## Tuesday, March 17, 2015

### Adaptive-Rate Sparse Signal Reconstruction With Application in Compressive Background Subtraction

Using DECOPT, one can envision evaluating the number of measurements for the next video frame by assuming that additional information to the next frame is going to be sparse. This is is what today's paper is looking into: Adaptive-Rate Sparse Signal Reconstruction With Application in Compressive Background Subtraction by Joao F. C. Mota, Nikos Deligiannis, Aswin C. Sankaranarayanan, Volkan Cevher, Miguel R. D. Rodrigues

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 $\ell_1$-$\ell_1$ 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 compressive video background subtraction, a problem that can be 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 with respect to state-of-the-art compressive background subtraction schemes.

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