Nonlinear noise reduction based on zero‐crossing representations of a wavelet transform

Abstract

AbstractA novel nonlinear noise reduction method that effectively reduces both impulsive and Gaussian noise is proposed and investigated. In the proposed method, a zero‐crossing representation that is a kind of compressed description of the coefficients of a multiscale wavelet transform is obtained first and then, using characteristics of the transform coefficients, any noise that is thought to have entered the zero‐crossing representation is suppressed. Noise reduction is achieved by reconstructing the image from the modified zero‐crossing representation. It is shown that, compared to nonlinear filtering methods, the proposed method is more effective for simultaneously reducing both impulsive and Gaussian noise for one‐ dimensional signals and two‐dimensional image signals.