A Comparative Simulation Study of Wavelet Shrinkage Estimators for Poisson Counts

Abstract

Using computer simulations, the finite sample performance of a number of classical and Bayesian wavelet shrinkage estimators for Poisson counts is examined. For the purpose of comparison, a variety of intensity functions, background intensity levels, sample sizes, primary resolution levels, wavelet filters and performance criteria are employed. A demonstration is given of the use of some of the estimators to analyse a data set arising in high-energy astrophysics. Following the philosophy of reproducible research, the MATLAB programs and real-life data example used in this study are made freely available.

Wavelets, Ridgelets, and Curvelets for Poisson Noise Removal

“…The low-intensity case apart, Bayesian approaches generally outperform the direct wavelet filtering [11], [12] (see also [20] for a comparative review). Poisson denoising has also been formulated as a penalized maximum likelihood (ML) estimation problem [21], [22]- [24] within wavelet, wedgelet and platelet dictionaries.…”

“…where is the gradient of , and in otherwise (20) where represents the projection onto the nonnegative orthant, and and are the projectors onto their respective constraint sets. The step sequence satisfies and (21) Suppose that in b)-e) below, represents a tight frame decomposition and its pseudo-inverse operator.…”

Enhancing precision in time-domain fluorescence lifetime imaging

“…Other TV or non-TV denoising methods have also been developed either to handle Poisson noise or to have varying regularization parameters that can potentially be used to remove Poisson noise. [19][20][21][22] However, although Poisson-distributed noise is a common form of noise for photon-counting devices, other forms of noise may appear due to nonunity gain and sometimes nonideal behaviors of real imaging systems. In addition, to directly denoise FLIM lifetime maps, the deformed noise distribution after lifetime determination and the dependence of this distribution on intensity and lifetime need to be considered as well.…”

Wavelet-based restoration methods: application to 3D confocal microscopy images

“…More recently, some authors proposed to use the wavelet transform 4,5 for biological image deconvolution. In the literature of Poisson noise, many people use a pre-processing like the Anscombe 6 transform or the Fisz transform 7 in order to stabilize the noise variance and to apply more usual methods 8 (i.e. techniques developed for Gaussian noise).…”