An augmented Lagrangian method for autofocused compressed SAR imaging

We present an autofocus algorithm for Compressed SAR Imaging. The technique estimates and corrects for 1-D phase errors in the phase history domain, based on prior knowledge that the reflectivity field is sparse, as in the case of strong scatterers against a weakly-scattering background. The algorithm relies on the Sparsity Driven Autofocus (SDA) method and Augmented Lagrangian Methods (ALM), particularly Alternating Directions Method of Multipliers (ADMM). In particular, we propose an ADMM-based algorithm that we call Autofocusing Iteratively Re-Weighted Augmented Lagrangian Method (AIRWALM) to solve a constrained formulation of the sparsity driven autofocus problem with an ℓp-norm, p ≤ 1 cost function. We then compare the performance of the proposed algorithm's performance to Phase Gradient Autofocus (PGA) and SDA [2] in terms of autofocusing capability, phase error correction, and computation time

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

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

Autofocused compressive SAR imaging based on the alternating direction method of multipliers

We present an alternating direction method of multipliers (ADMM) based autofocused Synthetic Aperture Radar (SAR) imaging method in the presence of unknown 1-D phase errors in the phase history domain, with undersampled measurements. We formulate the problem as one of joint image formation and phase error estimation. We assume sparsity of strong scatterers in the image domain, and as such use sparsity priors for reconstruction. The algorithm uses l(p)-norm minimization (p <= 1) [8] with an improvement by integrating the phase error updates within the alternating direction method of multipliers (ADMM) steps to correct the unknown 1-D phase error. We present experimental results comparing our proposed algorithm with a coordinate descent based algorithm in terms of convergence speed and reconstruction quality

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

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