title: Relating observability and compressed sensing of time-varying signals in recurrent linear networks.
abstract: In this paper, we study how the dynamics of recurrent networks, formulated as general dynamical systems, mediate the recovery of sparse, time-varying signals. Our formulation resembles the well-described problem of compressed sensing, but in a dynamic setting. We specifically consider the problem of recovering a high-dimensional network input, over time, from observation of only a subset of the network states (i.e., the network output). Our goal is to ascertain how the network dynamics may enable recovery, even if classical methods fail at each time instant. We are particularly interested in understanding performance in scenarios where both the input and output are corrupted by disturbance and noise, respectively. Our main results consist of the development of analytical conditions, including a generalized observability criterion, that ensure exact and stable input recovery in a dynamic, recurrent network setting.
authors.affiliation: Department of Electrical and Systems Engineering, Washington University in St. Louis, One Brookings Drive, Campus Box 1042, MO 63130, United States. Electronic address: kafashan@ese.wustl.edu.
authors.forename: MohammadMehdi
authors.initials: M
authors.lastname: Kafashan
authors.affiliation: Department of Electrical and Systems Engineering, Washington University in St. Louis, One Brookings Drive, Campus Box 1042, MO 63130, United States. Electronic address: nandia@ese.wustl.edu.
authors.forename: Anirban
authors.initials: A
authors.lastname: Nandi
authors.affiliation: Department of Electrical and Systems Engineering, Washington University in St. Louis, One Brookings Drive, Campus Box 1042, MO 63130, United States; Division of Biology and Biomedical Sciences, Washington University in St. Louis, One Brookings Drive, Campus Box 1042, MO 63130, United States. Electronic address: shinung@ese.wustl.edu.
authors.forename: ShiNung
authors.initials: S
authors.lastname: Ching
mesh_terms: D044962:Data Compression / Q000379:methods; D016571:Neural Networks, Computer; D013995:Time
keywords:  minimization; Linear dynamical systems; Over-actuated systems; Recurrent networks; Sparse input