Wavelet-based denoising methods: a comparative study with applications in microscopy

This paper describes different methodologies for noise reduction or denoising with applications in the field of microscopy. An in depth study on wavelet- and polynomial based denoising has been performed by considering standard test images and phantom tests with moderate and high levels of Gaussian noise. Different thresholding methods have been tested and evaluated and in particular a novel sigmoidal- type thresholding method has been proposed. In real applications, noise variance estimation problem becomes crucial because most of the thresholding estimators tends to overestimate this value. A comparison with the Hermite polynomial transform (HPT) and a modification of the HPT based in detecting the position and orientation of relevant edges has been accomplished. From this study one can conclude that both wavelet-based and polynomial-based denoising methods perform better than any other nonlinear filtering method both in terms of perceptual quality and edge-preserving characteristics.