Wavelet-based Denoising Methods. a Comparative Study with Applications in Microscopy

This paper describes di erent methodologies for noise reduction or denoising with applications in the eld of microscopy. An in depth study on waveletand polynomial based denoising has been performed by considering standard test images and phantom tests with moderate and high levels of Gaussian noise. Di erent thesholding 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 thesholding estimators tends to overestimate this value. A comparison with the Hermite polynomial transform (HPT) and a modi cation 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 non-linear ltering method both in terms of perceptual quality and edge-preserving characteristics.