Image Denoising Based On Hybrid Variation Model

Noise in images introduced by formation and transmission is unavoidable,which makes post-processing difficult.Commonly used image denoising model based on variational method are total variation model and harmonic model.Total variation model can keep edges well,but it will bring in staircase effect.Harmonic model denoises well in smooth areas,but it will blur edges when removing noise.In order to overcome the drawbacks of them,a hybrid model is proposed in this paper.Hybrid model is convex combination of total variation model and harmonic model.When combinatorial coefficient is large,hybrid model is close to total variation model.When combinatorial coefficient is small,hybrid model is close to harmonic model.We explain hybrid model from the view of local diffusion and verify its effectivity through numerical experiments.If combinatorial coefficient is appropriate,denoising result of hybrid model is better than total variation model and harmonic model.Compared with total variation model,hybrid model's denoising time is less.Since image can be divided into smooth areas and edge areas,choosing different combinatorial coefficients in different areas should achieve better result.Through altering combinatorial coefficients,hybrid model can be changed into adaptive.We adaptively select parameter(?)(x,y) which decides the strength of diffusion based on the gradient information of each pixel and set two thresholdsβ₁ andβ₂.When(?)(x,y)＜β₁,we consider the area as flat and use harmonic model to calculate. When(?)(x,y)＞β₂,we consider it's the edge of image and use total variation model to calculate.If(?)(x,y) is between two thresholds,we use hybrid model to calculate.Numerical experiments show that:Using same termination criteria,hybrid adaptive model and total variation adaptive model can reach almost the same denoising result,but the former's computing time is half of the latter.Hybrid adaptive model can reach significantly better result than hybrid model.