Overcoming polar‐format issues in synthetic aperture radar multichannel autofocus

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/166214/1/rsn2bf00419.pd

A sparsity-driven approach for joint SAR imaging and phase error correction

Image formation algorithms in a variety of applications have explicit or implicit dependence on a mathematical model of the observation process. Inaccuracies in the observation model may cause various degradations and artifacts in the reconstructed images. The application of interest in this paper is synthetic aperture radar (SAR) imaging, which particularly suffers from motion-induced model errors. These types of errors result in phase errors in SAR data which cause defocusing of the reconstructed images. Particularly focusing on imaging of fields that admit a sparse representation, we propose a sparsity-driven method for joint SAR imaging and phase error correction. Phase error correction is performed during the image formation process. The problem is set up as an optimization problem in a nonquadratic regularization-based framework. The method involves an iterative algorithm each iteration of which consists of consecutive steps of image formation and model error correction. Experimental results show the effectiveness of the approach for various types of phase errors, as well as the improvements it provides over existing techniques for model error compensation in SAR

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

A Generalized Phase Gradient Autofocus Algorithm

The phase gradient autofocus (PGA) algorithm has seen widespread use and success within the synthetic aperture radar (SAR) imaging community. However, its use and success has largely been limited to collection geometries where either the polar format algorithm (PFA) or range migration algorithm is suitable for SAR image formation. In this work, a generalized phase gradient autofocus (GPGA) algorithm is developed which is applicable with both the PFA and backprojection algorithm (BPA), thereby directly supporting a wide range of collection geometries and SAR imaging modalities. The GPGA algorithm preserves the four crucial signal processing steps comprising the PGA algorithm, while alleviating the constraint of using a single scatterer per range cut for phase error estimation which exists with the PGA algorithm. Moreover, the GPGA algorithm, whether using the PFA or BPA, yields an approximate maxi- mum marginal likelihood estimate (MMLE) of phase errors having marginalized over unknown complex-valued reflectivities of selected scatterers. Also, in this work a new approximate MMLE, termed the max-semidefinite relaxation (Max-SDR) phase estimator, is proposed for use with the GPGA algorithm. The Max-SDR phase estimator provides a phase error estimate with a worst-case approximation bound compared to the solution set of MMLEs (i.e., solution set to the non-deterministic polynomial- time hard (NP-hard) GPGA phase estimation problem). Moreover, in this work a specialized interior-point method is presented for more efficiently performing Max- SDR phase estimation by exploiting low-rank structure typically associated with the GPGA phase estimation problem. Lastly, simulation and experimental results produced by applying the GPGA algorithm with the PFA and BPA are presented

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

A Linear Algebraic Framework for Autofocus in Synthetic Aperture Radar

Synthetic aperture radar (SAR) provides a means of producing high-resolution microwave images using an antenna of small size. SAR images have wide applications in surveillance, remote sensing, and mapping of the surfaces of both the Earth and other planets. The defining characteristic of SAR is its coherent processing of data collected by an antenna at locations along a trajectory in space. In principle, we can produce an image of extraordinary resolution. However, imprecise position measurements associated with data collected at each location cause phase errors that, in turn, cause the reconstructed image to suffer distortion, sometimes so severe that the image is completely unrecognizable. Autofocus algorithms apply signal processing techniques to restore the focused image. This thesis focuses on the study of the SAR autofocus problem from a linear algebraic perspective. We first propose a general autofocus algorithm, called Fourier-domain Multichannel Autofocus (FMCA), that is developed based on an image support constraint. FMCA can accommodate nearly any SAR imaging scenario, whether it be wide-angle or bistatic (transmit and receive antennas at separate locations). The performance of FMCA is shown to be superior compared to current state-of-the-art autofocus techniques. Next, we recognize that at the heart of many autofocus algorithms is an optimization problem, referred to as a constant modulus quadratic program (CMQP). Currently, CMQP generally is solved by using an eigenvalue relaxation approach. We propose an alternative relaxation approach based on semidefinite programming, which has recently attracted considerable attention in other signal processing applications. Preliminary results show that the new method provides promising performance advantages at the expense of increasing computational cost. Lastly, we propose a novel autofocus algorithm based on maximum likelihood estimation, called maximum likelihood autofocus (MLA). The main advantage of MLA is its reliance on a rigorous statistical model rather than on somewhat heuristic reverse engineering arguments. We show both the analytical and experimental advantages of MLA over existing autofocus methods.Ph.D.Electrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/86443/1/khliu_1.pd

Joint sparsity-driven inversion and model error correction for SAR imaging

Image formation algorithms in a variety of applications have explicit or implicit dependence on a mathematical model of the observation process. Inaccuracies in the observation model may cause various degradations and artifacts in the reconstructed images. The application of interest in this thesis is synthetic aperture radar (SAR) imaging, which particularly suffers from motion-induced model errors. These types of errors result in phase errors in SAR data which cause defocusing of the reconstructed images. Particularly focusing on imaging of fields that admit a sparse representation, we propose a sparsity-driven method for joint SAR imaging and phase error correction. In this technique, phase error correction is performed during the image formation process. The problem is set up as an optimization problem in a nonquadratic regularization-based framework. The method involves an iterative algorithm each iteration of which consists of consecutive steps of image formation and model error correction. Experimental results show the effectiveness of the proposed method for various types of phase errors, as well as the improvements it provides over existing techniques for model error compensation in SAR

Sparsity-driven coupled imaging and autofocusing for interferometric SAR

In this thesis, we present a new joint image enhancement and reconstruction method and a software processing tool for SAR Interferometry. First, we propose a sparsity-driven method for coupled image formation and autofocusing based on multi-channel data collected in interferometric synthetic aperture radar (IfSAR). Relative phase between SAR images contains valuable information. For example, it can be used to estimate the height of the scene in SAR Interferometry. However, this relative phase could be degraded when independent enhancement methods are used over SAR image pairs. Previously, Ramakrishnan, Ertin, and Moses proposed a coupled multi-channel image enhancement technique, based on a dual descent method, which exhibits better performance in phase preservation compared to independent enhancement methods. Their work involves a coupled optimization formulation that uses a sparsity enforcing penalty term as well as a constraint tying the multichannel images together to preserve the cross-channel information. In addition to independent enhancement, the relative phase between the acquisitions can be degraded due to other factors as well, such as platform location uncertainties, leading to phase errors in the data and defocusing in the formed imagery. The performance of airborne SAR systems can be affected severely by such errors. We ii propose an optimization formulation that combines Ramakrishnan et al.'s coupled IfSAR enhancement method with the sparsity-driven autofocus (SDA) approach of Önhon and Çetin to alleviate the effects of phase errors due to motion errors in the context of IfSAR imaging. Our method solves the joint optimization problem with a Lagrangian optimization method iteratively. In our preliminary experimental analysis, we have obtained results of our method on synthetic SAR images and compared its performance to existing methods. As a second contribution of this thesis, we have developed a software toolbox for end-to-end interferometric SAR processing. This toolbox is capable of performing the fundamental steps of SAR Interferometry Processing. The thesis contains the detailed explanation of the algorithms implemented in the SAR Interferometry Toolbox. Test results are also provided to demonstrate the performance of the Toolbox under different scenarios