Efficient blind image restoration based on 1-D generalized cross validation

Restoring an image from its convolution with an unknown blur function is a well-known ill-posed problem in image processing. The generalized cross validation (GCV) approach was proposed to solve the problem and it has shown to have good performance in identifying the blur function and restoring the original image. However, in actual implementation, various problems incurred due to the large data size and long computational time of the approach are undesirable even with the current computing machines. h this paper, an efficient algorithm is proposed for blind image restoration. For this approach, the original 2-D blind image restoration problem is converted into 1-D ones by using the discrete periodic Radon transform, 1-D GCV algorithm is then applied hence the memory size and computational time required are greatly reduced. Experimental results show that the resulting approach is faster in almost an order of magnitude as compared with the traditional approach, while the quality of the restored image is similar.