SAR image reconstruction and autofocus by compressed sensing

Cataloged from PDF version of article.A new SAR signal processing technique based on compressed sensing is proposed for autofocused image reconstruction on subsampled raw SAR data. It is shown that, if the residual phase error after INS/GPS corrected platform motion is captured in the signal model, then the optimal autofocused image formation can be formulated as a sparse reconstruction problem. To further improve image quality, the total variation of the reconstruction is used as a penalty term. In order to demonstrate the performance of the proposed technique in wide-band SAR systems, the measurements used in the reconstruction are formed by a new under-sampling pattern that can be easily implemented in practice by using slower rate A/D converters. Under a variety of metrics for the reconstruction quality, it is demonstrated that, even at high under-sampling ratios, the proposed technique provides reconstruction quality comparable to that obtained by the classical techniques which require full-band data without any under-sampling. (C) 2012 Elsevier Inc. All rights reserved

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

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

Phase error estimation for synthetic aperture imagery.

The estimation of phase errors in synthetic aperture imagery is important for high quality images. Many methods of autofocus, or the estimation of phase errors from the measured data, are developed using certain assumptions about the imaged scene. This thesis develops improved methods of phase estimation which make full use of the information in the recorded signal. This results in both a more accurate estimate of the image phase error and improved imagery compared to using standard techniques. The standard phase estimation kernel used in echo-correlation techniques is shear-average. This technique averages the phase-difference between each ping over all range-bins, weighted by the signal strength. It is shown in this thesis that this is not the optimal method of weighting each phase estimate. In images where the signal to clutter ratio (SCR) is not proportional to the signal amplitude, shear-average does not meet the predicted error bound. This condition may be met by many image types, including those with shadows, distributed targets and varying surface structure. By measuring the average coherence between echos at each range-bin, it is possible to accurately estimate the variance of each phase estimate, and weight accordingly. A weighted phase-difference estimation (WPDE) using this coherence weighting meets the performance bound for all images tested. Thus an improved performance over shear-average is shown for many image types. The WPDE phase estimation method can be used within the framework of many echo-correlation techniques, such as phase-gradient autofocus (PGA), phase curvature estimation, redundant phase-centre or displaced phase-centre algorithms. In addition, a direct centre-shifting method is developed which reduces bias compared to the centre-shifting method used in PGA. For stripmap images, a weighted phase curvature estimator shows better performance than amplitude weighted shear-average for images with high SCR. A different method of phase estimation, known as sharpness maximisation, perturbs an estimate of the phase error to maximise the sharpness of the reconstructed image. Several improvements are made to the technique of sharpness maximisation. These include the reduction of over-sharpening using regularisation and an improvement in accuracy of the phase estimate using range-weighting based on the coherence measure. A cascaded parametric optimisation method is developed which converges significantly faster than standard optimisation methods for stripmap images. A number of novel insights into the method of sharpness maximisation are presented. A derivation of the phase that gives maximum intensity squared sharpness is extended from a noncoherent imaging system to a coherent spotlight system. A bound on the performance of sharpness-maximisation is presented. A method is developed which allows the direct calculation of the result of a sharpness maximisation for a single ping of a spotlight synthetic aperture image. The phase correction that maximises sharpness can be directly calculated from the signal in a manner similar to a high-order echo-correlation. This calculation can be made for all pings in a recursive manner. No optimisation is required, resulting in a significantly faster phase estimation. The techniques of sharpness maximisation and echo-correlation can be shown to be closely related. This is confirmed by direct comparisons of the results. However, the classical intensity-squared sharpness measure gives poorer results than WPDE and different sharpness measures tested for a distributed target. The standard methods of shear average and maximisation of the intensity-squared sharpness measure, both perform well below the theoretical performance bound. Two of the techniques developed, WPDE and direct entropy minimisation perform at the bound, showing improved performance over standard techniques. The contributions of this thesis add considerably to the body of knowledge on the technique of sharpness maximisation. This allows an improvement in the accuracy of some phase estimation methods, as well as an increase in the understanding of how these techniques work on coherent imagery in general

Novel methods for SAR imaging problems

Ankara : The Department of Electrical and Electronics Engineering and the Graduate School of Engineering and Science of Bilkent University, 2013.Thesis (Ph. D.) -- Bilkent University, 2013.Includes bibliographical references leaves 62-70.Synthetic Aperture Radar (SAR) provides high resolution images of terrain reflectivity. SAR systems are indispensable in many remote sensing applications. High resolution imaging of terrain requires precise position information of the radar platform on its flight path. In target detection and identification applications, imaging of sparse reflectivity scenes is a requirement. In this thesis, novel SAR image reconstruction techniques for sparse target scenes are developed. These techniques differ from earlier approaches in their ability of simultaneous image reconstruction and motion compensation. It is shown that if the residual phase error after INS/GPS corrected platform motion is captured in the signal model, then the optimal autofocused image formation can be formulated as a sparse reconstruction problem. In the first proposed technique, Non-Linear Conjugate Gradient Descent algorithm is used to obtain the optimum reconstruction. To increase robustness in the reconstruction, Total Variation penalty is introduced into the cost function of the optimization. To reduce the rate of A/D conversion and memory requirements, a specific under sampling pattern is introduced. In the second proposed technique, Expectation Maximization Based Matching Pursuit (EMMP) algorithm is utilized to obtain the optimum sparse SAR reconstruction. EMMP algorithm is greedy and computationally less complex resulting in fast SAR image reconstructions. Based on a variety of metrics, performances of the proposed techniques are compared. It is observed that the EMMP algorithm has an additional advantage of reconstructing off-grid targets by perturbing on-grid basis vectors on a finer grid.Uğur, SalihPh.D

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

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

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