Wavelet-based adaptive image denoising with edge preservation

This paper presents a state-of-the-art adaptive wavelet-based denoising method with edge preservation. More specifically, a redundant discrete dyadic wavelet transform (DDWT) is performed on the noisy image to get the wavelet frame decomposition at different scales. Based on the Lipschitz regularity theory, correlation analysis across scales is performed to detect the significant coefficients from the signal and the insignificant coefficients from the noise for each subband. Different denoising techniques are applied to the significant coefficients and insignificant coefficients separately, based on different statistical models. Unlike most of the existing image denoising methods, the proposed method is able to not only shrink but also increase the magnitude of the noisy wavelet coefficients. Simulation results show that the proposed method has a remarkably superior ability to preserve the edge information and to achieve better visual quality.