Dictionary learning and low-rank sparse matrix decomposition for sparsity driven SAR image reconstruction

Synthetic aperture radar (SAR) is one of the most widely used remote sensing modalities, providing images for a variety of applications including those in defense, environmental science, and weather forecasting. However, conventionally formed SAR imagery from undersampled observed data, arising in several emerging applications and sensing scenarios, suffers from artifacts that might limit effective use of such imagery in remote sensing applications. Recently, sparsity-driven SAR imaging has emerged as an e ective framework to alleviate such problems. Sparsity-based methods for SAR imaging have employed overcomplete dictionaries to represent the magnitude of the complex-valued eld sparsely. Selection of an appropriate dictionary with respect to the features of the particular type of underlying scene plays an important role in these methods. In this thesis, we develop two new sparsity-driven SAR imaging methods that significantly expand the domain of applicability of sparsity-based methods in SAR imaging. Our first contribution involves the development of a new reconstruction method that is based on learning sparsifying dictionaries and using such learned dictionaries in the reconstruction process. Adaptive dictionaries learned from data can represent the magnitude of complex-valued field more effectively and hence have the potential to widen the applicability of sparsity-based radar imaging. Our framework allows the use of both adaptive dictionaries learned offline from a training set and those learned online from the undersampled data used in image formation. We demonstrate the effectiveness of the proposed dictionary learning-based SAR imaging approach as well as the improvements it provides, on both synthetic and real data. The second contribution of this thesis involves the development of a 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. 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