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Title: Sparsity and Structure in UWB Synthetic Aperture Radar
Abstract: Synthetic Aperure Radar is a form of radar that uses the motion of radar to simulate a large antenna in order to create high resolution imagery. Low frequency ultra-wideband (UWB) SARs in particular uses low frequencies and a large bandwidth that provide them with penetration capabilities and high resolution. UWB SARs are typically used for near eld imaging applications such as foliage penetration, through the wall imaging and ground penetration. SAR imaging is traditionally done by matched ltering, by applying the adjoint of the projection operator that maps from the image to SAR data.The matched lter imaging suffers disadvantages such as sidelobe artifacts, poor resolution of point targets and lack of robustness to noise and missing data. Regularized imaging with sparsity priors is found to be advantageous; however the regularized imaging is implemented as an iterative process in which projections between the image domain and data domain must be done many times. The projection operations (backprojection and reprojection) are highly complex; a brute force implementation has a complexity of O(N3). In this dissertation, a fast implementation of backprojection and reprojection is investigated. The implementation is explored in the context of regularized imaging as well as compressive sensing SAR.
The second part of the dissertation deals with a problem pertinent to UWB SAR imaging. The VHF/UHF bands used by UWB SAR are shared by other communication systems and that poses two problems; i) RF interference (RFI) from other sources and ii Missing spectral bands because transmission is prohibited in certain bands. The rst problem is addressed by using sparse and/or low-rank modeling. The SAR data is modeled to be sparse. The projection operator from above is used to capture the sparsity of the SAR data. The RFI is modeled to be either sparse with respect to an appropriate dictionary or assumed to be of low-rank. The sparse estimation or the sparse and low-rank estimation is used to estimate the SAR signal and RFI simultaneously. It is demonstrated that the new methods perform much better than the traditional RFI mitigation techniques such as notched ltering. The missing frequency problem can be modeled as a special case of compressive sensing. Sparse estimation is applied to the data to recover the missing frequencies. Simulations show that the sparse estimation is robust to large spectral gaps.