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We propose and analyze an online algorithm for reconstructing a sequence of signals from a limited number of linear measurements. The signals are assumed sparse, with unknown support, and evolve over time according to a generic nonlinear dynamical model. Our algorithm, based on recent theoretical results for ℓ1-ℓ1 minimization, is recursive and computes the number of measurements to be taken at each time on-the-fly. As an example, we apply the algorithm to online compressive video background subtraction, a problem stated as follows: given a set of measurements of a sequence of images with a static background, simultaneously reconstruct each image while separating its foreground from the background. The performance of our method is illustrated on sequences of real images. We observe that it allows a dramatic reduction in the number of measurements or reconstruction error with respect to state-of-the-art compressive background subtraction schemes. Index Terms—State estimation, compressive video, background subtraction, sparsity, ℓ1 minimization, motion estimation.
Sabine Süsstrunk, Yufan Ren, Peter Arpad Grönquist, Alessio Verardo, Qingyi He
Edoardo Charbon, Andrei Ardelean, Mohit Gupta