Daniel E. Wahl

Phase gradient autofocus-a robust tool for high resolution SAR phase correction

The phase gradient autofocus (PGA) technique for phase error correction of spotlight mode synthetic aperture radar (SAR) imagery is examined carefully in the context of four fundamental signal processing steps that constitute the algorithm. We demonstrate that excellent results over a wide variety of scene content, and phase error function structure are obtained if and only if all of these steps are included in the processing. Finally, we show that the computational demands of the fun PGA algorithm do not represent a large fraction of the total image formation problem, when mid to large size images are involved. >

Eigenvector method for maximum-likelihood estimation of phase errors in synthetic-aperture-radar imagery

We develop a maximum-likelihood (ML) algorithm for estimation and correction (autofocus) of phase errors induced in synthetic-aperture-radar (SAR) imagery. Here, M pulse vectors in the range-compressed domain are used as input for simultaneously estimating M − 1 phase values across the aperture. The solution involves an eigenvector of the sample covariance matrix of the range-compressed data. The estimator is then used within the basic structure of the phase gradient autofocus (PGA) algorithm, replacing the original phase-estimation kernel. We show that, in practice, the new algorithm provides excellent restorations to defocused SAR imagery, typically in only one or two iterations. The performance of the new phase estimator is demonstrated essentially to achieve the Cramer–Rao lower bound on estimation-error variance for all but small values of target-toclutter ratio. We also show that for the case in which M is equal to 2, the ML estimator is similar to that of the original PGA method but achieves better results in practice, owing to a bias inherent in the original PGA phase estimation kernel. Finally, we discuss the relationship of these algorithms to the shear-averaging and spatial correlation methods, two other phase-correction techniques that utilize the same phase-estimation kernel but that produce substantially poorer performance because they do not employ several fundamental signal-processing steps that are critical to the algorithms of the PGA class.

New approach to strip-map SAR autofocus

This paper demonstrates how certain concepts from the Phase Gradient Autofocus (PGA) algorithm for automated refocus of spotlight mode SAR imagery may be used to design a similar algorithm that applies to SAR imagery formed in the conventional strip-mapping mode. The algorithm derivation begins with the traditional view of strip-map image formation as convolution (compression) using a linear FM chirp sequence. The appropriate analogies and modifications to the spotlight mode case are used to describe a working algorithm for strip-map autofocus.<<ETX>>

Refocus of constant velocity moving targets in synthetic aperture radar imagery

The detection and refocus of moving targets in SAR imagery is of interest in a number of applications. In this paper we address the problem of refocussing a blurred signature that has by some means been identified as a moving target. We assume that the target vehicle velocity is constant, i.e., the motion is in a straight line with constant speed. The refocus is accomplished by application of a 2D phase function to the phase history data obtained via Fourier transformation of an image chip that contains the blurred moving target data. By considering separately the phase effects of the range and cross-range components of the target velocity vector, we show how the appropriate phase correction term can be derived as a two-parameter function. We then show a procedure for estimating the two parameters, so that the blurred signature can be automatically refocused. The algorithm utilizes optimization of an image domain contrast metric. We present results of refocusing moving targets in real SAR imagery by this method.

Interferometric synthetic aperture radar terrain elevation mapping from multiple observations

All prior interferometric SAR imaging experiments to date dealt with pairwise processing. Simultaneous image collections from two antenna systems or two-pass single antenna collections are processed as interferometric pairs to extract corresponding pixel by pixel phase differences which encode terrain elevation height. The phase differences are wrapped values which must be unwrapped and scaled to yield terrain height. We propose two major classes of techniques that hold promise for robust multibaseline (multiple pair) interferometric SAR terrain elevation mapping. The first builds on the capability of a recently published method for robust weighted and unweighted least-squares phase unwrapping, while the second attacks the problem directly in a maximum likelihood (ML) formulation. We will provide several examples (actual and simulated SAR imagery) that illustrate the advantages and disadvantages of each method.<<ETX>>

Towed array shape estimation using frequency-wavenumber data

Towed array beamforming algorithms require accurate array shape information in order to perform properly. Very often, these algorithms assume the array is linear. Unfortunately, the mechanical forces on the array due to ship motion and sea dynamics can change the shape of the array, which degrades the performance of the beamforming algorithm. A data-driven approach to estimating the relative shape of a nominally linear array is presented. The algorithm is robust in that it optimally combines information contained in a wide band of frequencies and source bearings. At the heart of the algorithm is a maximum-likelihood (ML) estimation scheme. The Cramer-Rao lower bound is derived and compared to the performance of the ML estimator. The utility of the algorithm is verified using both simulated and actual towed array data experiments. >

An implementation of a fast backprojection image formation algorithm for spotlight-mode SAR

In this paper we describe an algorithm for fast spotlight-mode synthetic aperture radar (SAR) image formation that employs backprojection as the core, but is implemented such that its compute time is comparable to the often-used Polar Format Algorithm (PFA). (Standard backprojection is so much slower than PFA that it is impractical to use in many operational scenarios.) We demonstrate the feasibility of the algorithm on real SAR phase history data sets and show some advantages in the SAR image formed by this technique.

General formulation for wavefront curvature correction in polar-formatted spotlight-mode SAR images using space-variant post-filtering

We introduce a general formulation for wavefront curvature correction in spotlight-mode SAR images formed using the polar-formatting algorithm (PFA). This correction is achieved through the use of an efficient, image domain space-variant filter which is applied as a post-processing step to the PFA. Wavefront curvature defocus effects occur in certain SAR collection modes that include imaging at close range, using a low center frequency, and/or imaging very large scenes. Our formulation is general in that it corrects for wavefront curvature in broadside as well as squinted collection modes, with no computational penalty for correcting squint-mode images. Algorithms such as the range migration technique (also known as seismic migration), and an enhancement known as frequency domain replication, FReD, have been developed to accommodate these wavefront curvature effects. However, they exhibit no clear computational advantage over space-variant post-filtering in conjunction with polar formatting (PF2). This paper presents the basic concepts of the formulation, and provides computer results demonstrating the capabilities of space-variant post-filtering.

Terrain elevation mapping results from airborne spotlight-mode coherent cross-track SAR stereo

Coherent cross-track synthetic aperture radar (SAR) stereo is shown to produce high-resolution three-dimensional maps of the Earth surface. This mode utilizes image pairs with common synthetic apertures but different squint angles allowing automated stereo correspondence and disparity estimation using complex correlation calculations. This paper presents two Ku-band, coherent cross-track stereo collects over rolling and rugged terrain. The first collect generates a digital elevation map (DEM) with 1-m posts over rolling terrain using complex SAR imagery with spatial resolution of 0.125 m and a stereo convergence angle of 13.8/spl deg/. The second collect produces multiple DEMs with 3-m posts over rugged terrain utilizing complex SAR imagery with spatial resolutions better than 0.5 m and stereo convergence angles greater than 40/spl deg/. The resulting DEMs are compared to ground-truth DEMs and relative height root-mean-square, linear error 90-percent confidence, and maximum height error are reported.

Space-variant filtering for correction of wavefront curvature effects in spotlight-mode SAR imagery formed via polar formatting

Wavefront curvature defocus effects can occur in spotlight- mode SAR imagery when reconstructed via the well-known polar formatting algorithm under certain scenarios that include imaging at close range, use of very low center frequency, and/or imaging of very large scenes. The range migration algorithm, also known as seismic migration, was developed to accommodate these wavefront curvature effects. However, the along-track upsampling of the phase history data required of the original version of range migration can in certain instances represent a major computational burden. A more recent version of migration processing, the frequency domain replication and downsampling (FReD) algorithm, obviates the need to upsample, and is accordingly more efficient. In this paper we demonstrate that the combination of traditional polar formatting with appropriate space-variant post- filtering for refocus can be as efficient or even more efficient than FReD under some imaging conditions, as demonstrated by the computer-simulated results in this paper. The post-filter can be pre-calculated from a theoretical derivation of the curvature effect. The conclusion is that the new polar formatting with post filtering algorithm should be considered as a viable candidate for a spotight-mode image formation processor when curvature effects are present.