Topology-based denoising of chaos

In this article, we propose a denoising algorithm to denoise a time series yi = xi + ei, where {xi} is a time series obtained from a time-T map of a uniformly hyperbolic or Anosov flow, and lcubeircub a uniformly bounded sequence of independent and identically distributed (i.i.d.) random variables. Making use of observations up to time n, we create an estimate of xi for i is < n. We show under typical limiting behaviours of the orbit and the recurrence properties of xi, the estimation error converges to zero as n tends to infinity with probability 1