中文摘要：

综合应用冲激滤波器、改进的前向后向（forward and backward，FAB）扩散滤波器和全变差（totalvariation，TV）扩散算法，提出一种双正交映射约束的混合偏微分方程扩散图像放大算法。改进的FAB滤波器能够很好地增强图像的小边缘，参数约束的冲激滤波器可增强图像的强边缘，基于水平集方法实现的TV扩散可以消除边缘的锯齿波，使边缘光滑，所提算法综合以上优点。利用退化模型的低通滤波器的双正交滤波器得到一个空域双正交映射，放大图像完全满足退化模型，使放大图像对于退化模型可逆。仿真实验表明，与其他算法相比，所提算法有较好的性能，得到的放大图像更加自然，在弱边缘和中等强度边缘都有更好的视觉效果。

英文摘要：

Combined the improved forward-and-backward （FAB） diffusion and total-variation （TV） diffu- sion coupled to the parameter constrained shock filters under the projection of the bi-orthogonaI filter, a new hy- brid diffusion method of image enlargement is proposed. The improved FAB diffusion enhances weak edges, the shock filter constrained by adaptive coefficient enhances the strong edge and TV diffusion based on the level-set method smoothing along the edge diminishes edge jagged effect. The hybrid partial differential equation（PDE） diffu- sion has the advantage of the three above PDE diffusion. Furthermore, a bborthogonal projection is described to per- form an interpolation that is reversible, and the interpolated image satisfies the degradation model strictly. The simulation demonstrates the performance of the proposed method is prominent. Compared with other existing PDE based zoom methods, the zoomed image using the proposed method looks more natural and has better visu- al effect not only on the strong edges but also on weak edges.