Dynamic sparse state estimation using ℓ1-ℓ1 minimization: Adaptive-rate measurement bounds, algorithms and applications
João F. C. Mota, Nikos Deligiannis, Aswin C. Sankaranarayanan, Volkan Cevher, Miguel R. D. Rodrigues
Abstract
We propose a recursive algorithm for estimating time-varying signals from a few linear measurements. The signals are assumed sparse, with unknown support, and are described by a dynamical model. In each iteration, the algorithm solves an ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> minimization problem and estimates the number of measurements that it has to take at the next iteration. These estimates are computed based on recent theoretical results for ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> minimization. We also provide sufficient conditions for perfect signal reconstruction at each time instant as a function of an algorithm parameter. The algorithm exhibits high performance in compressive tracking on a real video sequence, as shown in our experimental results.
BibTeX
@inproceedings{icassp2015_dynamicsparsesta,
title = {Dynamic sparse state estimation using ℓ1-ℓ1 minimization: Adaptive-rate measurement bounds, algorithms and applications},
author = {João F. C. Mota and Nikos Deligiannis and Aswin C. Sankaranarayanan and Volkan Cevher and Miguel R. D. Rodrigues},
booktitle = {ICASSP 2015},
year = {2015}
}