Image Denoising Using the Hurst Exponent: A Fusion Based Approach

We propose in this paper a denoising method based on the texture roughness appreciation, realized using a semi-local estimation of the Hurst exponent. The estimation is made in the Dual Tree Complex Wavelet domain, by using techniques such as the least squares or the lasso. The Hurst exponent is used to correct the energy distribution of the wavelet coefficients. This removes the noise in homogeneous areas but can oversmooth the edges. In order to overcome this, we propose a fusion based approach, based on the observation that the noise is less visible on the edges. Both the denoised image as well as the original image are weighted by images that depend on the Hurst parameter, such that the edges are less degraded, and the correction is applied predominantly in the homogeneous areas. Our simulation results are promising for images containing both smooth areas as well as edges for the fusion based approach.