Truncated SVD-Based Compressive Sensing for Downward-Looking Three-Dimensional SAR Imaging With Uniform/Nonuniform Linear Array

Abstract

For downward-looking linear array 3-D synthetic aperture radar, the resolution in cross-track direction is much lower than the ones in range and azimuth. Hence, superresolution reconstruction algorithms are desired. Since the cross-track signal to be reconstructed is sparse in the object domain, compressive sensing algorithm has been used. However, the imaging processing on the 3-D scene brings large computational loads, which renders challenges in both data acquisition and processing. To cover this shortage, truncated singular value decomposition is utilized to reconstruct a reduced-redundancy spatial measurement matrix. The proposed algorithm provides advantages in terms of computational time while maintaining the quality of the scene reconstructions. Moreover, our results on uniform linear array are generally applicable to sparse nonuniform linear array. Superresolution properties and reconstruction accuracies are demonstrated using simulations under the noise and clutter scenarios. Index Terms-Compressive sensing (CS), nonuniform linear array (LA), superresolution, truncated singular value decomposition (TSVD), 3-D synthetic aperture radar (SAR).

Measurement Matrix Optimization and Mismatch Problem Compensation for DLSLA 3-D SAR Cross-Track Reconstruction

“…The 2-D focused images can be obtained by wave-propagation and along-track 2-D dimensional compression. Then, after performing the compensation for the residual video phase terms [4,5], the signal of each wave-propagation and along-track cell is given by: $s(x_m)={\displaystyle \underset{p=1}{\overset{N_p}{{\displaystyle \Sigma }}}{\gamma }_p\times \exp \{\mathrm{j}\frac{4\pi x_m{\hat{x}}_p}{\lambda r_0}\}},$ where γ p is the reflectivity coefficient of the target, λ is the nominal radar wavelength, N p is the total number of point targets, and r 0 is the projection distance of the target-to-APC on the zero-Doppler plane.…”

“…Thus, the 3-D regions of interested behave typically spatial sparsity, i.e., each wave-propagation and along-track pixel contains only a limited number of dominating scatterers compared with the total cross-track dimension [3,4,5]. Therefore, the cross-track imaging of DLSLA 3-D SAR can be regarded as the problem of sparse signal reconstruction.…”

“…With linear array antennas distributed along the wing of a rectilinearly moving platform and a downward-looking imaging geometry, DLSLA 3-D SAR can synthesize a 2-D plane array and obtain the 3-D resolution of the imaging scene [1,2,3,4,5,6]. …”

“…The former is caused by the length limitation of the array, which is restricted by the platform wingspan. The latter is mainly rendered by the sparse and non-uniform distribution of the APCs, due to the installation restriction, burden of expense and so on [3,4,5]. Considering the spatial sparsity of a 3-D imaging scene, compressive sensing (CS) [7] provides a solution for super-resolution.…”

“…Since the sparse and non-uniform configuration of APCs is a sampled subset of a uniform linear array, the measurement matrix can be viewed as a subset of the spatial Fourier basis matrix [5]. We give two metrics to improve the recovery property of the measurement matrix.…”