Fourier and filterbank analyses of signal-dependent noise

Owing to the lack of resolution of the measurement and the randomness inherent in the signal and the measuring devices, the measurement noise is often signal-dependent. Although the statistical modeling of filterbank, wavelets, and short-time Fourier coefficients enjoys immense popularity, transform-based estimation of signal is difficult because the effects of signal-dependent noise permeate across multiple coefficients and subbands. In this work, we show how a general class of signal-dependent noise can be characterized to an arbitrary precision in a Haar filterbank and Fourier representation. The structure of noise in the transform domain admits a variant of Stein´s unbiased estimate of risk conducive to processing the corrupted signal in the transform domain, and estimators involving Poisson processes are discussed.