Two-stage image denoising considering interscale and intrascale dependencies

Abstract

A solution to the problem of reducing the noise of grayscale images is presented. To consider the intrascale and interscale dependencies, this study makes use of a model. It is shown that the dependency between a wavelet coefficient and its predecessors can be modeled by the first-order Markov chain, which means that the parent conveys all of the information necessary for efficient estimation. Using this fact, the proposed method employs the Kalman filter in the wavelet domain for image denoising. The proposed method has two stages. The first stage employs a simple denoising algorithm to provide the noise-free image, by which the parameters of the model such as state transition matrix, variance of the process noise, the observation model, and the covariance of the observation noise are estimated. In the second stage, the Kalman filter is applied to the wavelet coefficients of the noisy image to estimate the noise-free coefficients. In fact, the Kalman filter is used to estimate the coefficients of high-frequency subbands from the coefficients of coarser scales and noisy observations of neighboring coefficients. In this way, both the interscale and intrascale dependencies are taken into account. Results are presented and discussed on a set of standard 8-bit grayscale images. The experimental results demonstrate that the proposed method achieves performances competitive with the state-of-the-art denoising methods in terms of both peak-signal-to-noise ratio and subjective visual quality.