Skip to Main Content
This paper addresses the problem of reconstructing a continuous function defined on Rd from a countable collection of samples corrupted by noise. The additive noise is assumed to be i.i.d. with mean zero and variance sigma2. We sample the continuous function / on the uniform lattice (1/m)Zd, and show for large enough m that the variance of the error between the frame reconstruction fepsiv,m from noisy samples of f and the function f satisfy var(fepsiv,m(x) - f(x)) ap(sigma2/md)Cx where Cx is the best constant for every x isin Rd. We also prove a similar result in the case that our data are weighted-average samples of / corrupted by additive noise.