Non-iterative spotlight SAR autofocusing using a modified phase-gradient approach

The phase-gradient autofocus (PGA) technique is robust over a wide range of imagery and phase error functions, but the convergence usually requires four-six iterations. It is necessarily iterative in an attempt to converge on a dominant target against clutter interference, while sufficiently capturing the blur function. The authors propose to speed the estimation convergence by selectively increasing the pool of quality synchronization sources and not be limited by the range pixels of the SAR map. This is highly probable since each range bin contains more than one prominent scatterer across the integration aperture. It is also highly probable that the least-brightest selected scatterer in a range gate may turn out to be of higher energy as compared to the maximum brightest scatterer of another gate. With appropriate target filtering to final select the quality scatterers out of the large pool and with higher order phase error measurement tool, the new algorithm achieves near-convergence focusing quality without iteration. The authors named this solution the quality PGA (QPGA) algorithm.

The phase gradient autofocus (PGA) is a state of art technique for phase error correction of synthetic aperture radar (SAR) and inverse synthetic aperture radar (ISAR). It exploits the redundancy of phase error information among range bins by selecting the strongest scatter for each range bin and then synthesizes them. The motivation of this paper is based on the observation that the redundancy of phase error information is also among the cross-range (azimuth) direction in the image domain. A new scatter selection scheme is proposed to better utilize the phase error information contained in the image. The validity of our new prominent scatters selection method for PGA algorithm is theoretically analyzed and tested with some numeral simulation. It shows that a faster convergence speed can be obtained by our new method.

Dual-polarized inverse synthetic aperture radar (ISAR) systems can provide more extra information than single-polarized ISAR systems, which can be used to increase image quality during the imaging process. However, there is limited research on the subject of dual-polarized ISAR. In this letter, an enhanced phase gradient autofocus (PGA) method was proposed for dual-polarized ISAR imaging. The Cloude-Pottier decomposition is employed to extract the polarization parameters <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula> from the dual-polarized primary image. Subsequently, the PGA is enhanced by selecting high-quality prominent scatterers based on these <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula> parameters. By making full use of the prominent scatterers selected by polarization information, the performance of PGA was improved, and thus, the imaging quality was significantly improved. Finally, both the real measurement data of aircraft targets and ship targets verified the effectiveness of the proposed method.

Phase gradient autofocus (PGA) is widely used in spotlight SAR autofocus with strong robustness. However, being the different nature of synthetic aperture sonar (SAS) imagery, traditional PGA algorithm usually fails to yield satisfactory result on SAS image without modification. Three measures are taken to ensure that PGA can be applied in stripmap SAS autofocus. A SAS image is divided into sub-images which ensures that the phase error is invariant in each sub-image; The image shift in azimuth can be avoided by removing the mean value of the phase gradient and by using strong point targets in the image; The estimation accuracy can be improved by selecting range bins according to energy criteria combined with quality criteria. The proposed method is successfully applied on SAS image and excellent results are attained.

PGA(phase gradient autofocus) has been widely used to remove motion induced phase errors in the ISAR(inverse synthetic aperture radar) imaging. The critical process for the processing time and image quality is windowing stage in PGA. In this paper, the new method to determine window size based on polynomial least square approximation is proposed. Moreover, dominant range bins are selected for efficient phase error estimation, which improve image quality and speed up convergence. The simulation results show that the proposed algorithm provides high quality ISAR images while computational efficiency of inherent PGA is retained.

Phase gradient autofocus (PGA) for maximum-likelihood estimation of phase error is most widely used in practice for its efficient realization and excellent robustness. However, because PGA employs adjacent pulses of the range-compressed data to estimate the gradient of phase error, the precision of PGA would be severely affected by the signal-to-noise ratio (SNR) of the range-compressed data. In order to overcome such difficulty, this paper proposes a novel autofocus algorithm to calculate the phase error (PEA) directly. The presented methodology is implemented by weighting average of the input range lines with the fixed phase difference removed. Monte Carlo tests and real SAR data validate that the new approach can achieve better performance than the mostly used PGA with comparable computational cost.

Current sonar autofocus techniques for blur removal originate in the radar community but have not provided a complete solution for Synthetic Aperture Sonar (SAS) imagery. The wide-beam, wide-band nature of SAS imagery makes implementation of Synthetic Aperture Radar (SAR) autofocus techniques difficult. This paper describes a generalisation of the standard Phase Gradient Autofocus (PGA) algorithm used in spotlight SAR that allows operation with stripmap SAS geometries. PGA uses prominent points within the target scene to estimate image blurring and phase errors. We show how PGA can be generalised to work with wide-band, wide-beam stripmap geometries. The SPGA method works by employing wave number domain 2D phase estimation techniques. The 2D phase errors are related to aperture position errors using the wave number transform. Robust sway estimates are obtained by using redundancy over a number of target points. We also present an improved Phase Curvature Autofocus (PCA) algorithm using the wave number transform. Preliminary results from the two algorithms (both on field-collected and simulated data sets) are presented and related to those obtained using previous methods. A discussion of SPGA's benefits over traditional algorithms and the limitations of the SPGA algorithm is presented. The SPGA algorithm was found to perform better than 2-D PCA on both simulated and field-collected data sets. Further testing on a variety of target scenes and imagery is required to investigate avenues of autofocus improvement.

Two methods of focusing synthetic aperture radar (SAR) images are compared. Both a conventional subaperture cross-correlation method and a new phase gradient autofocus (PGA) algorithm developed at Sandia National Laboratories are shown to perform well if high-order phase errors are not present. With the introduction of significant high-order phase errors [e.g., due to uncompensated platform motion], both algorithms suffer a loss in performance. However, relative performance degradation is less for PGA than for the subaperture focusing technique. An explanation is presented for the observed behavior of the two autofocus techniques.© (1991) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Phase errors deteriorate the quality of synthetic aperture radar (SAR) images drastically. In the practical automotive SAR data acquisition, the phase error varies for different regions of the observed area. It seems reasonable to consider a similar error for targets in a small region of the SAR image. In this work, we combine a generalized method of the phase gradient autofocus (PGA) and the fast factorized back-projection (FFBP) algorithm to estimate the phase error and reconstruct compensated sub-images. The proposed method is evaluated with multi-target scene simulations and practical experiments by using a 77-GHz radar system. We will show that the space-variant phase error estimator improves the image quality with a lower computational cost than conventional methods.

Video-SAR can produce sequential images at high frame rate, providing a continuous surveillance over a region of interest (ROI). To accelerate the speed of image processing, the whole circular path of Video-SAR is divided into several sub-apertures. However, due to the severe coupling of range and cross-range direction of the circular path, standard autofocus techniques as Phase Gradient Autofocus (PGA) fail since the direction of image blur changes for each sub-aperture image (sub-image). We have developed an algorithm for sub-aperture processing of Video-SAR that estimates the phase errors from strong scatters in the unfocused sub-image based on echo regeneration, regardless of the sub-aperture position. After phase compensation, more focused sub-images can be obtained before they are compiled into a SAR video. Thus the efficiency and utility of Video-SAR sub-aperture processing is retained, while image quality is not compromised due to platform motion errors.

Synthetic aperture radar (SAR) is a critical enabling technology for maritime surveillance. However, maneuvering ships often appear defocused in SAR images, posing significant challenges for subsequent ship detection and recognition. To address this problem, this study proposes an improved iteration phase gradient resampling autofocus (IIPGRA) method. First, we extract the defocused ships from SAR images, followed by azimuth decompression and translational motion compensation. Subsequently, a centerline-driven adaptive azimuth partitioning strategy is proposed: the geometric centerline of the vessel is extracted from coarsely focused images using an enhanced RANSAC algorithm, and the target is partitioned into upper and lower sub-blocks along the azimuth direction to maximize the separation of rotational centers between sub-blocks, establishing a foundation for the accurate estimation of spatially variant phase errors. Next, phase gradient autofocus (PGA) is employed to estimate the phase errors of each sub-block and compute their differential. Then, resampling the original echoes based on this differential phase error linearizes non-uniform rotational motion. Furthermore, this study introduces the Rotational Uniformity Coefficient (β) as the convergence criterion. This coefficient can stably and reliably quantify the linearity of the rotational phase, thereby ensuring robust termination of the iterative process. Simulation and real airborne SAR data validate the effectiveness of the proposed algorithm.

Large and spatially-linear phase errors along the frequency-encode direction may be induced by several common and hard-to-avoid system imperfections such as eddy currents. For data acquired in dual-echo Dixon techniques, the linear phase error can be more aggravated when compared to that acquired in a single echo and can pose challenges to a phase-correction algorithm necessary for successful Dixon processing. In this work, we propose a two-step process that first corrects the linear component of the phase errors with a modified Ahn-Cho algorithm (Ahn CB and Cho ZH, IEEE Trans. Med. Imaging 6:32, 1987) and then corrects the residual phase errors with a previously-developed region-growing algorithm (Ma J, Magn. Res. Med. 52:415, 2004). We demonstrate that successive application of the two-step process to data from a dual-echo Dixon technique provides a "1-2 punch" to the overall phase errors and can overcome local water and fat separation failures that are observed when the region-growing-based algorithm is applied alone.

The phase gradient autofocus (PGA) technique is used for automatic estimation and correction of phase errors in spotlight mode synthetic aperture radar (SAR) imagery. This paper presents an overview of the PGA algorithm in iterative and non-iterative versions and shows the results of implementation of this method in C language for real-time applications.

Precise beam-tilt alignment and collimation are required to minimize the phase error associated with coma in high-resolution cryo-EM

The phase errors resulting from in-phase/quadrature (I/Q) demodulation in phase-sensitive optical time-domain reflectometry (φOTDR) are investigated theoretically, numerically, and experimentally for two phase recovery schemes: one employing Kramers–Kronig (KK)-based coherent detection, and a second one based on a direct-detection scheme using an imbalanced Mach–Zehnder interferometer, a 3 × 3 coupler and 3 photodetectors. Mathematical models for the estimation of the differential phase variance are proposed and experimentally validated for these two schemes. The probability density function of the phase variance verifies an uneven longitudinal distribution of the phase errors in the two cases. Results point out that KK-based φOTDR sensors have no special advantages in terms of noise performance compared to standard full I/Q coherent detection, so that large phase errors can be verified at fading locations, leading to severe phase unwrapping problems. On the contrary, the direct-detection scheme based on interferometer is highly dependent on the signal difference between photodetectors, showing higher robustness against fading even if its probability density function is wider than the KK-based case. Experimental results also show the advantages of selecting data points with high in-phase and quadrature amplitudes to achieve reliable vibration measurements, especially in KK-based φOTDR sensors.