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It is a great challenge to maintain details while suppressing and eliminating noise of the image. Considering the nonconvexity property of the diffusion function and the hypersensitivity of the Laplace operator to noise in the Y-K model, a fourth-order PDE image denoising model (Con_G&L model) is proposed in this paper. This model is constructed by a new convexity-preserving diffusion function which guarantees the corresponding energy functional has a globally unique minimum solution. At the same time, the Gaussian filter is combined with the Laplace operator in this model, and as a result, the noisy image is smoothed before the diffusion process, which improves the ability of capturing the details and edges of the noisy image greatly. Furthermore, by analyzing the statistical properties of the undecimated discrete wavelet transform (UDWT) coefficients of noisy image, we observe that the noise information is mainly distributed in the high-frequency sub-bands, and based on this, the proposed Con_G&L model is applied in the high-frequency sub-bands of the UDWT to get the denoising method. The proposed method removes the image noise effectively with the image texture and other details of the image being maintained. Meanwhile, the generation of false edges and the staircase effect can be suppressed. A large number of simulation experiments verify the effectiveness of the proposed method.

The UDWT image denoising method based on the PDE model of a convexity-preserving diffusion function