Dynamic sparse state estimation using ℓ1-ℓ1 minimization: Adaptive-rate measurement bounds, algorithms and applications

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.