Template-Based SAR ATR Performance Using Different Image Enhancement Techniques. G.J. Owirka, S.M. Verbout, and L.M. Novak MIT Lincoln Laboratory

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1 Template-Based SAR ATR Performance Using Different Image Enhancement Techniques G.J. Owirka, S.M. Verbout, and L.M. Novak MIT Lincoln Laboratory Abstract The Lincoln Laboratory baseline ATR system for synthetic aperture radar (SAR) data applies a superresolution technique known as high definition imaging (HDI) before the input image is passed through the final target classification subsystem. In previous studies, it has been demonstrated that HDI improves target recognition performance significantly. Recently, however, several other viable SAR image enhancement techniques have been proposed and discussed in the literature which could be used in place of (or perhaps in conjunction with) the HDI technique. This paper compares the performance achieved by the Lincoln Laboratory template-based classification subsystem when these alternative image enhancement techniques are used instead of the HDI technique. In addition, empirical evidence is presented suggesting that target recognition performance could be further improved by fusing the classifier outputs generated by the best image enhancement techniques. 1 Introduction The Lincoln Laboratory baseline ATD/R system [1], which is depicted in Figure 1, consists of three basic data-processing stages: (1) detection; (2) discrimination; and (3) classification. In the detection and discrimination stages, the goal is to eliminate from further consideration any portions of the input imagery not containing targets, but simultaneously to allow all portions of the imagery containing targets to pass through to the classification stage. Classification is performed on each input subimage by finding the best matching target image from a database of stored target reference images or templates. The purpose of classification is to categorize the object in the input image either as a target of interest (of which there may be many types, e.g., T72 tank, M109 howitzer, etc.), or as an uninteresting clutter object. Objects that are determined to be in the former category are labeled with the target type corresponding to the best matching template, whereas objects in the latter category are simply labeled as "unknown." When the basic classification algorithm is performed, the best matching template is declared to be the one that yields the smallest mean squared error (MSE) value with respect to the input image. However, as we can see from Figure 1, this template-matching algorithm is actually performed twice within the new multiresolution classification stage. The initial MSE preclassifier is implemented using imagery that has the inherent sensor resolution. This preclassifier provides coarse classification information which is used to reduce the final template search space (target type, aspect angle, and spatial offset). After preclassification has been performed, a superresolution technique known as high definition imaging (HDI) is applied to the input image before the image is passed to the final high-resolution MSE classification algorithm. The purpose of this multiresolution architecture for the classification subsystem is to reduce computational expense. In this paper, we compare the levels of target recognition performance achieved when different image enhancement algorithms are used in place of the HDI technique (i.e., just prior to applying the final MSE classification algorithm). The following six enhancement techniques were compared: (1) simple coherent upsampling (UPSAMP); (2) high-definition imaging (HDI) [2, 3]; (3) eigenvector-based imaging (EV) [4,5], (4) spatially variant apodization (SVA) [6]; (5) superresolved SVA (SSVA) [7]; (6) and SSVA with median filter postprocessing (SSVA-MED). Detailed descriptions of each of these techniques are provided later in the paper. The paper is organized into six sections. In Section 2, we give a detailed description of the data used throughout the investigation, and we define the figure of merit that was used to measure target recognition performance. In Section 3, we give a mathematical description of each of the SAR image enhancement techniques tested. In Section 4, we present and discuss the performance results obtained for each enhancement technique individually; in addition, we give results that were obtained by fusing the outputs of the best enhancement techniques. In Section 5, we demonstrate that these initial performance results remain valid even when we augment the test data set with a large collection of new input images. Finally, in Section 6 we provide a summary of our results and state the main conclusions of our investigation. 2 Background and Data Description The SAR imagery used in our investigation was provided to Lincoln Laboratory by Wright Laboratories, WPAFB, Dayton, Ohio. These data were collected by the Sandia National Laboratory X-band, HH-polarization SAR sensor in support of the DARPA-sponsored MSTAR program. The MSTAR data set consists of a large assortment of military targets that have been imaged at 15-degree and 17-degree depression angles and over 360 degrees of aspect. For our initial studies we evaluated the recognition performance of the baseline MSE classifier using imagery of 18 distinct targets contained in the MSTAR-1 data set; these targets are depicted in Figure 2. The imagery from the following 10 of these 18 targets were used to construct classifier templates: BMP#l, M2#1, T72#1, BTR60, BTR70, Ml, M109, M110, M113, and M548. A total of 72 templates were constructed for each target, covering 360 degrees of aspect;

2 thus, the classifier database for this investigation contained a grand total of 720 target templates. Each classifier template was constructed using a two step process. First, an average image was formed by taking a sequence of five target images from the original data set (with each image in the sequence being distinct from its predecessor by approximately one degree in aspect angle), aligning them relative to each other, and then computing their arithmetic mean (in the log-magnitude image domain) at each pixel location. Next, a windowing operation was performed on the average image to remove the clutter from around the target signature. For the preclassifier, this template construction procedure was carried out using the original 1.0 m 1.0 m resolution imagery; each target image used to form the average was 36 pixels 36 pixels. For the final high-resolution classifier, however, template construction was performed using imagery produced by the particular image enhancement technique being tested; in this case, each target image was 108 pixels 108 pixels. In Figure 3, we show examples of five-degree average images of an M109 SPG (Self Propelled Gun) generated by each of the six image enhancement techniques evaluated. Classifier testing was carried out using independent MSTAR-1 target data. The following 6 targets were used as independent target test inputs: BMP#2, BMP#3, M2#2, M2#3, T72#2 and T72#3 (see Figure 2). The remaining two targets, namely the HMMWV and M35, were used as "confuser" vehicles, i.e., vehicles not included in the set of 10 targets that the classifier was trained to recognize. Confuser vehicles should ideally be classified as "unknown." There were 1,170 independent target test inputs and 390 confuser vehicle inputs, making a total of 1,560 classifier inputs used in our initial studies. Additional classifier evaluations were performed using independent MSTAR-2 target data. This data set also contains 18 distinct targets. The following seven targets were used as independent target test inputs: 3 BTR70's and 4 M109's. The following 11 targets were used as confuser vehicle inputs: 2S1, BRDM2, D7, M520, M577, M60, M88, M978, T62, ZIL131, and ZSU23. For the MSTAR-2 data set, there were 1,916 independent target test inputs and 3,008 confuser vehicle inputs, making a total of 4,924 inputs used in our additional classifier evaluations. Combining the MSTAR-1 and MSTAR-2 data sets provided 3,086 independent target test inputs and 3,398 confuser vehicle inputs for a grand total of 6,484 classifier inputs. The results of our evaluations are presented in the form of classifier confusion matrices, which show the number of correct and incorrect classifications achieved on test inputs of each type. The classifier's ability to recognize test inputs is measured by computing the probability of correct classification, or P cc, which is defined as the fraction of all target test inputs that were correctly classified. On the other hand, the classifier's ability to reject confuser vehicles is measured by computing the probability of rejection, or P rej, which is defined as the fraction of all confuser vehicle inputs that were classified as unknown. 1n order to simplify the comparisons between the classification results for the vaxious image enhancement techniques, we varied the MSE classification threshold independently in each case so that the same fixed value of P rej was achieved in all cases. 3 Description of Image Enhancement Techniques 3.1 Image Interpolation (UPSAMP) One of the simplest possible techniques for enhancing a SAR image before passing it through the MSE classifier is to interpolate or upsample the image by a fixed integer factor k. If the interpolation is done properly, the performance of the MSE classifier can actually improve substantially, provided that the sampling rate used to generate the original image was greater than the Nyquist rate. This may seem counter to intuition at first, because the pixel values in an interpolated image cannot collectively contain any more target information than the pixel values in the original image. But it is important to realize that the MSE classifier is not guaranteed to perform well simply because all of the raw target information has been preserved through an appropriate choice of sampling rate; rather, the success of the classifier will depend on whether it is provided with an accurate, detailed representation of the target signature, so that the intricate structure present in the signature can be directly compared to that of other stored target signatures. To understand why finer sample spacing can improve classification performance, suppose that a given test image is being compared to a reference image containing the same target type. Even though these may be images of the same target - and indeed may have been collected by the same radar at matching aspect, depression, and squint angles - the target itself might have been positioned differently relative to the radar aimpoint during the formation of the images, and hence the two target signatures being compared might be sampled with a slight offset relative to each other. Although such an offset represents only a fraction of a pixel in either image dimension, it could clearly lead to a significant change in the MSE score between the two images. This is especially true if there are sharp peaks or valleys in the underlying, continuousvalued target image, because in this case a two-dimensional shift in the sampling grid could produce a pixel value in one image and a different pixel value in the corresponding location of the other image. The effect on MSE score due solely to the positioning of one sampling grid relative to another can be greatly reduced by interpolating the images, so that the effective sampling rate is much higher than the Nyquist rate. Of course, there are many different ways of interpolating the values in a SAR image; these include pixel replication (sometimes referred to as the sample-and-hold method), bilinear interpolation, and higher-order polynomial interpolation. However, the technique that appears to be most suitable for the present application - and the technique we have chosen to use here - is bandlimited interpolation. With

3 this method, the pixel values in the interpolated image are precisely the values from the underlying continuous version of the original bandlimited image taken at sampling locations on a new, finer sampling grid; the interpolated image contains k times as many pixels in each dimension as the input image. In practice, bandlimited interpolation can be easily implemented in several stages with the use of a twodimensional discrete Fourier transform (2D-DFT). First, an inverse 2D-DFT is applied to the complex input image in order to recover the original signal history data. This signal history (i.e., frequency-domain) data is then appended on all sides with zeros, so that the resulting array is a factor of k larger than the original. In this new zero-padded signal history array, the lowfrequency portion is occupied by the non-zero samples, and the high-frequency portion is occupied by the appended zeros. Finally, a forward 2D-DFT is applied to the new zero-padded signal history array to yield the interpolated image. 3.2 High-Definition Imaging (HDI) The high-definition imaging (HDI) algorithm, which was developed by Benitz [2,3], is the image enhancement technique that is currently used in the Lincoln Laboratory baseline ATR system. HDI is a variation of the MLM technique originally published by Capon [8]. Unlike conventional Fourier imaging, which uses a predetermined (i.e., data-independent) set of weighting coefficients for each pixel in the output image, HDI is a data-adaptive image formation method that selects an optimal set of weighting coefficients for each pixel. The goal of this technique is to minimize the energy due to interfering sources at each pixel location, but simultaneously to pass with unit gain an ideal point scatterer that would normally appear at this location. The HDI technique produces an output image that exhibits a significant improvement in resolution over the original image, as well as a noticeable reduction in energy due to surrounding clutter and interfering scatterer sidelobes. The HDI procedure begins by creating a mosaic from the original complex-valued image, i.e., it decomposes the original image into 12-pixel 12-pixel subimages. These input subimages are all eventually processed by the HDI algorithm and are then put back together to form the final output image. The first steps in processing each subimage include the application of a 2D-DFT and the subsequent removal of any aperture weighting that may have been applied to form the original image. Once these preprocessing steps are completed, we are left with the unweighted signal history array associated with the scatterers that appeared in the original subimage. The central 10-pixel 10-pixel portion of this signal history will be processed with different weight vectors to generate the pixel values in the output subimage. Let us assume for convenience that the elements of this signal history array are ordered lexicographically and arranged to form a 100-dimensional signal vector x. The fundamental idea behind HDI is to find, for a given output image location (i, j), a weight vector w(i, j) (which, for the sake of brevity, we denote simply by w) such that the output pixel value y at this image location satisfies y = = = subject to the constraint min E w min E w w min w w v = 1, { 2 w x } { xx E{ w Rw} where v represents the ideal point scatterer response associated with image location (i,j), and R is the covariance matrix of the random signal vector x. In other words, the optimal weight vector allows an ideal point scatterer to pass with unit gain but simultaneously minimizes the total energy at the current image location. If the matrix R has full rank, then the solution to the above minimization problem is given by 1 y =. v R 1 v Unfortunately, there are several difficulties with this direct method, including the fact that the covariance matrix R is unknown and that the above constraint is not strong enough to prevent many scatterers from being nulled completely in the output image. The strategy suggested by Benitz for overcoming these difficulties is to use a severely rank-deficient estimate of the covariance matrix, and to incorporate additional constraints on the weight vector so that weak scatterers will not be nulled. To estimate the 100-dimensional covariance matrix R, we need to extract other neighboring portions of the signal history and use them to form a sample average. It can be readily verified that, if we include the center portion of the signal history in the estimate, there are a total of nine such sample vectors that can be extracted from the signal history. However, we can employ a clever technique from classical time series analysis (sometimes referred to as the forward-backward method) to create additional independent sample vectors from the same data array. Specifically, by simply reversing the direction of the column and row ordering of the original signal history, and then taking the complex conjugate of this spatially reversed array, we can obtain an additional nine sample vectors, and hence increase the rank of the final covariance estimate to 18. To describe the HDI technique in its present form, let us denote by Rˆ the reduced-rank estimate of the covariance matrix of the signal vector. In addition, let v proj be the projection of the ideal scatterer response v onto the column space of the matrix Rˆ ; we denote this subspace by span { } Rˆ. Then the goal of the HDI technique is to solve (1) (2) (3) (4) (5)

4 y = min w { w Rˆ w} subject to the following three constraints on the weight vector w: w v 2 proj β w vproj = v w span 2 proj { Rˆ } In the first constraint, the quantity β is a positive real number that serves to limit to degree to which the weight vector can deviate from the projected point scatterer response. This constraint, together with the subspace constraint on the weight vector, prevents scatterers in the image from being entirely canceled out, and therefore tends to preserve much of the original image background. 3.3 Eigenvector-Based Imaging (EV) The eigenvector (EV) approach to SAR image enhancement, which was developed by Johnson [4] and analyzed further by Johnson and DeGraaf [51, shares certain common attributes with the HDI technique. In particular, both of these techniques operate on the original image by decomposing it and processing it in many small (i.e., 12-pixel 12-pixel) subimages; moreover, both are data-dependent, but require only the covariance matrix of the signal history vector that is associated with each subimage. Unlike HDI, however, the EV technique does not attempt to solve a concrete optimization problem to suppress interfering sources. Instead, it generates an enhanced image based on an ad-hoc algebraic analysis of the signal history vector. In particular, the EV technique is based on the principle that the signal history is made up of two fundamentally distinct types of components, namely those belonging to a signal class and those belonging to a clutter class. Moreover, the signal and clutter classes are taken to be so structurally different that any signal component is assumed to be essentially orthogonal to any clutter component. Accordingly, the multi-dimensional space in which the signal history vector lies can be decomposed into two orthogonal subspaces, which we refer to as the signal subspace and the clutter subspace. Once this conceptual distinction is made, the EV algorithm can easily construct an output image designed to enhance any signal components contained in the data and simultaneously suppress any clutter components. The EV technique differs from the HDI technique in that it must have a full-rank estimate of the covariance matrix, so that it is able to fully characterize both the signal and clutter subspaces. Because the subimage size is taken to be under either method, this full-rank constraint implies that the aperture extracted from the signal history must be smaller than the aperture used for HDI. We selected an aperture size of 6 6, (6) (7) (8) (9) so that the signal history vector was only 36-dimensional; with this size parameter fixed, a total of 98 sample vectors (49 in each direction using the forward-backward method) could be included in the covariance estimate. For a given subimage, let Rˆ be the estimate of the covariance matrix of the signal history vector x. We can express Rˆ in terms of its eigenvectors {e i } and their corresponding eigenvalues {λ i } as 36 Rˆ e e (10) = Σ λi i i. i = 1 Suppose, without loss of generality, that the eigenvalues are arranged in ascending order, so that λ1 λ 2 L λ 36. In addition, assume that the clutter subspace is spanned by a subset of the eigenvectors corresponding to the M smallest eigenvalues, where M is a parameter that is also adaptively selected. Then we can express the inverse of the matrix Rˆ as Rˆ = Σ ei e i= 1 λ i i M = Σ ei e i + Σ eie i= 1 λ i M 1 i i = + λ i = Rˆ # clutter + Rˆ # signal (11) (12) (13) i.e., we can express the inverse 1 Rˆ as the sum of two pseudoinverses, one associated with the clutter subspace and the other associated with the signal subspace. Finally, for a given pixel location (i, j) in the output image, the value y produced by the EV algorithm at this location is defined by 1 y = v Rˆ # clutter v 1 =, 1 2 M Σ e v i= 1 λ i i (14) (15) where the vector v once again represents the response of an ideal point scatterer that would appear at pixel location (i,j). If the signal and clutter subspaces have been chosen properly, the vector v should lie almost entirely in the signal subspace. Hence, if there is indeed a point scatterer at location (i,j), each inner product e i v appearing in the denominator of the above expression should be nearly zero, and thus produce a very large output value y.

5 Of course, one of the key parts of the EV algorithm is deciding how to decompose the vector space into signal and clutter subspaces, and what dimension to assign to each of these subspaces. Some discussion of this problem is given in a recent survey paper by DeGraaf [9]. For the investigations described in this paper, we determined (after some experimentation) that the eigenvectors corresponding to the two largest eigenvalues formed a suitable basis for the signal subspace. The remaining 34 eigenvectors were therefore used in the construction of the output image. 3.4 Spatially Variant Apodization (SVA) Spatially variant apodization, or SVA, is a data-adaptive method whose goal is to eliminate the sidelobes of prominent scatterers in a SAR image, and simultaneously to preserve the widths of the mainlobes of these scatterers so that image resolution is not degraded. The SVA technique was developed at the Environmental Research Institute of Michigan by Stankwitz et al [6]. The rather unusual term apodization was borrowed from the field of optics; it originally referred to the process of applying a weighting or shaping function to a finite aperture in order to suppress diffraction sidelobes. In the present case, apodization refers to an analogous procedure that is used to suppress sidelobes in SAR imagery, whereby the signal history is weighted before applying a 2D-DFT to create the final SAR image. Recall that multiplying the signal history by a weighting function is equivalent to convolving the original SAR image (i.e., the image that would result from applying a 2D-DFT to the unweighted signal history) with a function that corresponds to the 2D-DFT of the weighting function. Therefore, when the conventional apodization technique (i.e., weighting of signal history followed by 2D-DFT) is applied, the final SAR image can be viewed as the result of processing the original SAR image with a spatially invariant two-dimensional linear filter. The main difference between the SVA technique and the conventional apodization technique is that SVA adaptively selects, from a parameterized family of weighting functions, an optimal aperture weighting for each individual pixel in the image, rather than using the same fixed aperture weighting for all pixels. Thus, when the SVA technique is applied, the final SAR image can be viewed as the result of processing the original SAR image with a spatially varying two-dimensional nonlinear filter. Before describing in greater detail how the SVA technique is implemented, let us assume, in order to simplify the exposition, that a SAR image is a one-dimensional, rather than a twodimensional, quantity. The family of weighting functions over which the pixel-by-pixel optimization is performed is the cosineon-pedestal family {c(n;a)} defined by c 2πn N ( n; a) = 1+ 2a cos, n = 0,1, L, N 1, (16) where N is the length of the one-dimensional aperture being weighted and a is a positive constant constrained to lie in the interval [0, 0.5]. This family of functions includes many of the aperture weightings that are commonly used in SAR image formation, such as the rectangular weighting (a = 0), the Hanning weighting (a = 0.5), and the Hamming weighting (a = 0.43). When implementing SVA, we typically assume that the original SAR image is critically sampled, i.e., sampled at precisely the Nyquist rate. A direct consequence of this assumption is that the filtering operation in the image domain can be carried out using only a three-point digital filter. This is easily demonstrated by taking the N-point DFT of the weighting function {c(n;a)}, which yields the symmetric filter {h(n;a)} given by ( n;a) aδ( n 1) + δ( n) + aδ( n 1), h = + (17) where δ(n) is a discrete-time sequence whose value is unity if n = 0, but is zero otherwise. It follows that when this filter is applied to the original image {x(n)}, the output image {y(n)} can be expressed as ( n) ax( n 1) + x( n) + ax( n 1). y = + (18) The objective of SVA is to choose, at each sample index n, the value of the parameter a that minimizes ( ) 2 y n, subject to the constraint that a lies in the interval specified above. Using traditional constrained optimization techniques, it is straightforward to show that the best possible value for a can be determined using the following simple algorithm: (1) Evaluate the unconstrained solution ii, which is given by ~ a Re = { x( n) * [ x( n 1) + x( n + 1) ]} x( n 1) + x( n + 1) 2 (19) (2) Check the validity of the unconstrained solution and apply a correction if the value is out of the desired range: (a) If a~ < 0, then put y(n) = x(n). (b) If 0 a~, then put y(n) = x(n) + a~ [x(n 1) + x(n + 1)]. (c) If a~ > 0.5, then put y(n) = x(n) + 0.5[x(n 1) + x(n + 1)]. A procedure analogous to the one just described can also be used when the sampling rate is an integer multiple of the Nyquist rate. If the image is sampled at exactly k times the Nyquist rate, the above equations are modified easily by using the sample indices n, n - k, and n + k, rather than the indices n, n - 1, and n + 1. To implement the SVA technique in two dimensions, we can simply apply the one-dimensional algorithm on the individual rows and columns of the image sequentially, i.e., apply it first to every row of pixels in the image, and subsequently apply it to every column. There are,

6 of course, more sophisticated SVA algorithms that can be developed in two dimensions (refer to [6] for variations on the basic problem), but a sequential application of the onedimensional algorithm has a number of advantages, including the fact that it is much simpler to implement, it is more computationally efficient, and it generally yields very good sidelobe suppression. 3.5 Superresolved Spatially Variant Apodization (SSVA) Shortly after the SVA technique was published, an enhanced version was developed which attempted to achieve two objectives simultaneously: (1) suppression of the sidelobes of prominent scatterers in the image (as was done in the original SVA technique); and (2) reduction of the mainlobe widths of these scatterers. Because this enhanced version of SVA relies on the concept of bandwidth extrapolation to achieve superresolution, it was termed Super-SVA by its original developers, Stankwitz and Kosek [7]. In the sequel, we shall refer to their technique by the abbreviated label SSVA. To describe the basic principle behind SSVA, let us begin with the assumption that the original SAR image (which, for convenience, we once again take to be a one-dimensional image sampled at k times the Nyquist rate) was created without the use of aperture weighting, and furthermore that this image contains only a single ideal point scatterer, i.e., it consists of samples of a sinc function, which has the general form sin(πx)/ (πx). We observe that, because the signal history associated with this image necessarily has a finite region of support, the image itself is clearly bandlimited. In the first stage of SSVA, we apply the basic SVA technique to the input image in an attempt to eliminate the sidelobes of the single scatterer in the image. Although the SVA technique cannot do a perfect job of sidelobe removal, the output image resulting from this first stage of processing now contains, at least approximately, only the mainlobe of the scatterer in the original image. In fact, it is useful to think of the effect of the SVA procedure as being essentially equivalent to truncating the original sinc function in such a way that the mainlobe is perfectly retained, but all sinc function values outside the mainlobe are nulled. An important consequence of this nonlinear SVA operation is that it significantly alters the frequency content of the original image, and in fact produces an image that is no longer bandlimited. This last observation is the key to the SSVA technique. The bandwidth of the new SVA-processed image is substantially greater than that of the original image; the new frequencydomain data no longer has a rectangular shape, but instead possesses a broad, gradually tapering shape that extends to higher frequencies and eventually includes some frequency nulls. Because the shape of this new signal history will correspond approximately to the 2D-DFT of the mainlobe of a sinc function, we can calculate its magnitude response well in advance, and then, once SVA has been performed, apply an appropriate equalization filter to attempt to correct the SVAinduced distortion. In practice, we do not attempt to equalize the distortion over the entire frequency-domain function, since this function becomes extremely small (and occasionally attains a value of zero) at high frequencies. Instead, we equalize only over an aperture that is slightly larger (approximately a factor of 2 ) than the original rectangular aperture, and set all values outside of this aperture to zero. After this partial equalization has been performed, the new signal history is transformed back to the image domain using a 2D-DFT, and the next iteration of the SSVA technique (i.e., the SVA operation followed by the equalization operation) can begin. Using this basic procedure, only two iterations are required to extrapolate the original bandwidth by a factor of two. To improve the overall quality of the output image produced by SSVA, we incorporated a refinement into the above iterative algorithm that was suggested in the original paper by Stankwitz and Kosek. Specifically, at the end of each iteration, we removed the center portion of the extrapolated signal history and inserted the original signal history in its place. Although this replacement strategy tends to produce an abrupt discontinuity between the center and outer portions of the signal history, the discontinuity can be subsequently smoothed by performing several more iterations of the algorithm with no extrapolation. 3.6 SSVA with Median Filter Post-Processing (SSVA-MED) While it is true that the SSVA technique noticeably reduces the mainlobe width of each prominent scatterer in the image, this technique also causes the speckle in the image to increase dramatically. In fact, we have observed that when the original signal history is extrapolated by a factor of two using SSVA, the standard deviation of the image (measured in the logmagnitude image domain) also increases by a factor of two. The rise in image standard deviation causes the average MSE scores computed by the classifier to increase sharply, and consequently has a detrimental effect on overall classification performance. In an attempt to mitigate this effect, we applied a 3 3 sliding median filter to the log-magnitude output image produced by SSVA. It was hoped that such a technique would not only preserve the basic shape of a target signature contained in the image, but also substantially reduce the gross fluctuations in the ambient clutter. 4 Initial Studies Using MSTAR-1 data The confusion matrices presented in this section summarize the results using the MSTAR-1 data set for the six image enhancement techniques evaluated in our initial studies. In all cases the MSE classification rejection threshold was set to provide P rej = 56.2% (219/390). Table 1 presents the classifier confusion matrix for the baseline classification system which

7 uses HDI processing prior to the final MSE classification stage; for this case P cc = 66.2%. Table 2 presents the classifier confusion matrix using EV processing prior to the final MSE classification stage; for this case P cc = 67.1%. The EV system provides very good performance (very similar to HDI). Table 3 presents the classifier confusion matrix using upsampling prior to the final MSE classification stage; for this case P cc = 54.5%. This case was evaluated as a very simple processing technique that would provide an output image with one third the pixel spacing of the input image. The upsampling system provided surprisingly good results. Table 4 presents the classifier confusion matrix using SVA processing prior to the final MSE classification stage; for this case P cc = 46.8%. Table 5 presents the classifier confusion matrix using SSVA processing prior to the final MSE classification stage; for this case P cc = 21.8%. The relatively poor performance of the SSVA classifier can be attributed to the increase in clutter variance, as discussed in the previous section. To improve the quality of the SSVA output image, we applied a 3 3 sliding median filter as a post-processor to SSVA. Median filtering enhances the SSVA output image by reducing the overall variance and removing the very low pixel values. Table 6 presents the classifier confusion matrix using SSVA processing with median filtering prior to the final MSE classification stage; for this case P cc = 46.2%. As shown by these confusion matrices, the best classification performance was provided by the HDI and EV resolution enhancement algorithms. Observe that HDI and EV both yielded approximately the same value for P cc, but that these two techniques performed well on different types of targets. By comparing Table 1 and Table 2, we can see that the EV system correctly classified more BMP2 targets than did HDI, but that the HDI system correctly classified more T72 targets than did EV. Moreover, the EV system correctly rejected more M35 confuser vehicles, and the HDI system correctly rejected more HMMWV confuser vehicles. From these observations, we conjectured that overall classifier performance might be increased by fusing the HDI and EV classifier outputs. We chose to use a very simple scheme for fusing the outputs generated by the HDI and EV systems, namely a convex linear combination of their final MSE scores, as shown by MSE fused = 0.72 MSE HDI MSE EV. (20) The weighting coefficients (0.72, 0.28) for this linear combination were determined empirically by exhaustively α, 1 α, subject to the searching over pairs of the form ( ) constraint 0 α 1, until the particular pair was found that yielded the largest measured value of P cc. Table 7 summarizes the results for the fused HDI/EV classification system. Again, the classifier rejection threshold was set to provide P rej = 56.2% (219/390); for this case P cc = 72.9%, which is better than either the HDI or EV classifier alone. This result is significant because it indicates that the HDI and EV superresolution techniques enhance somewhat different characteristics of the SAR target signatures. 5 ADDITIONAL STUDIES USING MSTAR-1 AND MSTAR-2 DATA Because the HDI and EV classification systems provided the best results, and the performance from these two classification systems were so similar, it was decided that more extensive testing of these two classification systems should be performed. The test target inputs and the confuser vehicle inputs from the MSTAR-1 data set were combined with test target inputs and the confuser vehicle inputs from the MSTAR-2 data set; this provided 3,086 test target inputs and 3,398 confuser vehicle inputs. The confusion matrices shown in Table 8, Table 9 and Table 10 present the classification performance results using the combined MSTAR-1 and MSTAR-2 data sets. The correct classification entries in the confusion matrices are shown as percentages, because the number of test inputs from the MSTAR-1 and MSTAR-2 data sets are significantly different. Also, the confusion matrix rows showing the confuser vehicle rejection are not presented, but again the classifier rejection threshold was set to provide P rj = 56.2% (1908/3398) for each case. Table 8 presents the classifier confusion matrix for HDI processing prior to the final MSE classification stage; using the combined MSTAR-1 and MSTAR-2 data sets, we have P cc = 71.5%. Table 9 presents the classifier confusion matrix using EV processing prior to the final MSE classification stage; using the combined MSTAR-1 and MSTAR-2 data sets, for this case we have P cc = 71.2%. Using the combined MSTAR-1 and MSTAR-2 data sets provided a more statistically significant sample size, and again the HDI and EV systems yielded similar classification performance. Table 10 summarizes the results using the fused HDI/EV classifier outputs on the combined MSTAR-1 and MSTAR-2 data sets; for this case P cc = 77.3%, which again is better than either the HDI or EV classifier alone. The same weighting coefficients (0.72, 0.28) that were used for the MSTAR-1 data set were also used to fuse the HDI/EV classifier outputs on the combined MSTAR-1 and MSTAR-2 data sets. 6 Summary Table 11 provides an overall summary of the classification performance achieved for all of the cases evaluated in our investigation. Clearly, the HDI and EV image enhancement techniques yield the best performance individually; in fact, these two techniques appear to be equally good. Furthermore, as we have already pointed out, the HDI and EV techniques evidently enhance target signatures in very different ways; hence, the classifier outputs for these two techniques can be fused to yield an overall performance level that is better than

8 that achieved by either technique alone. We chose to combine the two classification results by using a simple convex linear combination of the associated MSE scores; of course, it is possible that more powerful data-fusion strategies exist. The coherent upsampling technique gave unexpectedly good recognition results, particularly when we take into account the simplicity of the algorithm and the fact that it does not improve the inherent resolution of the input image. SVA processing gave only fair classification performance, but, somewhat surprisingly, its associated superresolved version, SSVA, yielded performance that was exceedingly poor. Applying median filtering as a post-processor to SSVA did yield an significant improvement over its initial performance, but not to the level attained by HDI or EV processing. Because median filtering was a simple, arbitrarily selected technique, it is reasonable to conjecture that a more sophisticated postprocessing technique could be designed to yield even better classification performance. Alternatively, instead of attempting to improve the output image quality of SSVA through postprocessing, perhaps certain constraints could be incorporated directly into the basic SSVA algorithm in order to simultaneously control sidelobe interference and reduce the clutter variance in the output image. P cc (%) MSTAR-1 MSTAR-1 & 2 HDI 66.2% 71.5% EV 67.1% 71.2% HDI/EV 72.9% 77.3% UPSAMP 54.5% SVA 46.8% SSVA 21.8% SSVA-MED 46.2% [4] D. H. Johnson, "The Application of Spectral Estimation Methods to Bearing Estimation Problems," Proceedings of the IEEE, vol. 70, pp , September [5] D. H. Johnson and S. R. DeGraaf, "Improving the Resolution of Bearing in Passive Sonar Arrays by Eigenvalue Analysis," IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. ASSP-30, pp , August [6] H. C. Stankwitz, R. J. Dallaire, and J. R. Fienup, "Non-linear apodization for sidelobe control in SAR imagery," IEEE Transactions on Aerospace and Electronic Systems, vol. 31, no. 1, January [7] H. C. Stankwitz and M. R. Kosek, "Super-resolution for SAR/ISAR RCS measurement using spatially variant apodization," Proceedings of the AMTA Symposium, Williamsburg, VA, November [8] J. Capon, "High-resolution frequency-wavenumber spectrum analysis," Proceedings of the IEEE, no. 57, pp , August [9] S. R. DeGraaf, "SAR imaging via modern 2-D spectral estimation methods," IEEE Transactions on Image Processing, vol. 7, no. 5, pp , May Table 11: Summary of enhanced resolution classifier performance. 7 References [1] G. J. Owirka, A. L. Weaver, and L. M. Novak, "Performance of a multiresolution classifier using enhanced resolution SAR data," SPIE Conference on Radar Technology, Orlando, FL, pp , [2] G. R. Benitz, "Adaptive high-definition imaging," Proceedings of the SPIE Conference on Algorithms for SAR Imagery, Orlando, FL, pp , April [3] G R. Benitz, "High-definition vector imaging for synthetic aperture radar," Proceedings of the 31st Asilomar Conference on Signals, Systems, and Computers, Monterey, CA, October 1997.

9 Figure 1: Block diagram of the Lincoln Laboratory baseline ATR system. Figure 2: Vehicles included in the MSTAR-1 target set.

10 Figure 3: Five-degree average images of an M109 SPG produced by different enhancement techniques. Top row (from left to right): UPSAMP, HDI, and EV. Bottom row: SVA, SSVA, and SSVA-MED. Number of Targets Classified As BMP2# BMP2# M2# M2# T72# T72# HMMWV M Table 1: Confusion matrix using HDI processing (P cc = 66.2%). Number of Targets Classified As BMP2# BMP2# M2# M2# T72# T72# HMMWV M Table 2: Confusion matrix using EV processing (P cc = 67.1%).

11 Number of Targets Classified As BMP2# BMP2# M2# M2# T72# T72# HMMWV M Table 3: Confusion matrix using upsampling (P cc = 54.5%). Number of Targets Classified As BMP2# BMP2# M2# M2# T72# T72# HMMWV M Table 4: Confusion matrix using SVA processing (P cc = 46.8%). Number of Targets Classified As BMP2# BMP2# M2# M2# T72# T72# HMMWV M Table 5: Confusion matrix using SSVA processing (P cc, = 21.8%).

12 Number of Targets Classified As BMP2# BMP2# M2# M2# T72# T72# HMMWV M Table 6: Confusion matrix using SSVA processing with median filtering (P cc = 46.2%). Number of Targets Classified As BMP2# BMP2# M2# M2# T72# T72# HMMWV M Table 7: Confusion matrix using fused HDI/EV classifier outputs (P cc = 72.9%). Percent of Targets Classified As BMP2 (2) BTR70 (3) M109 (4) M2 (2) T72 (2) Table 8: Combined MSTAR-1/MSTAR-2 confusion matrix for HDI processing (P cc = 71.5%). The numbers appearing in parentheses in the left-hand column indicate the number of distinct (i.e., different serial number) targets used.

13 Percent of Targets Classified As BMP2 (2) BTR70 (3) M109 (4) M2 (2) T72 (2) Table 9: Combined MSTAR-1/MSTAR-2 confusion matrix for EV processing (P cc = 71.2%). Percent of Targets Classified As BMP2 (2) BTR70 (3) M109 (4) M2 (2) T72 (2) Table 10: Combined MSTAR-1/MSTAR-2 confusion matrix for fused HDI/EV classifier outputs (P cc = 77.3%).