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 â„“1-â„“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.
Mota, J, Deligiannis, N, Sankaranarayanan, A, Cevher, V & Rodrigues, M 2016, 'Adaptive-rate reconstruction of time-varying signals with application in compressive foreground extraction', IEEE Transactions on Signal Processing, vol. 64, no. 14, pp. 3651-3666. https://doi.org/10.1109/TSP.2016.2544744
Mota, J., Deligiannis, N., Sankaranarayanan, A., Cevher, V., & Rodrigues, M. (2016). Adaptive-rate reconstruction of time-varying signals with application in compressive foreground extraction. IEEE Transactions on Signal Processing, 64(14), 3651-3666. https://doi.org/10.1109/TSP.2016.2544744
@article{1e390ac86a1e4d8a9b96a9fde5ddef39,
title = "Adaptive-rate reconstruction of time-varying signals with application in compressive foreground extraction",
abstract = "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 â„“1-â„“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.",
keywords = "State estimation, compressive video, background subtraction, sparsity, l1 minimization, motion estimation",
author = "Jo{\~a}o Mota and Nikolaos Deligiannis and Aswin Sankaranarayanan and Volkan Cevher and Miguel Rodrigues",
year = "2016",
month = jul,
day = "15",
doi = "10.1109/TSP.2016.2544744",
language = "English",
volume = "64",
pages = "3651--3666",
journal = "IEEE Transactions on Signal Processing",
issn = "1053-587X",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
number = "14",
}