Paul H. Eichel

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. >

Speckle processing method for synthetic-aperture-radar phase correction

Uncompensated phase errors present in synthetic-aperture-radar data can have a disastrous effect on reconstructed image quality. We present a new iterative algorithm that holds promise of being a robust estimator and corrector for arbitrary phase errors. Our algorithm is similar in many respects to speckle processing methods currently used in optical astronomy. We demonstrate its ability to focus scenes containing large amounts of phase error regardless of the phase-error structure or its source. The algorithm works extremely well in both high and low signal-to-clutter conditions without human intervention.

Phase-gradient algorithm as an optimal estimator of the phase derivative.

The phase-gradient algorithm represents a powerful new signal-processing technique with applications to aperture-synthesis imaging. These include, for example, synthetic-aperture-radar phase correction and stellar-image reconstruction. The algorithm combines redundant information present in the data to arrive at an estimate of the phase derivative. We show that the estimator is in fact a linear, minimum-variance estimator of the phase derivative.

Compression of complex-valued SAR images

Synthetic aperture radars (SAR) are coherent imaging systems that produce complex-valued images of the ground. Because modern systems can generate large amounts of data, there is substantial interest in applying image compression techniques to these products. We examine the properties of complex-valued SAR images relevant to the task of data compression. We advocate the use of transform-based compression methods but employ radically different quantization strategies than those commonly used for incoherent optical images. The theory, methodology, and examples are presented.

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.

Comparison of synthetic-aperture radar autofocus techniques: phase gradient versus subaperture

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.

Autofocus Of Sar Imagery Degraded By Ionospheric-Induced Phase Errors

It has been suggested that synthetic aperture radar (SAR) images obtained from platforms such as SEASAT are subject to potential degradation by ionospheric-induced phase errors. This premise is based upon data from various satellite experiments that indicate large levels of phase scintillation in auroral zone data. Current models for phase errors induced by the ionosphere suggest that the phase error power spectrum is power law. This implies that the resulting phase errors contain significant components up to the Nyquist limit. Traditional sub-aperture based autofocus techniques, designed to correct uncompensated platform motion errors, are inadequate due to their inability to estimate higher order error terms. A new non-parametric phase error correction scheme developed at Sandia National Laboratories, however, has been demonstrated to remove phase errors of arbitrary structure. Consequently, our new algorithm is a viable candidate for correcting ionospheric phase errors. In this paper we show examples of SAR images degraded by simulated ionospheric phase errors. These images demonstrate that such errors cause smearing with complicated sidelobe structure. Restoration of these images via the new algorithm illustrates its superiority to classical sub-aperture based autofocus techniques.

Very low rate compression of speckled SAR imagery

SAR produce coherent, and speckled, high resolution images of the ground. Because modern systems can generate large amounts of imagery, there is substantial interest in applying image compression techniques to these products. In this paper, we examine the properties of speckled imagery relevant to the task of data compression. In particular, we demonstrate the advisability of compressing the speckle mean function rather than the literal image. The theory, methodology, and an example are presented.

Interpolated spatially variant apodization in synthetic aperture radar imagery.

The original formulation of spatially variant apodization for complex synthetic aperture radar imagery concentrated on integer-oversampled data. Noninteger-oversampled data presented previously [IEEE Trans. Aerosp. Electron. Syst. 31, 267 (1995)] suggested use of different weightings in the algorithm. An alternative noninteger-oversampled approach that employs the same apodization concept but uses local spatial interpolation is presented. With this approach the combined image formation, apodization, and detection of 1.3x-versus-2.0x oversampled data can be performed in half the time without loss of image quality.

New formulation for interferometric synthetic aperture radar for terrain mapping

The subject of interferometric synthetic aperture radar (IFSAR) for high-accuracy terrain elevation mapping continues to gain importance in the arena of radar signal processing. Applications to problems in precision terrain-aided guidance and automatic target recognition, as well as a variety of civil applications, are being studied by a number of researchers. Not unlike many other areas of SAR processing, the subject of IFSAR can, at first glance, appear to be somewhat mysterious. In this paper we show how the mathematics of IFSAR for terrain elevation mapping using a pair of spotlight mode SAR collections can be derived in a very straightforward manner. Here, we employ an approach that relies entirely on Fourier transforms, and utilizes no reference to range equations or Doppler concepts. The result is a simplified explanation of the fundamentals of interferometry, including an easily-seen link between image domain phase difference and terrain elevation height. The derivation builds upon previous work by the authors in which a framework for spotlight mode SAR image formation based on an analogy to 3D computerized axial tomography (CAT) was developed. After outlining the major steps in the mathematics, we show how a computer simulator which utilizes 3D Fourier transforms can be constructed that demonstrates all of the major aspects of IFSAR from spotlight mode collections.