一种新的基于高阶非线性扩散的图像平滑方法

A New Noise Removal Method Based on Fourth-Order Nonlinear Diffusion

该文首先基于方向曲率模值提出描述图像平滑度的泛函,并推导出新的高阶偏微分方程(PDE)图像降噪模型,在有效降噪的同时,能较好地保持特征.低阶非线性扩散方法处理结果是分段恒定图像,而文中方法得到的分段线性图像,视觉效果更加理想.与其它高阶方法相比,新方法具有理论和计算上的优势.其次,针对非线性扩散中出现的过度平滑现象,该文提出利用泄漏修补算子对偏微分方程进行补充,实验表明,泄漏修补机制对图中重要的、细微的特征有较好的保持作用.最后,文中还提出一种新的非线性扩散过程——复合扩散,以扩大方法的使用范围,提高其适应性.同以往的非线性扩散相比,复合扩散不但能自适应地调整扩散方向,而且可并行处理不同类型噪声.

A class of fourth-order partial differential equations(PDEs) are proposed to optimize the trade-off between noise removal and edge preservation. The time evolution of these PDEs seeks to minimize a cost functional, which is an increasing function of the directional curvature magnitude of the image intensity function. These PDEs attempt to remove noise and preserve edges by approximating an observed image with a piecewise planar image. Piecewise planar images look more natural than step images which (second order) nonlinear diffusion uses to approximate an observed image. So the proposed PDEs are able to avoid the blocky effects and false edges widely seen in images processed by second order nonlinear diffusion, while achieving the degree of noise removal and edge preservation comparable to second order PDEs. Other fourth-order nonlinear diffusion processes need despeckle algorithms to remove speckles after processing, while the PDEs proposed in this paper have no such problem. Since the fixed, finite spacing between pixels, “leakage” problem is common in nonlinear diffusion. Small leaks over many timesteps gradually erode the image boundaries and eventually destroy them all. In this paper a self-adjusting leakage fix for pixel is proposed, and it has been proven to be efficient in preserving details of image. As the diffusion coefficient is locally adjusted according to image features such as edges, textures and moments, FAB diffusion is introduced into the proposed PDEs. By adding the diffusion direction function in diffusion coefficient a new class of adaptive nonlinear diffusion processes named as Composite Diffusion are proposed, which can switch the diffusion process from a backward to a forward mode to smooth the pixel corrupted by impulsive noise and Gaussian noise, so the proposed Composite Diffusion processes can enhance features while locally denoising the signal or image corrupted by blended additive noises.