基于改进复扩散自适应耦合非局部变换域模型的图像放大

针对二阶偏微分方程（PDE）放大算法丢失弱边缘和纹理细节的不足，提出一种改进复扩散自适应耦合非局部变换域模型的图像放大算法。利用复扩散具有边缘定位准确的特点耦合冲击滤波器，改进复扩散模型能够较好地增强强边缘；而通过对相似图像块构成图像组的三维变换系数的稀疏特性进行建模，非局部变换域模型能够很好地利用图像中相似图像块的非局部信息，对弱边缘和纹理细节有较好的处理效果；最后利用复扩散得到图像的二阶导数作为参数实现改进复扩散模型和非局部变换域模型自适应耦合。所提算法与偏微分方程放大算法、非局部变换域放大算法和偏微分方程耦合空域非局部模型放大算法进行仿真实验比较，在强边缘、弱边缘和细节纹理具有较好的放大效果，弱边缘和纹理细节图像在平均结构相似性测度上高于改进复扩散放大算法、非局部变换域放大算法。所提算法验证了空域模型和变换域模型、局部模型和非局部模型耦合结合的有效性。

Image enlargement based on improved complex diffusion adaptivly coupled nonlocal transform domain model

Concerning the loss of weak edges and texture details of the second-order Partial Differential Equation (PDE) amplification algorithm, an image enlargement algorithm was proposed based on improved complex diffusion adaptively coupled nonlocal transform domain model. By utilizing the advantage of accurate edge location of the complex diffusion model, the improved complex diffusion coupled impulse filter to enhance strong edges better; by modeling the sparse characteristics of the transform coefficients coming from three dimensional transformation of the image group composed of similar image blocks, the nonlocal transform domain model could make good use of the nonlocal information of the similar image blocks and had better processing effects on weak edges and texture details. Finally, the second-order derivation of the image obtained by the complex diffusion was used as the parameter to realize the adaptive coupling of the improved complex diffusion model and the nonlocal transform domain model. Compared with partial differential equation amplification algorithm, nonlocal transformation domain amplification algorithm and partial differential equation coupled space domain nonlocal model amplification algorithm, the proposed algorithm has better amplification effect on strong edges, weak edges and detail textures, the mean structural similarity measures of weak edges and texture detail images are higher than those of improved complex diffusion magnification algorithm and the nonlocal transform domain amplification algorithm. The proposed algorithm also confirms the validity of the coupling between the space domain model and the transform domain model, local model and nonlocal model.