Low-rank sparse matrix decomposition for sparsity-driven SAR image reconstruction

We consider the development of a synthetic aperture radar (SAR) image reconstruction method that decomposes the imaged field into a sparse and a low-rank component. Such a decomposition is of interest in image analysis tasks such as segmentation and background subtraction. Conventionally, such operations are performed after SAR image formation. However image formation methods may produce images that are not well suited for such interpretation tasks since they do not incorporate interpretation objectives to the SAR imaging problem. We exploit recent work on sparse and low-rank decomposition of matrices and incorporate such a decomposition into the process of SAR image formation. The outcome is a method that jointly reconstructs a SAR image and decomposes the formed image into its low-rank background and spatially sparse components. We demonstrate the effectiveness of the proposed method on both synthetic and real SAR images.