Target Detection Studies Using Fully Polarimetric Data Collected by the Lincoln Laboratory MMW SAR. L.M. Novak MIT Lincoln Laboratory

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1 Target Detection Studies Using Fully Polarimetric Data Collected by the Lincoln Laboratory MMW SAR Abstract L.M. Novak MIT Lincoln Laboratory Under DARPA sponsorship, MIT Lincoln Laboratory is investigating the detection and identification of stationary ground targets in high resolution, fully polarimetric, synthetic aperture radar (SAR) imagery. This paper compares two techniques for improving target detection performance by optimally processing the fully polarimetric SAR data. Introduction Target detection performance depends upon two fundamental radar parameters: () the target-to-clutter ratio (T/C), and (2) the standard deviation (σc) of the background clutter. This is reflected in the equation that defines the classical two-parameter CFAR (constant false alarm rate) detector []: if ( T / C) σc > K CFAR, declare target present. The detector uses clutter data around each cell under test to calculate the (T/C)-to-σc ratio and then compares the ratio with a CFAR constant, KCFAR (see Figure ). When a target is present, we would like the ratio to be as large as possible; when there is no target present, we would like the ratio to be small. To make the (T/C)-to-σc ratio as large as possible we may either maximize T/C or minimize σc (or both). This paper compares two basic approaches for processing fully polarimetric, complex HH, HV, and VV data to increase the (T/C)-to-σc ratio. The first approach maximizes the targetto-clutter ratio by coherently combining the complex HH, HV, and VV data using an optimal set of (complex) weights this is called polarimetric matched filter (PMF) processing [2]. The PMF weights are selected to maximize T/C; the standard deviation of the clutter, σc, is not reduced; it remains approximately the same as for a single-polarimetric-channel radar. The second approach minimizes the clutter standard deviation, σc, by processing the fully polarimetric, complex HH, HV, and VV data using a polarimetric whitening filter (PWF). In PWF processing [3] we first apply a whitening filter to the complex HH, HV, and VV data, resulting in a set of three uncorrelated complex images having equal power; these three uncorrelated images are then noncoherently summed to obtain the minimum speckle SAR image (noncoherent averaging of three uncorrelated "looks"). () Although the PWF approach produces a small loss in T/C (a "noncoherent-integration" loss), the standard deviation of the clutter background is significantly reduced. This reduction in σc has been found to result in significantly improved detection performance [4,5,6]. Using real, fully polarimetric SAR imagery of targets and clutter gathered by the Lincoln Laboratory sensor [7], we investigate () the increase in (T/C) achievable through optimal polarimetric matched filter (PMF) processing and (2) the reduction in σc achievable through optimal polarimetric whitening filter (PWF) processing. Also, the CFAR detection statistic (quation ) obtained using PMF and PWF imagery is compared with that obtained using single-polarimetric-channel imagery and the best polarimetric processing approach for CFAR detection of stationary targets in ground clutter is determined. Algorithm Descriptions This section describes two approaches for processing the fully polarimetric SAR data into SAR intensity images: () the polarimetric matched filter (PMF), and (2) the polarimetric whitening filter (PWF). There are, of course, other approaches which have been investigated elsewhere (see References [2,3,4]). In this section, we also briefly describe the twoparameter CFAR detector used to detect targets in SAR intensity images. Polarimetric Whitening Filter (PWF): In Reference [3], a simple quadratic processor was derived which combined the three complex HH, HV, and VV polarimetric images into a SAR intensity image having the desirable property that the speckle (or equivalently, the standard deviation of the background clutter) is minimized. This polarimetric processor, the PWF, is given by the quadratic y X = c X where the radar measurement vector X consists of three complex elements, HH, HV, and VV, HH I + jhhq X = HVI + jhvq VVI + jvvq (2) (3) and c is the polarization covariance matrix of the radar return

2 from typical terrain clutter (c = Ε {X X }). Note that this algorithm requires a priori knowledge of the clutter polarization covariance only. A theoretical analysis of the detection performance using PWF imagery was reported in Reference [4]; it was shown that the detection performance of the PWF is essentially identical to that of an optimal polarimetric detector. Polarimetric Matched Filter (PMF): In Reference [2] a linear processor for combining the polarimetric measurements HH, HV, and VV, known as the polarimetric matched filter (PMF) was derived; this detector was designed to produce the maximum target-to-clutter ratio in the SAR intensity image. This optimal processor is given by the equation 2 y = W X (4) where W is a set of optimal weights used to combine the complex HH, HV, and VV data. The optimal weight vector, W, is obtained as the solution to the following eigenvalueeigenvector problem c t W = λw (5) where c is the polarization covariance of the clutter, t is the polarization covariance of the target, and W is the eigenvector corresponding to the eigenvalue, λ. The optimal weight vector, W, is the eigenvector corresponding to the maximum eigenvalue of the matrix c t. Note that this processing approach requires a priori knowledge of both the target and clutter polarization covariances. Single-Channel Detectors ( HH 2, HV 2, VV 2): The simplest detectors would make use of a singlepolarimetric-channel SAR image. We will compare detection performance using PWF and PMF imagery with that obtained using single-polarimetric-channel SAR imagery. In this case, the image is obtained by computing the magnitude squared of, say, the HH channel, as indicated below: Two-Parameter CFAR Detector: 2 y = HH (6) We define CFAR to mean the detection rule t arget X t < > µ ˆ c + K CFARσˆ c clutter (7) where Xt is the scalar pixel value of the cell under test. Also, ˆµ c is the estimated clutter mean (obtained from the clutter data in the CFAR stencil), ˆσ c is the estimated clutter standard deviation (also obtained from the clutter data in the CFAR stencil), and KCFAR is a constant that defines the false alarm rate (see Figure ). Since the SAR intensity images are converted to units of db (by taking 0 log y prior to running the CFAR detector over the image) quation 7 is easily shown to have the form given previously in quation. Results of Polarimetric Processing The data used for this experiment were collected near Stockbridge, NY by the Lincoln Laboratory MMW SAR. Figure 2 shows a.0 m.0 m resolution SAR image (HH polarization) of the specific area from which we chose to take intensity measurements of targets and clutter. This image was formed by spoiling the 0.3 m 0.3 m HH intensity image to an effective.0 m.0 m resolution by noncoherent averaging of 4 pixel by 4 pixel clusters. Clearly visible in the upper and lower portions of the image are two regions of trees separated by a narrow strip of coarse scrub. Also visible in the image, though somewhat faint, are four powerline towers positioned in the scrub region (one pair of towers in the upper left of the image and one pair in the lower right). We used the scrub region located in the vicinity of the powerline towers as our background clutter and calculated the polarization covariance, c, to be.00 + j j j0.05 c = j j j0.00 (8) 0.55 j j j0.00 Note that the polarization covariance for scrub clutter may be approximated (quite accurately) by the general form reported in Reference [2]: and ρ = c = σhh 0 * ρ γ ( * VV ) 2 2 HH VV 0 ε 0 ρ γ 0 γ 2 2 HV VV 2 where σ HH = HH, ε =, γ =, 2 2 HH HH HH Next we evaluated the polarization covariances of tree, grass, and shadow regions. For each region, we estimated the clutter polarization covariance parameters σhh, ε, γ, and ρ defined in quation 0; these estimates are given in Table. (9) (0)

3 Since the polarimetric processing techniques presented in this paper are invariant with respect to scale (σhh), and since the normalized polarization covariance parameters (ε, γ, and ρ) of trees, scrub, and grass (Table ) were found to be very similar, a single clutter polarization covariance was used to process the entire image without sacrificing enhancement performance; thus, we selected a constant value for c corresponding to the measured covariance of the scrub region. Region Table Polarization Covariance Parameters σhh ε γ Trees Scrub Grass Shadow For convenience, we considered the powerline towers shown in Figure 2 to be our hypothetical targets of interest. We estimated the target covariance from several hundred bright peaks in the vicinity of each tower. The value obtained for t was.00 + j0.00 t = j j j j j0.6 ρ 0.39 j j j0.00 γ () From this target covariance we see that ( HV 2) =.4( HH 2) which implies that the powerline towers give an unusually large HV-polarized return. This is due to the physical structure of the towers. As shown in Figure 3, the tower frames are reinforced with steel-strut lattices oriented at many different angles. With numerical values assigned to c and t, we constructed PWF, PMF, and single-polarimetric-channel HH, HV, and VV images at 0.3 m 0.3 m resolution. We then extracted target and clutter data and computed the following four statistics from these data: Standard-deviation-to-mean ratio (s/m): The quantity s/m (in which the numerator and denominator are in units of power) is a measure of image speckle. To quantify the speckle-reduction capability of each processor we computed the s/m ratio for the clutter regions (trees, scrub, grass, and shadows) and also for the target. Log standard deviation: This quantity is simply the standard deviation of the clutter data after being converted to units of db. The log standard deviation is an important statistic to examine because it directly affects the target detection performance of a two-parameter CFAR algorithm []. To quantify the variance-reduction capability of each processor we computed the log standard deviation for the clutter regions (trees, scrub, grass, and shadows) and also for the target. Target-to-clutter ratio (T/C): The quantity T/C, computed as the difference of target and clutter means (in units of db), measures the average output power in the target region relative to the average output power in the clutter region. Since in this case the targets (i.e., the powerline towers) are located in the scrub region, we computed this quantity only for the clutter data representing the scrub. Deflection ratio: This quantity is the two-parameter CFAR detection statistic (see quation ); it is defined as the targetto-clutter ratio (in units of db) divided by the clutter standard deviation (in units of db). Once again, since the targets are located in the scrub region, we computed this quantity only for the clutter data representing the scrub. Table 2 presents the computed standard-deviation-to-mean ratios. Clearly, the PWF performs best under this criterion since it was designed to minimize s/m ratio for clutter. Notice that for all processors the s/m ratios for trees are larger than those for scrub, and the s/m ratios for scrub are larger than those for grass. This is an expected result because the s/m ratio depends not only on speckle, but also on the underlying terrain roughness. Table 3 shows the corresponding standard deviation (in db) of each clutter type. For this statistic, the PWF again yields the lowest value among all processors evaluated, achieving significant variance reduction for each clutter type. Table 4 shows the target-to-clutter ratios and deflection ratios for each polarimetric processor. For these statistics, the targets were defined to be the powerline towers and the clutter was defined to be the region of scrub in which the towers are positioned. Note that the PWF shows an increase in the T/C ratio relative to the HH and VV polarizations, but shows a decrease relative to the HV polarization. However, the deflection ratio for the PWF is by far the highest among all processors. The PMF also shows improvements in the T/C ratio and the deflection ratio over the individual polarizations HH, HV, and VV. Table 2 Standard Deviation-to-Mean (Power) of 0.3 m 0.3 m Resolution Data Processor Trees Scrub Grass Shadow Target HH HV VV PWF PMF Table 3 Standard Deviation (db) of 0.3 m 0.3 m Resolution Data Processor Trees Scrub Grass Shadow Target HH HV VV PWF PMF

4 Table 4 Target-to-Clutter Ratio (db) and Deflection Ratio of 0.3 m 0.3 m Resolution Data Processor T/C Ratio Deflection Ratio HH HV VV PWF PMF To demonstrate these results visually, Figure 4 shows a PWF image of the powerline tower scene; note that after PWF processing, the powerline towers have much greater intensity than they had in the single-polarimetric-channel HH image. In Figure 5, we give a graphical example of how the target and clutter distributions are changed by polarimetric processing. Clearly, the histograms for the PWF-processed data exhibit much less intensity variation than do the histograms for the HH-polarized data. In addition, since the PWF greatly reduces speckle in the scrub region, the features of the projected powerline tower shadow are easily discerned. Figure 6 shows the powerline tower and its shadow projected onto the ground. Notice the intricate shadow structure in the area below the tower in this image, and the corresponding physical structure of the actual tower as shown in Figure R.D. Chaney, et al., "On the Performance of Polarimetric Target Detection Algorithms", I International Radar Conference, May W.W. Irving, et al., "Adaptive Processing of POL-SAR Imagery", Asilomar, Conference, November L.M. Novak, et al., "Optimal Polarimetric Processing for nhanced Target Detection", I Trans. AS, January J.C. Henry, "The Lincoln Laboratory 35 GHz Airborne Polarimetric SAR Imaging System", I National Telesystems Conference, March 99. Summary This paper has presented the results of a study of two approaches for processing fully polarimetric SAR data into SAR intensity imagery. The approaches are () the polarimetric matched filter (PMF), and (2) the polarimetric whitening filter (PWF). Using a database of 0.3 m 0.3 m, fully polarimetric SAR data, it was shown that the PMF did indeed maximize target-to-clutter ratio; however, the PMF clutter standard deviation was shown to be approximately the same as for single-polarimetric-channel imagery. Although the PWF exhibited a small loss in target-to-clutter ratio (about db compared to the PMF), the PWF reduced the standard deviation of the background clutter significantly (about 2.3 db more than the PMF for scrub clutter). As a result, PWF processing significantly increased the two-parameter CFAR detection statistic (the (T/C)-to-σc ratio); thus, under this criterion, the best polarimetric processing approach for CFAR detection of stationary targets in ground clutter is the PWF. Figure : Two-parameter CFAR detector. References. G.B. Goldstein, "False Alarm Regulation in Log Normal and Weibull Clutter", I Trans. AS, January L.M. Novak, et al., "Studies of Target Detection Algorithms That Use Polarimetric Radar Data", I Trans. AS, March L.M. Novak, et al., "Optimal Speckle Reduction in POL- SAR Imagery", I Trans. AS, March 990. Figure 2: HH image of powerline tower scene (.0 m.0 m).

5 Figure 5: Histograms of target and clutter data. Figure 3: Photograph of one of the powerline towers. Figure 4: PWF image of the powerline tower scene (.0 m.0 m). Figure 6: PWF (0.3 m 0.3 m) image of a single powerline tower and its shadow projected onto the ground.