基于混合阶偏微分方程的图像放大

摘要

A method of the image enlargement is proposed,which combines the isotropic forth order PDE and the improved TV model based on the analysis of the characteristic of four order PDE avoiding the staircase effect.Using the bi-orthogonal projection to realize the constraint of the degradation model, for low gradient pixel the forth-order partial differential equation (PDE) diffusion is performed and for high gradient pixel the second-order PDE diffusion is strengthened with shock filters.Comparing with other existing PDE-based zoom methods, it is proved that the proposed method has better visual effect not only on the strong edges but also on weak edges and the zoomed image using the proposed method looks more natural and visual effective on minor textures is better.%针对二阶偏微分方程进行图像放大产生的阶梯效应和对弱边缘纹理增强不足的缺点,利用四阶偏微分方程具有去阶梯效应特性和反向扩散特性,提出了一种各向同性扩散的四阶偏微分方程耦合改进的全变差模型的图像放大算法.使用双正交映射操作实现图像退化模型约束,在低梯度区进行各向同性四阶偏微分方程结合二阶各向异性扩散,弱边缘反向扩散进行增强,同时避免了平滑区域产生阶梯效应,在高梯度区采用二阶偏微分方程扩散耦合冲激滤波器对强边缘进行增强.本文算法和其他算法进行了比较,仿真实验证明:本文算法在保证边缘、细节有较好视觉效果的前提下,得到的放大图像更加自然,对强弱边缘的增强效果都较好.