In past research, two-pass repeat-geometry synthetic aperture radar (SAR) coherent change detection (CCD) predominantly utilized the sample degree of coherence as a measure of the temporal change occurring between two complex-valued image collects. Previous coherence-based CCD approaches tend to show temporal change when there is none in areas of the image that have a low clutter-to-noise power ratio. Instead of employing the sample coherence magnitude as a change metric, in this paper, we derive a new maximum-likelihood (ML) temporal change estimate-the complex reflectance change detection (CRCD) metric to be used for SAR coherent temporal change detection. The new CRCD estimator is a surprisingly simple expression, easy to implement, and optimal in the ML sense. This new estimate produces improved results in the coherent pair collects that we have tested.

Introduction: The Mini-RF team is acquiring bistatic radar measurements of the lunar surface to understand the scattering properties of materials as a function of bistatic angle. These observations have produced the first lunar radar images ever collected with non-zero bistatic angles. The goal of these observations is to test the hypothesis that some permanently shadowed areas near the lunar poles contain water ice. Rationale: The bistatic angle is determined by the positions and orientations of the radar transmitter and receiver. For radar observations that use the same antenna to transmit and receive a signal, the bistatic angle is zero, and they are referred to as monostatic. NASA’s Mini-RF instrument on the Lunar Reconnaissance Orbiter is currently operating in a bistatic mode with the Arecibo Observatory acting as the transmitter and the Mini-RF antenna acting as the receiver. In this mode, Arecibo transmits a circular polarized S-band signal at a transmitted power of 200 kW. The portion of the signal reflected off the lunar surface and into the MiniRF antenna is received in orthogonal linear polarizations as well as their relative phase. This architecture is equivalent to the hybrid dual-polarimetric architecture of the monostatic mode for the Mini-RF instrument [1] and, therefore, allows for the calculation of the Stokes parameters (S1, S2, S3, S4) that characterize the backscattered signal (and the products derived from those parameters). The circular polarization ratio,

We have employed the Arecibo Observatory Planetary Radar (AO) transmitter and the Mini-RF radar onboard NASA's Lunar Reconnaissance Orbiter (LRO) as a receiver to collect bistatic data of the lunar surface. In this paper, we demonstrate the ability to form bistatic polarimetric imagery with spatial resolution on the order of 50m, and to create polarimetric maps that could potentially reveal the presence of ice in lunar permanently shadowed craters. We discuss the details of the signal processing techniques that are required to allow these products to be formed.

Beamforming is a methodology for collection-mode-independent SAR image formation. It is essentially equivalent to backprojection. The authors have in previous papers developed this idea and discussed the advantages and disadvantages of the approach to monostatic SAR image formation vis-a-vis the more standard and time-tested polar formatting algorithm (PFA). In this paper we show that beamforming for bistatic SAR imaging leads again to a very simple image formation algorithm that requires a minimal number of lines of code and that allows the image to be directly formed onto a three-dimensional surface model, thus automatically creating an orthorectified image. The same disadvantage of beamforming applied to monostatic SAR imaging applies to the bistatic case, however, in that the execution time for the beamforming algorithm is quite long compared to that of PFA. Fast versions of beamforming do exist to help alleviate this issue. Results of image reconstructions from phase history data are presented.

In recent papers the authors discussed the advantages of forming spotlight-mode SAR imagery from phase history data via a technique that is rooted in the principles of phased-array beamforming, which is closely related to back-projection. The application of a traditional autofocus algorithm, such as Phase Gradient Autofocus (PGA), requires some care in this situation. Specifically, a stated advantage of beamforming is that it easily allows for reconstruction of the SAR image onto an arbitrary imaging grid. One very useful grid, for example, is a Cartesian grid in the ground plane. Autofocus via PGA for such an image, however, cannot be performed in a straightforward manner, because in PGA a Fourier transform relationship is required between the image domain and the range-compressed phase history, and this is not the case for such an imaging grid. In this paper we propose a strategy for performing autofocus in this situation, and discuss its limitations. We demonstrate the algorithm on synthetic phase errors applied to real SAR imagery.

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.

In this paper we show that the technique for spotlight-mode SAR image formation generally known as "backprojection" or "time-domain" is most easily derived and described in terms of the well-known methods of phased-array beamforming. By contrast, backprojection has been typically developed via analogy to tomographic imaging, which restricts this technique to the case of planar wavefronts. We demonstrate how the very simple notion of delay-and-sum beamforming leads directly to the backprojection algorithm for SAR, including the case for curved wavefronts. We further explain why backprojection offers a certain elegant simplicity for SAR imaging, and allows direct one-step computation of several useful SAR products, including an orthographically correct image free of any geometric or defocus effects from wavefront curvature and also free of the effects of terrain-elevation-induced defocus. (This product requires as an input a pre-existing digital elevation map (DEM) of the scene to be imaged.) In addition, we'll demonstrate why beamforming yields a mode-independent SAR image formation algorithm, i.e. one that can just as easily accommodate strip-map or spotlight-mode phase histories collected on an arbitrary flight path.

In this paper we describe a new method for creating three-dimensional images using pairs of synthetic aperture radar (SAR) images obtained from a unique collection geometry. This collection mode involves synthetic apertures that have a common centei: In this sense the illumination directions for the two SAR images are the same, while the slant planes are at different spatial orientations. The slant plane orientations give rise to cross-range layover (foreshortening) components in the two images that are of equal magnitude but opposite directions. This differential crossrange layover is therefore proportional to the elevation of a given target, which is completely analogous to the situation in stereo optical imaging, wherein two $lm planes (corresponding to the two slant planes) result in elevationdependent parallax. Because the two SAR collections are coherent in this particular collection mode, the images have the same speckle patterns throughout. As a result, the images may be placed into stereo correspondence via calculation of correlations between micro-patches of the complex image data. The resulting computed digital stereo elevation map can be quite accurate. Alternatively, an analog anaglyph can be displayed for 3-0 viewing, avoiding the necessity of the stereo correspondence calculation.

Automated synthetic aperture radar (SAR) stereo correspondence becomes increasingly difficult when imaging high-relief terrain utilizing large stereo crossing-angle geometries because high-relief SAR image features can undergo significant spatial distortions, causing a failure of traditional correlation matching. This paper presents eight coherent spotlight-mode cross-track stereo pairs with stereo crossing angles averaging 93.7deg collected over a terrain with slopes greater than 20deg. These stereo pairs suffer from terrain-induced distortions, resulting in a decrease in complex correlation (coherence) when utilizing scanning-window correlation calculations. The search to maximize complex correlation is changed from a shift-only (disparity) search to a shift-and-scale search using the downhill simplex method. This approach is tested against complex imagery with simulated distortions and then employed on the eight wide-angle stereo collects. The resulting digital terrain maps (DTMs) are compared to ground truth. Using a shift-and-scale correlation approach to estimate disparity, the relative height errors decrease, and the number of reliable DTM posts increase

A new spotlight-mode synthetic aperture radar im- age formation approach is presented that directly utilizes the reflected electromagnetic returns collected on a polar grid. This approach eliminates polar-to-rectangular grid interpolation by employing chirp z-transforms in two dimensions. Since the chirp z-transform can be implemented via fast Fourier transforms (FFTs), this image formation algorithm consists almost entirely of FFTs allowing it to exploit computationally-efficient FFT engines for fast image formation speeds. This paper presents the algo- rithm, and compares the operation counts and execution time between the new algorithm and traditional polar formatting, which employs interpolation. The paper also presents conditions for which the chirp z-transform in two dimensions is advanta- geous.

While the chief cause of defocus in airborne spotlight-mode imagery is uncompensated errors in the measurement of the aircraft position as it traverses the synthetic aperture, another physical phenomenon can cause blurring in the formed SAR image as well. This is the injection of phase errors into the collected SAR phase history data by random fluctuations in the index of refraction as the microwave pulses propagate through an atmosphere that contains irregularities in the tropospheric water vapor distribution. In this paper, we show that in SAR imagery collected under certain conditions, these phase errors can be detected and corrected using a robust autofocus algorithm such as Phase Gradient Autofocus (PGA). The phase errors are confirmed as having been propagation-induced by demonstrating that they exhibit a power-law spectrum described by Tatarski, based on the turbulence model of Kolmogorov.

The convolution/back-projection (CBP) algorithm has recently once again been touted as the "gold standard" for spotlight-mode SAR image formation, as it is proclaimed to achieve better image quality than the well-known and often employed polar formatting algorithm (PFA). In addition, it has been suggested that PFA is less flexible than CBP in that PFA can only compute the SAR image on one grid and PFA cannot add or subtract pulses from the imaging process. The argument for CBP acknowledges the computational burden of CBP compared to PFA, but asserts that the increased image accuracy and flexibility of the formation process is warranted, at least in some imaging scenarios. Because CBP can now be sped up by the proper algorithm design, it becomes, according to this line of analysis, the clear algorithm of choice for SAR image formation. In this paper we reject the above conclusion by showing that PFA and CBP achieve the same image quality, and that PFA has complete flexibility, including choice of imaging plane, size of illuminated beam area to be imaged, resolution of the image, and others. We demonstrate these claims via formation of both simulated and real SAR imagery using both algorithms.

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.

This paper compares three algorithms for potential use in a real-time, on-board implementation of spotlight-mode SAR image formation. These include: the polar formatting algorithm (PFA), the range migration algorithm (RMA), and the overlapped subapertures algorithm (OSA). We conclude that for any reasonable spotlight-mode imaging scenario, PFA is easily the algorithm of choice because its computational efficiency is significantly higher than that of either RMA or OSA. This comparison specifically includes cases in which wavefront curvature is sufficient to cause image defocus in conventional PFA, because a post-processing refocus step can be performed with PFA to yield excellent image quality for only a minimal increase in computation time. We demonstrate that real-time image formation for many imaging scenarios is achievable using PFA implemented on a single Pentium(R) M* processor. OSA is quite slow compared to PFA, especially for the case of moderate to high resolution (9 inches and better). RMA is not competitive with PFA for situations that do not require wavefront curvature correction. For those cases in which PFA requires post-processing to correct for wavefront curvature, RMA comes closer in efficiency to PFA, but is still outperformed by the modified PFA.

Coherent stereo pairs from cross-track synthetic aperture radar (SAR) collects allow fully automated correlation matching using magnitude and phase data. Yet, automated feature matching (correspondence) becomes more difficult when imaging rugged terrain utilizing large stereo crossing angle geometries because high-relief features can undergo significant spatial distortions. These distortions sometimes cause traditional, shift-only correlation matching to fail. This paper presents a possible solution addressing this difficulty. Changing the complex correlation maximization search from shift-only to shift-and-scaling using the downhill simplex method results in higher correlation. This is shown on eight coherent spotlight-mode cross-track stereo pairs with stereo crossing angles averaging 93.7°. collected over terrain with slopes greater than 20°. The resulting digital elevation maps (DEMs) are compared to ground truth. Using the shift-scaling correlation approach to calculate disparity, height errors decrease and the number of reliable DEM posts increase.