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

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

Backprojection Autofocus for Synthetic Aperture Radar

In synthetic aperture radar (SAR), many adverse conditions may cause errors in the raw phase-history data. Autofocus methods are commonly used in SAR to mitigate the effects of these problems. Over the years, many types of autofocus have algorithms have been created, however, each has implicit assumptions restricting their use. The backprojection image formation algorithm places few restrictions on SAR imaging, thus it is desirable to have an autofocus algorithm that is similarly unconstrained. This paper presents a versatile autofocus method that is accordant with backprojection

Optimized Minimum-Search for SAR Backprojection Autofocus on GPUs Using CUDA

Autofocus techniques for synthetic aperture radar (SAR) can improve the image quality substantially. Their high computational complexity imposes a challenge when employing them in runtime-critical implementations. This paper presents an autofocus implementation for stripmap SAR specially optimized for parallel architectures like GPUs. Thorough evaluation using real SAR data shows that the tunable parameters of the algorithm allow to counterbalance runtime and achieved image quality.© 2020 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works

Overcoming polar‐format issues in synthetic aperture radar multichannel autofocus

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

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

Effects of Motion Measurement Errors on Radar Target Detection

This thesis investigates the relationships present between signal-to-clutter ratios, motion measurement errors, image quality metrics, and the task of target detection, in order to discover what factor merit greater focus in order to attain the highest probability of target detection success. This investigation is accomplished by running a high number of Monte Carlo trials through a coherent target detector and analyzing the results. The aforementioned relationships are demonstrated via sample synthetic aperture radar imagery, histograms, receiver operating characteristics curves, and error bar plots

Factorized Geometrical Autofocus for Synthetic Aperture Radar Processing

Synthetic Aperture Radar (SAR) imagery is a very useful resource for the civilian remote sensing community and for the military. This however presumes that images are focused. There are several possible sources for defocusing effects. For airborne SAR, motion measurement errors is the main cause. A defocused image may be compensated by way of autofocus, estimating and correcting erroneous phase components. Standard autofocus strategies are implemented as a separate stage after the image formation (stand-alone autofocus), neglecting the geometrical aspect. In addition, phase errors are usually assumed to be space invariant and confined to one dimension. The call for relaxed requirements on inertial measurement systems contradicts these criteria, as it may introduce space variant phase errors in two dimensions, i.e. residual space variant Range Cell Migration (RCM). This has motivated the development of a new autofocus approach. The technique, termed the Factorized Geometrical Autofocus (FGA) algorithm, is in principle a Fast Factorized Back-Projection (FFBP) realization with a number of adjustable (geometry) parameters for each factorization step. By altering the aperture in the time domain, it is possible to correct an arbitrary, inaccurate geometry. This in turn indicates that the FGA algorithm has the capacity to compensate for residual space variant RCM. In appended papers the performance of the algorithm is demonstrated for geometrically constrained autofocus problems. Results for simulated and real (Coherent All RAdio BAnd System II (CARABAS II)) Ultra WideBand (UWB) data sets are presented. Resolution and Peak to SideLobe Ratio (PSLR) values for (point/point-like) targets in FGA and reference images are similar within a few percents and tenths of a dB. As an example: the resolution of a trihedral reflector in a reference image and in an FGA image respectively, was measured to approximately 3.36 m/3.44 m in azimuth, and to 2.38 m/2.40 m in slant range; the PSLR was in addition measured to about 6.8 dB/6.6 dB. The advantage of a geometrical autofocus approach is clarified further by comparing the FGA algorithm to a standard strategy, in this case the Phase Gradient Algorithm (PGA)