Inspired by the recent developments in computer vision, low-rank and structured sparse matrix decomposition can be potentially be used for extract moving objects in satellite videos. This set of approaches seeks for rank minimization on the background that typically requires batch-based optimization over a sequence of frames, which causes delays in processing and limits their applications. To remedy this delay, we propose an Online Low-rank and Structured Sparse Decomposition (O-LSD). O-LSD reformulates the batch-based low-rank matrix decomposition with the structured sparse penalty to its equivalent frame-wise separable counterpart, which then defines a stochastic optimization problem for online subspace basis estimation. In order to promote online processing, O-LSD conducts the foreground and background separation and the subspace basis update alternatingly for every frame in a video. We also show the convergence of O-LSD theoretically. Experimental results on two satellite videos demonstrate the performance of O-LSD in term of accuracy and time consumption is comparable with the batch-based approaches with significantly reduced delay in processing.
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