autofocus solutions for the same radar data

Factorized Geometrical Autofocus for Synthetic Aperture Radar Processing

This paper describes a factorized geometrical autofocus (FGA) algorithm, specifically suitable for ultrawideband synthetic aperture radar. The strategy is integrated in a fast factorized back-projection chain and relies on varying track parameters step by step to obtain a sharp image; focus measures are provided by an object function (intensity correlation). The FGA algorithm has been successfully applied on synthetic and real (Coherent All RAdio BAnd System II) data sets, i.e., with false track parameters introduced prior to processing, to set up constrained problems involving one geometrical quantity. Resolution (3 dB in azimuth and slant range) and peak-to-sidelobe ratio measurements in FGA images are comparable with reference results (within a few percent and tenths of a decibel), demonstrating the capacity to compensate for residual space variant range cell migration. The FGA algorithm is finally also benchmarked (visually) against the phase gradient algorithm to emphasize the advantage of a geometrical autofocus approach

Mixed Compressive Sensing Back-Projection for SAR Focusing on Geocoded Grid

This article presents a new scheme called 2-D mixed compressive sensing back-projection (CS-BP-2D), for synthetic aperture radar (SAR) imaging on a geocoded grid, in a single measurement vector frame. The back-projection linear operator is derived in matrix form and a patched-based approach is proposed for reducing the dimensions of the dictionary. Spatial compressibility of the radar image is exploited by constructing the sparsity basis using the back-projection focusing framework and fast solving the reconstruction problem through the orthogonal matching pursuit algorithm. An artifact reduction filter inspired by the synthetic point spread function is used in postprocessing. The results are validated for simulated and real-world SAR data. Sentinel-1 C-band raw data in both monostatic and space-borne transmitter/stationary receiver bistatic configurations are tested. We show that CS-BP-2D can focus both monostatic and bistatic SAR images, using fewer measurements than the classical approach, while preserving the amplitude, the phase, and the position of the targets. Furthermore, the SAR image quality is enhanced and also the storage burden is reduced by storing only the recovered complex-valued points and their corresponding locations

Signal Processing for Synthetic Aperture Sonar Image Enhancement

This thesis contains a description of SAS processing algorithms, offering improvements in Fourier-based reconstruction, motion-compensation, and autofocus. Fourier-based image reconstruction is reviewed and improvements shown as the result of improved system modelling. A number of new algorithms based on the wavenumber algorithm for correcting second order effects are proposed. In addition, a new framework for describing multiple-receiver reconstruction in terms of the bistatic geometry is presented and is a useful aid to understanding. Motion-compensation techniques for allowing Fourier-based reconstruction in widebeam geometries suffering large-motion errors are discussed. A motion-compensation algorithm exploiting multiple receiver geometries is suggested and shown to provide substantial improvement in image quality. New motion compensation techniques for yaw correction using the wavenumber algorithm are discussed. A common framework for describing phase estimation is presented and techniques from a number of fields are reviewed within this framework. In addition a new proof is provided outlining the relationship between eigenvector-based autofocus phase estimation kernels and the phase-closure techniques used astronomical imaging. Micronavigation techniques are reviewed and extensions to the shear average single-receiver micronavigation technique result in a 3 - 4 fold performance improvement when operating on high-contrast images. The stripmap phase gradient autofocus (SPGA) algorithm is developed and extends spotlight SAR PGA to the wide-beam, wide-band stripmap geometries common in SAS imaging. SPGA supersedes traditional PGA-based stripmap autofocus algorithms such as mPGA and PCA - the relationships between SPGA and these algorithms is discussed. SPGA's operation is verified on simulated and field-collected data where it provides significant image improvement. SPGA with phase-curvature based estimation is shown and found to perform poorly compared with phase-gradient techniques. The operation of SPGA on data collected from Sydney Harbour is shown with SPGA able to improve resolution to near the diffraction-limit. Additional analysis of practical stripmap autofocus operation in presence of undersampling and space-invariant blurring is presented with significant comment regarding the difficulties inherent in autofocusing field-collected data. Field-collected data from trials in Sydney Harbour is presented along with associated autofocus results from a number of algorithms

Autofocus and Back-Projection in Synthetic Aperture Radar Imaging.

Spotlight-mode Synthetic Aperture Radar (SAR) imaging has received considerable attention due to its ability to produce high-resolution images of scene reflectivity. One of the main challenges in successful image recovery is the problem of defocusing, which occurs due to inaccuracies in the estimated round-trip delays of the transmitted radar pulses. The problem is most widely studied for far-field imaging scenarios with a small range of look angles since the problem formulation can be significantly simplified under the assumptions of planar wavefronts and one-dimensional defocusing. In practice, however, these assumptions are frequently violated. MultiChannel Autofocus (MCA) is a subspace-based approach to the defocusing problem that was originally proposed for far-field imaging, with a small range of look angles. A key motivation behind MCA is the observation that there exists a low-return region within the recovered image, due to the weak illumination near the edges of the antenna footprint. The strength of the MCA formulation is that it can be easily extended to more realistic scenarios with polar-format data, spherical wavefronts, and arbitrary terrain, due to its flexible linear-algebraic framework. The main aim of this thesis is to devise a more broadly effective autofocus approach by adopting MCA to the aforementioned scenarios. By forming the solution space in a domain where the defocusing effect is truly one-dimensional, we show that drastically improved restorations can be obtained for applications with small to fairly wide ranges of look angles. When the terrain topography is known, we utilize the versatile backprojection-based imaging methods in the model formulations for MCA to accurately account for the underlying geometry. The proposed extended MCA shows reductions in RMSE of up to 50% when the underlying terrain is highly elevated. We also analyze the effects of the filtering step, the amount of wave curvature, the shape of the terrain, and the flight path of the radar, on the reconstructed image via backprojection. Finally, we discuss the selection of low-return constraints and the importance of using terrain elevation within MCA formulation.PHDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/135868/1/zzon_1.pd

Iterative synthetic aperture radar imaging algorithms

Synthetic aperture radar is an important tool in a wide range of civilian and military imaging applications. This is primarily due to its ability to image in all weather conditions, during both the day and the night, unlike optical imaging systems. A synthetic aperture radar system contains a step which is not present in an optical imaging system, this is image formation. This is required because the acquired data from the radar sensor does not directly correspond to the image. Instead, to form an image, the system must solve an inverse problem. In conventional scenarios, this inverse problem is relatively straight forward and a matched lter based algorithm produces an image of suitable image quality. However, there are a number of interesting scenarios where this is not the case. Scenarios where standard image formation algorithms are unsuitable include systems with data undersampling, errors in the system observation model and data that is corrupted by radio frequency interference. Image formation in these scenarios will form the topics of this thesis and a number of iterative algorithms are proposed to achieve image formation. The motivation for these proposed algorithms is primarily from the eld of compressed sensing, which considers the recovery of signals with a low-dimensional structure. The rst contribution of this thesis is the development of fast algorithms for the system observation model and its adjoint. These algorithms are required by large-scale gradient based iterative algorithms for image formation. The proposed algorithms are based on existing fast back-projection algorithms, however, a new decimation strategy is proposed which is more suitable for some applications. The second contribution is the development of a framework for iterative near- eld image formation, which uses the proposed fast algorithms. It is shown that the framework can be used, in some scenarios, to improve the visual quality of images formed from fully sampled data and undersampled data, when compared to images formed using matched lter based algorithms. The third contribution concerns errors in the system observation model. Algorithms that correct these errors are commonly referred to as autofocus algorithms. It is shown that conventional autofocus algorithms, which work as a post-processor on the formed image, are unsuitable for undersampled data. Instead an autofocus algorithm is proposed which corrects errors within the iterative image formation procedure. The proposed algorithm is provably stable and convergent with a faster convergence rate than previous approaches. The nal contribution is an algorithm for ultra-wideband synthetic aperture radar image formation. Due to the large spectrum over which the ultra-wideband signal is transmitted, there is likely to be many other users operating within the same spectrum. These users can produce signi cant radio frequency interference which will corrupt the received data. The proposed algorithm uses knowledge of the RFI spectrum to minimise the e ect of the RFI on the formed image

Recent Techniques for Regularization in Partial Differential Equations and Imaging

abstract: Inverse problems model real world phenomena from data, where the data are often noisy and models contain errors. This leads to instabilities, multiple solution vectors and thus ill-posedness. To solve ill-posed inverse problems, regularization is typically used as a penalty function to induce stability and allow for the incorporation of a priori information about the desired solution. In this thesis, high order regularization techniques are developed for image and function reconstruction from noisy or misleading data. Specifically the incorporation of the Polynomial Annihilation operator allows for the accurate exploitation of the sparse representation of each function in the edge domain. This dissertation tackles three main problems through the development of novel reconstruction techniques: (i) reconstructing one and two dimensional functions from multiple measurement vectors using variance based joint sparsity when a subset of the measurements contain false and/or misleading information, (ii) approximating discontinuous solutions to hyperbolic partial differential equations by enhancing typical solvers with l1 regularization, and (iii) reducing model assumptions in synthetic aperture radar image formation, specifically for the purpose of speckle reduction and phase error correction. While the common thread tying these problems together is the use of high order regularization, the defining characteristics of each of these problems create unique challenges. Fast and robust numerical algorithms are also developed so that these problems can be solved efficiently without requiring fine tuning of parameters. Indeed, the numerical experiments presented in this dissertation strongly suggest that the new methodology provides more accurate and robust solutions to a variety of ill-posed inverse problems.Dissertation/ThesisDoctoral Dissertation Mathematics 201

Analyse temps-frequence et traitement des signaux RSO à haute résolution spatiale pour la surveillance des grands ouvrages d'art

The thesis is composed of two research axis. The first one consists in proposing time-frequency signal processing tools for frequency modulated continuous wave (FMCW) radars used for displacements measurements, while the second one consists in designing a spaceborne synthetic aperture radar (SAR) signal processing methodology for infrastructure monitoring when an external point cloud of the envisaged structure is available. In the first part of the thesis, we propose our solutions to the nonlinearity problem of an X-band FMCW radar designed for millimetric displacement measurements of short-range targets. The nonlinear tuning curve of the voltage controlled oscillator from the transceiver can cause a dramatic resolution degradation for wideband sweeps. To mitigate this shortcoming, we have developed two time warping-based methods adapted to wideband nonlinearities: one estimates the nonlinear terms using the high order ambiguity function, while the other is an autofocus approach which exploits the spectral concentration of the beat signal. Onwards, as the core of the thesis, we propose a novel method for scattering centers detection and tracking in spaceborne SAR images adapted to infrastructure monitoring applications. The method is based on refocusing each SAR image on a provided 3D point cloud of the envisaged infrastructure and identifying the reliable scatterers to be monitored by means of four dimensional (4D) tomography. The refocusing algorithm is compatible with stripmap, spotlight and sliding spotlight SAR images and consists of an azimuth defocusing followed by a modified back-projection algorithm on the given set of points which exploits the time-frequency structure of the defocused azimuth signal. The scattering centers of the refocused image are detected in the 4D tomography framework by testing if the main response is at zero elevation in the local elevation-velocity spectral distribution. The mean displacement velocity is estimated from the peak response on the zero elevation axis, while the displacements time series for detected single scatterers is computed as double phase difference of complex amplitudes.Finally, we present the measurement campaigns carried out on the Puylaurent water-dam and the Chastel landslide using GPS measurements, topographic surveys and laser scans to generate the point clouds of the two structures. The comparison between in-situ data and the results obtained by combining TerraSAR-X data with the generated point clouds validate the developed SAR signal processing chain.Cette thèse s'articule autour de deux axes de recherche. Le premier axe aborde les aspects méthodologiques liés au traitement temps-fréquence des signaux issus d'un radar FMCW (à onde continue modulée en fréquence) dans le contexte de la mesure des déplacements fins. Le second axe est dédié à la conception et à la validation d'une chaîne de traitement des images RSO (radar à synthèse d'ouverture) satellitaire. Lorsqu'un maillage 3D de la structure envisagée est disponible, les traitements proposés sont validés par l'intercomparaison avec les techniques conventionnelles d'auscultation des grands ouvrages d'art.D'une part, nous étudions la correction de la non-linéarité d'un radar FMCW en bande X, à courte portée, conçu pour la mesure des déplacements millimétriques. La caractéristique de commande non linéaire de l'oscillateur à large bande, entraine une perte de résolution à la réception. Afin de pallier cet inconvénient, nous avons développé deux méthodes basées sur le ré-échantillonnage temporel (time warping) dans le cas des signaux à large bande non-stationnaires. La première approche estime la loi de fréquence instantanée non linéaire à l'aide de la fonction d'ambiguïté d'ordre supérieur, tandis que la deuxième approche exploite la mesure de concentration spectrale du signal de battement dans un algorithme d'autofocus radial.D'autre part, nous proposons un cadre méthodologique général pour la détection et le pistage des centres de diffusion dans les images RSO pour la surveillance des grands ouvrages d'art. La méthode est basée sur la ré-focalisation de chaque image radar sur le maillage 3D de l'infrastructure étudiée afin d'identifier les diffuseurs pertinents par tomographie 4D (distance – azimut – élévation – vitesse de déformation). L'algorithme de ré-focalisation est parfaitement compatible avec les images RSO acquises dans les différents modes (« stripmap », « spotlight » et « sliding spotlight ») : dé-focalisation en azimut suivie par rétroprojection modifiée (conditionnée par la structure temps-fréquence du signal) sur l'ensemble donné des points. Dans la pile d'images ré-focalisées, les centres de diffusion sont détectés par tomographie 4D : test de conformité à l'hypothèse d'élévation zéro dans le plan élévation – vitesse de déformation. La vitesse moyenne correspond au maximum à l'élévation zéro, tandis que la série temporelle des déplacements est obtenue par double différence de phase des amplitudes complexes pour chaque diffuseur pertinent.Nous présentons également les campagnes in situ effectuées au barrage de Puylaurent (et glissement de Chastel) : les relevés GPS, topographiques et LIDAR sol employées au calcul des maillages 3D. La comparaison entre les déplacements mesurés in situ et les résultats obtenus par l'exploitation conjointe de la télédétection RSO satellitaires et les maillages 3D valident la chaîne de traitement proposée.Teza cuprinde două axe principale de cercetare. Prima axă abordează aspecte metodologice de prelucraretimp-frecvenţă a semnalelor furnizate de radare cu emisie continuă şi modulaţie de frecvenţă (FMCW)în contextul măsurării deplasărilor milimetrice. În cadrul celei de-a doua axe, este proiectată şi validatăo metodă de prelucrare a imaginilor satelitare SAR (radar cu apertură sintetică) ce este destinatămonitorizării infrastructurii critice şi care se bazează pe existenţa unui model 3D al structurii respective.În prima parte a tezei, sunt investigate soluţii de corecţie a neliniarităţii unui radar FMCW în bandaX destinat măsurării deplasărilor milimetrice. Caracteristica de comandă neliniară a oscilatorului debandă largă determină o degradare a rezoluţiei în distanţă. Pentru a rezolva acest inconvenient, au fostelaborate două metode de corecţie a neliniarităţii, adaptate pentru semnale de bandă largă, ce se bazeazăpe conceptul de reeşantionare neuniformă sau deformare a axei temporare. Prima abordare estimeazăparametrii neliniarităţii utilizând funcţii de ambiguitate de ordin superior, iar cea de-a doua exploateazăo măsură de concentraţie spectrală a semnalului de bătăi într-un algoritm de autofocalizare în distanţă.În a doua parte a lucrării, este propusă o metodologie generală de detecţie şi monitorizare a centrilorde împrăştiere în imagini SAR în scopul monitorizării elementelor de infrastructură critică. Metoda sebazează pe refocalizarea fiecărei imagini radar pe un model 3D al structurii investigate în scopul identificăriicentrilor de împrăştiere pertinenţi (ţinte fiabile ce pot fi monitorizate în timp) cu ajutorul tomografiei SAR4D (distanţă-azimut-elevaţie-viteză de deplasare). Algoritmul de refocalizare este compatibil cu imaginiSAR achiziţionate în moduri diferite (« stripmap », « spotlight » şi « sliding spotlight ») şi constă într-odefocalizare în azimut urmată de o retroproiecţie modificată (condiţionată de structura timp-frecvenţă asemnalului) pe modelul 3D al structurii. Ţintele sunt identificate în stiva de imagini refocalizate cu ajutorultomografiei 4D prin efectuarea unui test de conformitate cu ipoteza că centrii de împrăştiere pertinenţivor avea elevaţie zero în planul local elevaţie-viteză. Viteza medie de deformare corespunde maximuluide pe axa de elevaţie nulă, iar seria temporară a deplasărilor se obţine printr-o dublă diferenţă de fază aamplitudinilor complexe corespunzătoare ţintelor identificate.În final sunt prezentate campaniile de măsurători pe teren efectuate la un baraj şi o alunecare de terendin regiunea Puylaurent (Franţa) destinate obţinerii modelului 3D al celor două elemente de infrastructurăprin măsurători GPS, topografice şi LIDAR. Comparaţia între deformările măsurate pe teren şi rezultateleobţinute prin combinarea imaginilor SAR cu modelele 3D au permis validarea metodologiei propuse