基于局部坐标二次微分的自适应全变分去噪复原

针对传统TV去噪复原算法以梯度模值作为图像的边缘检测算子,无法清晰地识别边缘和灰度渐变区及去除平坦区内的孤立噪声的问题,提出了一种基于局部坐标二次微分的边缘检测算子对传统模型进行改进。改进后的模型能根据各像素点的新检测算子信息,自适应选取复原模型中决定扩散强弱的参数,并且利用图像局部信息对正则化项和保真项进行加权。同时在数值实现上,采用一种基于梯度矢量的方向变化的方法来实现散度离散化,以更加有效地保留图像的局部细节信息。数值试验表明,该算法在克服灰度渐变区内的阶梯效应和保留图像的细节边缘方面明显优于传统算法。

Adaptive Total Variation Image Denoising and Restoration Based on the Quadratic Differential in the Local Coordinate System

Aiming at the algorithm of traditional total variation image denoising and restoration based on the image gradient as its edge indicator, which cannot effectively distinguish between edges and ramps and remove the isolated noise in flat regions, a new edge indicator based on the quadratic differential in the local coordinate system is proposed to improve the traditional model. The improved model can adaptively select the most appropriate denoising scheme based on the edge indicator information of each pixel, and its regularization term and fidelity term can be weighted by the image fine information. And in the aspect of the numerical implementation, a new method based on the variation of the image gradient direction is adopted to discrete the divergence term to better preserve fine details effectively. Numerical experiments demonstrate that the new algorithm is superior to the traditional ones in the aspect of avoiding the staircase effect in ramp regions and preserving fine details.