Abstract:
We consider the problem of spatiotemporal sampling in an evolutionary process xn = Anx where an unknown operator A driving an unknown initial state x is to be recovered f...Show MoreMetadata
Abstract:
We consider the problem of spatiotemporal sampling in an evolutionary process xn = Anx where an unknown operator A driving an unknown initial state x is to be recovered from a combined set of coarse spatial samples {χ|Ωο, x(1)|Ωι,· · ·, x(N)|ΩN}. In this paper, we will study the case of infinite dimensional spatially invariant evolutionary process, where the unknown initial signals x are modeled as ℓ2(Z) and A is an unknown spatial convolution operator given by a filter α ε ℓ1 (Z) so that Ax = a · x. We show that {x|Ωm, x(1)|Ωm, ···, x(N)|Ωm:N≥2m -, Ωm = mZ} contains enough information to recover the Fourier spectrum of a typical low pass filter a, if x is from a dense subset of ℓ2 (Z). The idea is based on a nonlinear, generalized Prony method similar to [2]. We provide an algorithm for the case when a and x are both compactly supported. Finally, We perform the accuracy analysis based on the spectral properties of the operator A and the initial state x and verify them in several numerical experiments.
Date of Conference: 25-29 May 2015
Date Added to IEEE Xplore: 09 July 2015
Electronic ISBN:978-1-4673-7353-1