Sparse Multipass 3D SAR Imaging: Applications to the GOTCHA Data Set

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1 Sparse Multipass 3D SAR Imaging: Applications to the GOTCHA Data Set Christian D. Austin, Emre Ertin, and Randolph L. Moses The Ohio State University Department of Electrical and Computer Engineering 2015 Neil Avenue, Columbus, OH ABSTRACT Typically in SAR imaging, there is insufficient data to form well-resolved three-dimensional (3D) images using traditional Fourier image reconstruction; furthermore, scattering centers do not persist over wide-angles. In this work, we examine 3D non-coherent wide-angle imaging on the GOTCHA Air Force Research Laboratory (AFRL) data set; this data set consists of multipass complete circular aperture radar data from a scene at AFRL, with each pass varying in elevation as a result of aircraft flight dynamics. We compare two algorithms capable of forming well-resolved 3D images over this data set: regularized l p least-squares inversion, and non-uniform multipass interferometric SAR (IFSAR). Keywords: SAR, Interferometric SAR, Sparse, GOTCHA, Three Dimensional Imaging 1. INTRODUCTION Two-dimensional (2D) narrow-angle synthetic aperture radar (SAR) imaging is prevalent, but three-dimensional (3D) wide-angle imaging provides an extra dimension of height information and angular information. This additional information can be useful in applications such as automatic target recognition (ATR) and tomographic mapping. However, generating high-resolution wide-angle 3D images using traditional Fourier processing requires more data collection in azimuth and elevation angle and may be cost and time prohibitive in practice. When Fourier imaging is applied to sparsely sampled apertures, image resolution suffers. Poor resolution is typical in the height direction for data collected on circular paths at multiple elevation angles, where it may only be possible to collect a small number of passes for small elevation angle extent. Furthermore, radar scattering is typically anisotropic over wide angles and violates the isotropic point scattering assumption of traditional radar imaging. In this paper, we form wide-angle 3D images of the 2006 circular SAR (CSAR) GOTCHA data collection, performed by AFRL and released as the Volumetric SAR Data Set, Version The aforementioned imaging problems are manifest in this data set. We examine two 3D imaging algorithms utilizing a sparse scattering assumption to improve resolution over traditional Fourier imaging. The first algorithm is a regularized l p - norm least-squares (LS) processing. This approach is also know as Basis Pursuit Denoising when p = 1. 2,3 This method has been shown to produce well-resolved, 2D SAR image reconstructions over approximately linear flight paths 4 6 and 3D images over circular and pseudo-random flight paths. 7, 8 The second algorithm is a nonuniform multipass IFSAR approach and uses the scattering sparsity assumption to improve height resolution. Non-uniformly spaced SAR pulses are interpolated to uniformly spaced pulses in elevation, and then, spectral estimation methods are used to estimate the height of scattering centers in a resolution cell in a method similar to traditional IFSAR processing. This approach has been previously used to reconstruct 3D images from CSAR synthetic data. 9 We address anisotropic scattering over wide angles by using non-coherent subaperture imaging, where scattering is assumed to be isotropic over narrow-angle subapertures. The next section of this paper provides a model of the SAR data. The GOTCHA dataset is described in Section 3. There is error present in the flight path locations of this dataset which needs to be corrected, and areas of interest in the scene must be spatially filtered before imaging to avoid aliasing during the imaging operation. Prominent-point autofocusing is used to correct for flight path location errors, and scene spotlighting is used to spatially filter the imaging area; both of these methods are discussed in Section 3. In Section 4, the regularized l p LS imaging algorithm is presented, and in Section 5 the multipass IFSAR algorithm is discussed. We conclude

2 with reconstructed images of a tophat and vehicles from the GOTCHA scene. An alternative imaging technique is considered in a companion paper DATA MODEL In this section, we present the radar data model used for the GOTCHA dataset. The radar transmits an FM chirp signal, e j(ωct+αt2 ), (1) where α is the chirp rate, and ω c is the center frequency of the radar. The bandwidth of this signal, BW = 2ατ c, is given by the product of the chirp rate and the chirp duration τ c. We assume that the imaged scene is small compared to the standoff distance of the radar, and that wavefront curvature is negligible; so we can use a planar wave model. We will see in the following sections from radar collection geometry that our imaging scenarios satisfy this assumption. After mixing the return signal with the transmitted signal, delayed by the time to scene center, demodulating, and neglecting a quadratic phase term, the final received signal under the plane wave assumption is 11 r(t,θ az,θ el,f,pol) = Bz B z By B y Bx B x a(x,y,z,θ az,θ el,f,pol) (2) e jx(t)x dxdydz. The coordinate x is defined as the radial line from the radar to scene center, and y, and z are orthogonal to x and each other. This coordinate system changes over the radar s flight path. The scene reflectivity function is given by a(x,y,z,θ az,θ el,f,pol). Angles θ az and θ el are the azimuth and elevation angles of the radar with respect to a fixed ground plane coordinate system; f is the frequency of the radar signal, and pol is the polarization of the radar signal. Boundaries of the scene in each dimension are B ( ). The function X(t) is a linear function of time and is supported on [ 2 c (ω 2 c πbw), c (ω c + πbw)] rad/m, where c is the speed of light in m/s, and BW is the chirp bandwidth in Hz. Since e jx(t)x is the Fourier kernel, (2) is the Fourier transform of the scene reflectivity function projected onto the x dimension. By the projection-slice theorem, 11 it follows that the Fourier transform of the scene reflectivity function projection onto the x dimension is equivalent to a line along the x-axis in 3D k-space of the scene reflectivity function. The frequency support of each line is that of X(t); so, each line has a bandwidth of 4πBW c rad/m centered at 2ωc c rad/m. The flight path defines which lines in k-space are collected, and hence what subset of k-space is sampled. In traditional Fourier processing, a subset of k-space as defined by the flight path is collected, and the scene reflectivity function is recovered by inverse Fourier transformation. Due to the incomplete collection of k-space data, reconstructed images may have high sidelobes and poor resolution. We model a SAR scene as a collection of polarization-dependent anisotropic scattering centers. The scene reflectivity function of this model is the image that we wish to recover and is ideally represented as a summation of N s complex weighted impulses at the location of each point scattering center. In k-space, the scattering center model is N s F(X,Y,Z) = a k (θ az,θ el,f,pol)e j(xx k+y y k +Zz k ). (3) k=1 Variables x k, y k, and z k are the (x,y,z) spatial coordinates of scattering center k in units of meters, and X, Y, and Z are the spatial frequency coordinates of 3D k-space in units of rad/m. The complex amplitude of scattering center k, a k, is a function of the radar azimuth angle, θ az, elevation angle, θ el, frequency, f, and polarization, pol. 3. THE GOTCHA DATASET The GOTCHA dataset, Volumetric SAR Data Set, Version 1.0, is used in the imaging examples presented here. This dataset consists of fully polarimetric data from 8, 360 CSAR passes ideally spaced in elevation at el = 0.18 in the range [43.7, 45 ]. However, the actual flight path is not perfectly circular, as shown

3 in Figure 1. The center frequency of the radar is f c = 9.6GHz, and the corresponding center wavelength is λ c = 0.031; bandwidth of the radar is 640MHz. Resolution and aliasing bounds for traditional Fourier based imaging are presented in the paper by Ertin. 12 Figure 1. Actual GOTCHA passes. Scale is in meters Autofocus Radar flight location information for the GOTCHA data set contains errors. These errors must be corrected across passes before coherent 3D image reconstruction is performed. If these errors are not corrected, images will exhibit defocusing (see e.g. Ferrara 10 ), which will prohibit the formation of high quality imagery. We correct these errors using the prominent-point (PP) autofocus 13 solution provided with the GOTCHA dataset. The autofocus solution uses the edge of a tophat reflector, shown in Figure 3(a), with known ground truth information as the prominent point source. Both the phase ramp, γ k, and constant phase offset θ k needed in PP autofocus are included in the dataset; subscript k indexes pulses across aspect angles and polarizations. The autofocus solution is applied by multiplying the kth radar return pulse r(t,θ az,θ el,f,pol) in (2) by e j(γ kx(t) θ k ) Scene Spotlighting The area illuminated by the radar in the GOTCHA data set contains a field of calibration targets and a parking lot of civilian vehicles, as shown in Figure 2. In imaging applications, it may be of interest to only reconstruct a small area of the illuminated radar scene. Here, we will demonstrate image reconstruction on a Toyota Camry, and Ford Taurus from the parking lot and a calibration tophat; Figure 3 shows photographs of both of these. When imaging only small areas of the scene, it may be desirable to downsample k-space to the critical sampling rate required for the extent of the imaging areas. By downsampling, reconstruction algorithms require less memory and computation time to perform reconstruction. Before downsampling, it is necessary to spatially filter the area of interest to avoid aliasing during reconstruction of downsampled data. The digital spotlight algorithm proposed by Soumekh 14 spatially filters by effectively reshaping the area illuminated by the radar to a smaller spotlighted area of interest by post-processing. This approach requires knowledge of radar parameters not included in the dataset. We take a Fourier imaging k-space based approach to scene spotlighting. This approach only requires information about the location of Fourier samples in 3D k-space. Each pass is decomposed into d azimuth subapertures. The k-space data in these subapertures is then projected into the ground plane. Ground plane coordinates remain the same for all subapertures to ensure that each 2D image is registered to the same coordinate system. Nearest neighbor processing is then used to interpolate non-uniformly spaced samples in the ground plane to a uniform grid, and a 2D ground plane image is formed using a 2D IFFT operation; a type-1 non-uniform FFT (NUFFT) could also be used to perform this operation. A spatial window centered about the area of interest is then applied to each 2D image, filtering the spatial image. The filtered image is then transformed back into k-space to the original pre-interpolation ground plane k-space locations using a type-2 NUFFT operation. Finally, the ground plane samples are projected back into the locations in 3D k-space that original unfiltered data was located at. The result of this processing is spotlighted k-space data that can be downsampled.

4 Figure 2. 2D SAR image of whole GOTCHA scene. (a) Tophat (b) Camry (c) Taurus Figure 3. Photographs from the GOTCHA scene. 4. REGULARIZED l P LS IMAGING ALGORITHM The regularized l p LS imaging algorithm attempts to fit a model to the measured data under a penalty on the number of non-zero voxels. The algorithm assumes that the complex magnitude response of each scattering center is approximately constant over narrow aspect angles and across the radar frequency bandwidth, and that the image is sparse, meaning that there are a small number of significant magnitude scattering centers in the scene. Define a set of N locations as candidate scattering center locations, The M N data measurement matrix is given by [ ] A = e j(xmx k+y my k +Z mz k ), C = {(x k,y k,z k )} N k=1. (4) where m indexes M measured k-space frequencies down rows, and k indexes the N coordinates in C across columns. Under the assumption that scattering center amplitude is constant over narrow aspect angle extent and throughout the radar bandwidth, the measured data from the scattering center model, (3), can be written in matrix form as y = Ax + n, (5) where x is the N-dimensional vectorized image that we wish to reconstruct; it has complex amplitude value a k in row k if a scattering center is located at (x k,y k,z k ) and zero otherwise; the image vector x maps to the 3D image, I(x k,y k,z k ), by the relation I(x k,y k,z k ) = x(i) if and only if column i of A is from coordinate (x k,y k,z k ). The vector n is an M dimensional i.i.d. circular complex Gaussian noise vector with zero mean and variance σ 2 n, and y is an M-dimensional vector of noisy k-space measurements.

5 The reconstructed image, ˆx, is the solution to the sparse optimization problem 4,5 ˆx = argmin x { y Ax λ x p } p, (6) where the p-norm is denoted as p, where 0 < p 1, and λ is a sparsity penalty parameter. Define uniform partitions on the x, y, and z spatial axes with partition spacings of x, y, and z, respectively. Let the set of candidate coordinates C in (4) consist of all permutations of (x, y, z) coordinates from the partitioned axes; then, the set C defines a uniform 3D grid on the scene. If, in addition, the k-space samples are on a uniform 3D frequency grid centered at the origin, the operation Ax can be implemented using the computationally efficient 3D Fast Fourier Transform (FFT) operation. In many scenarios, including the one here, k-space samples are not on a uniform grid, and the FFT cannot be used directly. Instead an interpolation step, followed by an FFT is needed. We follow the approach in Austin, 8 using nearest-neighbor (NN) interpolation to a uniform k-space grid, followed by FFT operations. An alternative approach would be to use type-2 nonuniform FFTs (NUFFT)s to process data directly to the non-uniform k-space grid. We did not pursue this approach here, since empirical results on this data set suggest that NN interpolation results in well-resolved images. Scattering centers in model (3) are anisotropic and polarization dependent. The scattering center model, (5), used in image reconstruction assumes that data is collected over narrow aspect angles so that the complex amplitude is approximately constant. We wish to form wide angle images containing information from all aspects; so, we utilize (5) to form narrow angle images and combine the images using the noncoherent max magnitude operator over all narrow-angle images. This approach is considered an approximation to GLRT image formation in some cases. 7,15 We use an extended form of this noncoherent imaging operation 8 I(x k,y k,z k ) = max θ azc,θ elc,pol I(x k,y k,z k ;θ azc θ elc,pol). (7) Coordinates x k, y k, and z k are locations of reconstructed image voxels, and I(x k,y k,z k ;θ azc,θ elc,pol) denotes a subaperture image formed using data centered at azimuth and elevation angles θ azc, θ elc and from polarization pol. We note that the final image is a real-valued image of voxel magnitude. 5. NON-UNIFORM MULTIPASS IFSAR IMAGING ALGORITHM As an alternative to the regularized l p LS 3D reconstruction strategy discussed in previous section, one can use the relative phase information in 2D images to resolve scatterers in 3D using 1D spectral estimation techniques. Multibaseline generalizations of IFSAR have been considered for linear collection geometries in. 16,17 Here we consider combining parametric spectral estimation techniques with 2D image enhancement techniques for 3D target reconstruction in circular SAR systems Multipass IFSAR The input to the multipass IFSAR algorithm is a set of baseband modulated ground plane images {I B j,m (x,y,0)} at a given subaperture centered at φ m of data collected at elevation cuts θ j. We denote the image sequence as {I j (x,y)} and consider without loss of generality φ m = 0. We consider a finite number of scattering centers at each resolution cell (x,y) and reparameterize the scene reflectivity f(x,y,z) as g p (x,y) = f(x,y,h p (x,y)), (8) where g p (x,y) denotes the reflectivity of the scattering center at location (x,y,h p (x,y)). In general the number of scattering centers per resolution cell varies spatially and needs to be estimated from the data. Then, the ground plane image for elevation θ i can can be written as I j (x l,y l ) = s(x,y) p g p (x,y)e ı tan(θj)k0 y hp(x,y) e ıyk0 y, (9) where s(x,y) is the inverse Fourier transform of the 2D windowing function used in imaging and ky 0 = ( 4πfc c )cos( θ) is the center frequency used in baseband modulation. The ground locations (x,y,h p (x,y)) and the image coordinates (x l,y l ) are related through layover :

6 x l = x y l = y + tan(θ j )h p (x,y). (10) We assume that the difference between the elevation angles for the different passes is small enough so that for each elevation pass the scattering center (x,y,h(x,y)), falls in the same resolution cell (x l,y l ). Without loss of generality we consider M + 1 circular passes at elevation angles θ j = θ + j θ for j = M/2,...,M/2. Then, the baseband images from each pass can be modeled as I j (x l,y l ) = p g p (x l,y l )e ık0 y tan(θj)hp(x l,y l ). (11) Using the approximation we obtain the sum of complex exponential model tan(θ j ) tan( θ) + 1 j θ, (12) cos 2 ( θ) I j (x l,y l ) = p g p (x l,y l )e ıkp(x l,y l )j, (13) where the complex constant e j tan( θ)k 0 y hp(x l,y l ) is absorbed into the reflectivity g p (x l,y l ), and the frequency factor k p is given by k p (x l,y l ) = 4πf c ccos( θ) (θ)h p(x l,y l ). (14) Estimation of parameters of complex exponentials in noise is a fundamental problem in spectral estimation and array signal processing. 18 If the the number of distinct complex exponentials is known, several high resolution methods can be used to estimate the frequencies. Model order selection for the sum of complex exponential model has been studied widely in literature. 19, 20 Here, we employ a simple model order selection method based on thresholding the eigenvalues of the sample covariance matrix for the vector {I j (x l,y l )} to estimate the model order P(x l,y l ). Using this model order we then use the ESPRIT 21 method to estimate the frequencies k p (x l,y l ) from the signal eigenvectors of the sample covariance matrix. The frequency estimates ˆk p are then transformed into height estimates ĥp using ĥ p = ˆk ccos( θ) p 4πf c (θ). (15) Each estimated scattering location (x l,y l,h p (x l,y l )) is then mapped to ground coordinates using 5.2. Nonuniform Elevation Spacing x = x l y = y l tan( θ)h p (x l,y l ). (16) In the previous section, we considered a system model where multiple passes were equi-spaced in elevation. Realistic acquisition geometries deviate from this assumption as discussed in Section 3. As an example, GOTCHA CSAR passes have a planned (ideal) separation of θ = 0.18 in elevation. Actual flight paths differ from the planned paths, with the mean of elevation passes at 44.27, 44.18, 44.1, 44.01, 43.92, 43.53, 43.01, degrees. Elevation varies as the aircraft circles the scene, as shown in Figure 1. Figure 4 shows a zoomed in image of the variation in elevation angle over a 10 azimuth window. Interpolated array methods estimate the output of a uniform virtual array by interpolating the outputs of the actual array. 22,23 The simplest method of interpolation is to use linear interpolation to a regular grid. A new interpolated array method based on sparsity regularized reconstruction of single pulse image I φ (r,h) obtained by coherently processing returns for multiple elevations {θ i } at a given azimuth angle φ have been proposed in Ertin. 9 The range (r) and height (h) are measured with respect to slant plane coordinates. Specifically, the relationship between the single pulse image I φ (r,h) and the projection of the scene reflectivity function f φ (r,h) on the azimuth plane φ is given by I φ (r,h) = H φ f φ (r,h) + n(r,h), (17)

7 Figure 4. Variation in elevation angle over a 10 azimuth window. where H φ is the convolution matrix of the system point spread function corresponding to the elevation spacing at azimuth angle φ, and n(r, h) represents noise and modeling errors. The deconvolution problem aims to reconstruct the scene reflectivity function f φ (r,h) from the measured single pulse image I φ (r,h), given the knowledge of the deconvolution kernel H φ. The deconvolution kernel H φ acts like a low-pass filter and does not have a bounded inverse; therefore, in the absence of any constraints on f φ (r,h), the deconvolution problem is ill-posed. 24 We obtain an enhanced single pulse image through minimization of the regularized l p LS cost, as in (6); however, the measured data and operator are different than in (6). In this case, an enhanced scene reflectivity estimate is given by { ˆf φ (r,h) = arg min I Hf λ f p } p, (18) f where I is the vector of pixels of the measured single pulse image I φ (r,h), f is the vector of deconvolved scene reflectivity sampled at appropriate pixel spacing, and H is the Toeplitz matrix that represents convolution with the given spread function, H φ. Fourier inversion of the enhanced image ˆf φ (r,h) results in phase histories (kspace lines) from a virtual array with equal spacing. The parametric estimation method for 3D reconstruction technique discussed in Section 5.1 can be applied to the interpolated phase histories. 6. EXAMPLES In this section, we compare image reconstructions of the GOTCHA dataset formed using both the regularized l p reconstruction and the non-uniform multipass IFSAR imaging algorithm. We reconstruct spotlighted areas of the scene centered on the tophat and Toyota Camry. For the regularized l p reconstructions, we use 5 subapertures from 0 to 360 with no overlap, giving a total of 72 subaperture images that are non-coherently combined by (7). Reconstructed regularized l p image voxels are spaced at 0.1 m in all three dimensions. The dimensions of the reconstructed tophat and Camry images in (x,y,z) dimensions are [ 2, 1.9] [ 2, 1.9] [ 2, 1.9] and [ 5, 4.9] [ 5, 4.9] [ 5, 4.9] meters respectively. These dimensions define the k-space bandwidth of the bounding box and grid used for NN interpolation. The bounding box bandwidth used in both images is rad/m in all dimensions. The interpolation grid inside of the bounding box for the tophat and Camry consists of 50 samples and 100 samples in each dimension for the tophat and Camry respectively. We use a modified version of the monotonic iterative algorithm code from 5 to solve the optimization problem. The modified version operates directly on k-space data and does not require the formation or convolution with a PSF, reducing computation time and memory requirements. An important aspect of image reconstruction using regularized l p LS is the selection of the penalty term λ. There exists several methods for λ selection ; however, here we choose λ manually to generate images that produce qualitatively good reconstructions. Figure 5 shows images of the tophat and Camry formed by non-coherently combining traditional inverse Fourier images using (7). A reconstructed image of the Taurus looks similar to the Camry and is not included

8 here. Fourier imaging is performed on the same NN interpolated 3D data from the same 5 subapertures used in Regularized l p processing below. The VV polarization channel is used, and only the top 20 db of voxels are shown. Lighter colors and smaller points indicate lower magnitude scattering and larger points with darker color indicate larger magnitude scattering. These images are very similar to ones generated using filtered backprojection processing. The images have poor resolution, especially in height due to the sparse support of k-space data in elevation angle; the support window of this collection geometry results in a point spread function with spreading and high sidelobes. 12 (a) Tophat (b) Camry Figure 5. Traditional Fourier images Different views of the regularized l p LS reconstruction of the tophat are shown in Figure 6. Images are reconstructed using the VV polarization, λ = 0.01 and p = 1, and, in contrast to the Fourier images, the top 40 db of voxels are shown. Color and size encode scattering magnitude as in Figure 5. The corner between the base and cylinder of the tophat is clearly visible. From the image, the radius of the tophat is clearly 1 m, agreeing with the true radius of the tophat. Furthermore, there are no visible artifacts in the image. (a) 3D view (b) Side view (c) Top view Figure 6. Regularized l p LS tophat reconstructions with λ = 0.01 and p = 1. The top 40 db magnitude voxels are shown. Figure 7 shows regularized l p LS reconstructions of the Toyota Camry for VV and HH and combined VV-HH polarization channels. Polarizations are combined into one image by (7). The parameters λ = 10, and p = 1 are used in the reconstructions, and the top 40 db of scattering centers are shown. In all of the images, the outline of the Camry is clearly visible. There appears to be some artifacts in the VV polarization below the front of the car and to the side of the car in the 3D view, but this is really scattering from an adjacent vehicle not completely removed by spotlighting. The HH images appear to show more scattering off of the ground than the

9 VV images, as there is a more pronounced line below the car; there is also some scattering above the windshield in HH image, which may be an artifact, and does not appear in the VV image. (a) 3D view, VV polarization (b) Side view, VV polarization (c) Top view, VV polarization (d) 3D view, HH polarization (e) Side view, HH polarization (f) Top view, HH polarization (g) 3D view, VV-HH polarization (h) Side view, VV-HH polarization (i) Top view, VV-HH polarization Figure 7. Regularized l p LS Camry reconstructions with λ = 10 and p = 1. The top 40 db magnitude voxels are shown. For multipass IFSAR processing we divided the data on 36 overlapping windows of width = 20 centered at φ m {0,10,...,350 } and used the entire 640 MHz bandwidth centered at 9.6 GHz for the single VV polarization. For each subaperture window we created a virtual array of 32 uniformly sampled passes, using (18) with p = 1, covering the same elevation range achieved by the SAR sensor in that subaperture. Using the sparsity regularized interpolation method we interpolated the k-space data collected at nonlinear flight paths to the data collected at virtual array geometry. In constructing the single pulse images we used the prior knowledge about the target dimensions to restrict the height and range support of the single pulse image to 5 meters. For each of the virtual 32 passes, and for each of the subapertures, ground plane images are constructed using filtered backprojection. Next, we applied the ESPRIT based parametric spectral estimation method to the top 20dB of pixels to construct three dimensional points representing observed strong scattering mechanisms. The 3D point clouds from each subaperture window is rotated and overlayed to a common reference frame, and all subaperture images are combined using (7) to form a wide-angle image.

10 (a) 3D perspective (b) Top view (c) Side view (d) Front view Figure 8. 3D reconstruction of a Taurus station wagon using non-uniform multipass IFSAR algorithm. Figure 8 shows a Taurus reconstruction overlayed with the CAD model of the Taurus; reconstructed points are black and do not encode magnitude in the color. We observe that the point cloud encompasses the CAD model and strong returns from the ground plane-side panel (double bounce mechanism) and the curved surfaces (single bounce mechanism) are clearly visible. 7. CONCLUSION In this paper, two 3D reconstruction algorithms were applied to the CSAR GOTCHA dataset: A regularized l p LS reconstruction method and a non-uniform multipass IFSAR method that uses spectral estimation methods to resolve scatters in 3D from relative phase information in 2D images. Although the GOTCHA dataset is a multipass CSAR collection, resolution in height is limited by the small amount of elevation diversity provided by the multiple passes. Lack of elevation diversity results in traditional Fourier images that have poor resolution in height. Both of the proposed algorithms produce improved 3D images with respect to traditional 3D Fourier imaging, as demonstrated on a calibration tophat, Toyota Camry, and Ford Taurus. The improved image quality can be attributed to additional information on scattering center sparsity that is incorporated into the algorithms. The regularized l p LS reconstruction method provides excellent localization accuracy of 3D scatterers in the scene. In contrast, the non-uniform multipass IFSAR based method appears to produce higher variability in 3D position of the scatterers, but can provide more filled reconstructions. In addition, the non-uniform multipass IFSAR technique requires closely spaced elevation passes to restrict the layover to a single pixel. The regularized l p LS reconstruction does not place any restrictions on the elevation sampling and is applicable to more general collection scenarios.

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