基于Neumann边界条件的图像局部复原

图像复原是图像处理中的一个重要课题。人们通常将其当作全局问题来处理,这可能会导致非常庞大而不可行的l2问题。为了克服这个困难,本文提出一种新的局部图像复原算法;将大的降晰图像分成若干子图像块,分别对各块进行复原。该算法用经典的Tikhonov正则化方法求解病态反问题。为了抑制分块导致的边界噪声,算法引入Neumann边界条件和块部分重叠的思想。实验结果表明,该算法有效地降低了图像处理的复杂度,而且与全局算法相比,两者复原图像的质量很接近。

Image Local Deblurring with Neumann Boundary Conditions

Blur removal is a fundamental issue in signal and image processing. It is generally treated as a global problem, which may result in a very large and infeasible l2 problem. To overcome this difficulty, a new local deblurring algorithm is proposed in this paper. It averagely divides a large noisy and blurred image into blocks and utilizes the classical Tikhonov regularization to restore them individually to produce the whole restored image. Local deblurring inevitably involves boundary problems. We consider two measures to damp boundary errors: the use of Neumann boundary conditions and partly overlapping blocks. Experimental results indicate that appropriate blocking effectively reduces the computational complexity and the performance of the new algorithm is close to that of the global one.