基于四阶非线性偏微分方程的图像去噪算法

Image denoising algorithm based on nonlinear fourth-order PDE

为了更好的实现图像模糊消除和有效地去除斑点噪声,提出了一种新的基于偏微分方程的图像去噪方法,它是基于非线性四阶扩散模型。首先提出了该非线性偏微分方程的方案,然后对微分模型进行数学处理,研究它的适定性,最后证明了此模型在一定条件下是适定的,并且存在了弱解,所得到的弱解近似于基于有限差分数值离散格式。实验结果表明,新模型在图像去噪和保边缘等细节信息方面都达到较好的效果,峰值信噪比有了大幅提高,去噪性能较经典模型更具优越性。

To provide a better image deblurring and remove successfully the speckle noise,a novel PDE-based image denoising approach is proposed in this paper. It is based on a nonlinear fourth-order diffusion model. The nonlinear PDE scheme is described first. Then,a mathematical treatment is provided for this differential model,its well-posedness being investigated. It is proved that the model is wellposed in some certain conditions and admits a weak solution. The weak solution of the obtained PDE is approximated by developing an explicit finite-difference based numerical discretization scheme. The experimental results show that the new model proposed in this paper can achieve good results in image denoising and preserving edges and other details. Compared with the classical model,the peak signal to noise ratio is greatly improved and the denoising performance is more better.