Passive Synthetic Aperture Radar Imaging Using Low-Rank Matrix Recovery Methods

Abstract

We present a novel image formation method for passive synthetic aperture radar (SAR) imaging. The method is an alternative to widely used Time Difference of Arrival (TDOA) or correlation-based backprojection method. These methods backprojection work under the assumption that the scene is composed of a single or a few widely separated point targets.The new method overcomes this limitation and can reconstruct heterogeneous scenes with extended targets.We assume that the scene of interest is illuminated by a stationary transmitter of opportunity with known illumination direction, but unknown location. We consider two airborne receivers and correlate the fast-time bistatic measurements at each slow-time. This correlation process maps the tensor product of the scene reflectivity with itself to the correlated measurements. Since this tensor product is a rank-one positive semidefinite operator, the image formation lends itself to low-rank matrix recovery techniques. Taking into account additive noise in bistatic measurements, we formulate the estimation of the rank-one operator as a convex optimization with rank constrain. We present a gradient-descent based iterative reconstruction algorithm and analyze its computational complexity. Extensive numerical simulations show that the new method is superior to correlation-based backprojection in reconstructing extended and distributed targets with better geometric fidelity, sharper edges and better noise suppression.1932-4553 (c)

Moving target imaging using sparse and low-rank structure

“…Thus, we use a projected gradient descent method with a Nesterov accelerated update scheme to perform the optimization. 7 This first order method requires only the gradient of the objective functional and the constraint can be enforced efficiently using the proximity operator of the PSD cone, which is a hard thresh-holding of the eigenvalues, setting all the negative eigenvalues to zero. The scene reflectivity is obtained by keeping the largest eigenvalue/eigenvector pair, we refer to this as the eigen image.…”

“…It is solved utilizing the same algorithm used in synthetic aperture radar (SAR) imaging. 7,8 In the case of velocity estimation, we take advantage of the sparsity of the velocity function and pose the problem as a cardinality constrained least squares problem. This is then solved using the iterative hard thresh-holding algorithm (IHTA), which is a greedy algorithm that uses a hard thresh-holding operator to enforce the sparsity constraint.…”

Passive synthetic aperture radar imaging based on low-rank matrix recovery

“…To solve (15), we use a Nesterov gradient-based iterative approach [24], [25], [30]. Details of the algorithmic implementation and an analysis of the computational complexity can be found in [31]. …”

Multi-linear sparse reconstruction for SAR imaging based on higher-order SVD

“…Imaging algorithm is the key point of SAR application, which extracts the scatter coefficients of targets and reconstructs the image of target scene from the radar echoes [5,6]. On the azimuth direction, a larger aperture can be synthesized by the coherent processing and relative motions between the antenna and targets.…”