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This paper addresses the problem of video inpainting, that is seamlessly reconstructing missing portions in a set of video frames. We propose to solve this problem proceeding as follows: (i) finding a set of descriptors that encapsulate the information necessary to reconstruct a frame, (ii) finding an optimal estimate of the value of these descriptors for the missing/corrupted frames, and (iii) using the estimated values to reconstruct the frames. The main result of the paper shows that the optimal descriptor estimates can be efficiently obtained by minimizing the rank of a matrix directly constructed from the available data, leading to a simple, computationally attractive, dynamic inpainting algorithm that optimizes the use of spatio/temporal information. Moreover, contrary to most currently available techniques, the method can handle non-periodic target motions, non-stationary backgrounds and moving cameras. These results …