2014/08/01 by MohammadMehdi Kafashan, Kafashan, MohammadMehdi, Anirban Nandi +3
Computer Science · Engineering · Neuroscience · #Blind Source Separation Techniques #FOS: Mathematics #Neural dynamics and brain function #Optimization and Control (math.OC) #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.1408.0202
openalex publication_date 2014/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Recent interest has developed around the problem of dynamic compressed\nsensing, or the recovery of time-varying, sparse signals from limited\nobservations. In this paper, we study how the dynamics of recurrent networks,\nformulated as general dynamical systems, mediate the recoverability of such\nsignals. We specifically consider the problem of recovering a high-dimensional\nnetwork input, over time, from observation of only a subset of the network\nstates (i.e., the network output). Our goal is to ascertain how the network\ndynamics lead to performance advantages, particularly in scenarios where both\nthe input and output are corrupted by disturbance and noise, respectively. For\nthis scenario, we develop bounds on the recovery performance in terms of the\ndynamics. Conditions for exact recovery in the absence of noise are also\nformulated. Through several examples, we use the results to highlight how\ndifferent network characteristics may trade off toward enabling dynamic\ncompressed sensing and how such tradeoffs may manifest naturally in certain\nclasses of neuronal networks.\n