各向异性四阶偏微分方程耦合二阶偏微分方程的图像放大

Image enlargement based on anisotropic forth-order partial differential equation coupled to second-order partial differential equation

针对增强图像中的弱边缘、细节纹理和消除二阶偏微分方程在图像平滑部分的阶梯效应问题,提出一种各向异性四阶偏微分方程耦合二阶偏微分方程的图像放大算法。算法通过像素的局部方差自适应约束阈值,实现图像中不同结构的各向异性四阶扩散,增强弱边缘和细节纹理,去除平滑部分阶梯效应,同时耦合改进的总变差方法和受梯度约束的冲激滤波器对边缘进行增强,放大算法采用双正交映射实现图像退化模型的约束。仿真实验证明该算法能够很好地增强边缘、细节和纹理,去除阶梯效应。与其他二阶偏微分方程放大算法比较,算法具有较好的主观视觉效果,算法放大图像的峰值信噪比(PSNR)和平均结构相似性测度(MSSIM)也高于其他二阶偏微分方程算法,其中平滑部分较多图像的PSNR比基于改进的总变差放大算法提高1 d B左右,细节纹理较多的图像提高0.5 d B以上。该算法的放大图像更加自然,弱边缘和细节能够得到分辨率增强。

To enhance the weak edges and textures and to avoid the staircase effect, an image enlargement method was proposed which coupled anisotropic forth-order partial differential equation to second-order partial differential equation. In the method, the weak edges and textures were enhanced and staircase was reduced by improved anisotropic forth-order partial differential equation with adaptive diffusion coefficient to threshold value constrained by pixel＇s local variance, improved total variance and adaptive amplitude shock filters controlled by gradient were coupled with the forth-order differential equation to enhance the edges, and the bi-orthogonal projection was used to realize the constraint of the degradation model. Simulation experiment results validate the proposed method on enhancing the edges, details and textures and reducing staircases.Compared with other existing second-order PDE-based zoom methods, the zoomed images using the proposed method have better visual effect and higher Peak Signal-to-Noise Ratio（ PSNR） and Mean Structural Similarity Measure（ MSSIM）, for example, PSNR of zoomed image with larger smooth part by the proposed method is about 0. 1 d B higher than that by improved Total Variance（ TV） enlargement method and PSNR of zoomed image with larger weak edges and textures by the proposed method is above 0. 5 d B higher than that by improved TV enlargement method. Therefore, the zoomed image of the method looks more natural, and the resolution of the weak edges and textures of the image are enhanced better.