Dynamic Sparse State Estimation Using ℓ1-ℓ1 Minimization: Adaptive-rate Measurement Bounds, Algorithms and Applications
journal contributionposted on 2015-04-01, 00:00 authored by Joao F.C. Mota, Nikos Deligiannis, Aswin C. Sankaranarayanan, Volkan Cevher, Miguel Rodrigues
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 ℓ1-ℓ1 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 ℓ1-ℓ1 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.