热扩散和整体变分模型自适应调整的图像放大模型

近年来基于偏微分方程的图像处理因其具有更强的局部自适应特性和高度的灵活性而成为继小波图像处理之后新的研究热点。本文在对热扩散模型和TV（Total Variation）模型分析的基础上，针对二模型在图像平滑区域及边缘或纹理区域扩散所表现出的不同特性和优势，提出一种基于图像局部特性的自适应混合图像放大模型，该模型以双线性插值后的放大图像为初始值，根据像素点梯度特性在平滑区域和边缘或纹理区域自适应的调整扩散模型，使得在平滑区域进行热传导的同性扩散，而在边缘和纹理区域处则进行沿与梯度方向相垂直的方向扩散。该模型很好的抑制了图像插值放大后所带来的块状效应，以及放大后边缘或纹理区域的假边缘现象。理论上证明了所提出模型解的存在性，同时大量的仿真实验验证了所提出模型的有效性。

Image magnification model based on adaptive adjustment of thermal diffusion and TV model

In recent years, image processing based on the partial differential equation because of its strong local adaptive characteristics and a high degree of flexibility becomes new research hot spot after wavelet image processing. Based on thermal diffusion model and TV (Total Variation), and in view of the two models in the image smooth area and edge or texture area diffusion represented by the different characteristic and the superiority, this paper proposes the adaptive hybrid image magnification model based on image local characteristics of. This model initializes the amplification image after double linear interpolation, and adaptively adjusts diffusion model according to the pixel gradient characteristic in the smooth area and edge or texture area, which makes the smooth area of heat conduction of gay diffusion, and the edge and texture in the region has made with gradient direction along the vertical direction phase diffusion. This model inhibits the image interpolation after amplification brought by the massive effect, and amplifies trailing edge or texture area of the false edge phenomenon. The proposed model is proved the existence of the solution, and at the same time, a lot of simulation results show the effectiveness of the proposed model.