Adaptive-Rate Sparse Signal Reconstruction With Application in Compressive Background Subtraction
This addresses the challenge of efficient signal reconstruction in dynamic settings like video processing, though it appears incremental as it builds on existing minimization techniques.
The authors tackled the problem of reconstructing sparse signals from limited linear measurements over time, proposing an online algorithm that adaptively determines the number of measurements needed. They applied it to compressive background subtraction, achieving a dramatic reduction in measurements compared to state-of-the-art methods.
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.