Non-quadratic regularization based image formation is a recently proposed framework for feature-enhanced radar imaging. Specific image formation techniques in this framework have so far focused on enhancing one type of feature, such as strong point scatterers, or smooth regions. However, many scenes contain a number of such features. We develop an image formation technique that simultaneously enhances multiple types of features by posing the problem as one of sparse signal representation based on overcomplete dictionaries. Due to the complex-valued nature of the reflectivities in SAR, our new approach is designed to sparsely represent the magnitude of the complex-valued scattered field in terms of multiple features, which turns the image reconstruction problem into a joint optimization problem over the representation of the magnitude and the phase of the underlying field reflectivities. We formulate the mathematical framework needed for this method and propose an iterative solution for the corresponding joint optimization problem. We demonstrate the effectiveness of this approach on various SAR images.
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