Joint SAR Imaging and Multi-Feature Decomposition From 2-D Under-Sampled Data Via Low-Rankness Plus Sparsity Priors

In this paper, we introduce a multi-feature decomposition approach to the problem of synthetic aperture radar (SAR) image reconstruction from under-sampled data in both range and azimuth directions. Conventional SAR image formation methods may produce images that are not appropriate for interpretation tasks such as segmentation and automatic target recognition. We deal with this problem using an efficient joint SAR image reconstruction-decomposition framework in which features of interest are enhanced and decomposed simultaneously. Unlike conventional methods, our proposed framework provides multiple segment images along with a composite SAR image. In the composite image not only the resolution is improved but also both the speckle and sidelobe artifacts are reduced. In the decomposed images, different components can be roughly attributed to different potential segments, which facilitate the subsequent interpretation tasks such as shape-based recognition or region segmentation. Moreover, these decomposed images contain easier-to-segment regions rather than taking the entire scene for segmenting the feature of interest. By formulating the SAR image reconstruction as a low-rank plus multi-feature decomposition problem, the optimization problem is solved based on the alternating direction method of multipliers. Using combined dictionaries, multiple transform-sparse components are represented efficiently by a linear combination of multiple sparsifying matrices associated with the features of interest in the scene. Our proposed method jointly reconstructs and decomposes different pieces of the imaged SAR scene, in particular the low-rank part of the background and sparsely represented features of interest, from under-sampled observed data. Using extensive experimental results we show the effectiveness of the proposed method on both synthetic and real SAR images.