Error analysis of frame, reconstruction from noisy samples
Abbreviated Journal Title
IEEE Trans. Signal Process.
frames; reconstruction from averages; sampling; SHIFT-INVARIANT SPACES; WAVELET SUBSPACES; THEOREM; Engineering, Electrical & Electronic
This paper addresses the problem of reconstructing a continuous function defined on R-d from a countable collection of samples corrupted by noise. The additive noise is assumed to be i.i.d. with mean zero and variance sigma(2). We sample the continuous function f on the uniform lattice (1/m)Z(d), and show for large enough m that the variance of the error between the frame reconstruction f(epsilon,m) from noisy samples of f and the function f satisfy var(f(epsilon,m)(x) - f(x))approximate to Z (sigma(2)/m(d))C-x where C-x is the best constant for every x is an element of R-d. We also prove a similar result in the case that our data are weighted-average samples of f corrupted by additive noise.
Ieee Transactions on Signal Processing
"Error analysis of frame, reconstruction from noisy samples" (2008). Faculty Bibliography 2000s. 60.