中文摘要：

在对凸集投影超分辨率图像复原方法的研究中发现，图像的边缘区域与其他区域并不需要使用相同的松弛算子，据此提出一种快速的凸集投影方法，解决了传统凸集投影方法中一直存在的运算量大的问题，提高其实际应用性能．在凸集投影图像复原过程中引入模糊熵进行边缘检测，根据其邻域一致性测度构造一单调递增函数，以此作为定义迭代步长的松弛算子，从而可以根据图像各部分的区域特征来自适应选取迭代步长，大大减少了运算量．实验表明，快速凸集投影方法经过几十次的迭代能得到近似甚至优于传统凸集投影方法上百次迭代后的复原效果，并且由于复原过程中引入了边缘先验信息，对振铃效应也有很好的抑制作用．

英文摘要：

In the research on the project onto convex set （POCS） super-resolution image restoration algorithm, it is obseryed that the edge region does not need the same relaxation factor as the uniform region. Revising this problem can reduce the large computational complexity of POCS and improve its practical application quality. Consequently, a fast POCS （FPOCS） is proposed. By quoting fuzzy entropy in the POCS image restoration process for edge detection, a monotonous increasing function that defines the relaxation factor is constructed based on the neighborhood homogeneous measurement （NHM）. Therefore, the proposed approach can select the relaxation factor adaptively by the local character of the image. Experimental results show that the new approach can achieve a similar or even better restoration performance after dozens of iterations while the traditional POCS needs hundreds of iterations.