Learning based restoration of Gaussian blurred images using weighted geometric moments and cascaded digital filters

Image moments such as zernike, tchebichef and geometric moments have been widely used in image processing applications. They have useful properties to detect edges. In this paper, we present how one of the moment families, in particular geometric moments (GM) can be utilized in estimating the sigma and size of the Gaussian point spread function (PSF) that degrades the images. With the knowledge of how edges vary in the presence of Gaussian blur, a method that uses low order geometric moments is proposed to estimate the PSF parameter. This is achieved by using the difference of the GMs of the original and the reblurred images as feature vectors to train extreme learning machine (ELM) to estimate the PSF parameters respectively. Further, a novel method that uses a cascaded digital filters operating as subtractors is proposed to transform the image from geometric moment domain to spatial domain. The effectiveness of the proposed method of estimating the PSF parameters is examined using cross database validation. The results show that the proposed method in most of the cases performs better than the three existing methods when examined in terms of the visual quality evaluated using structural similarity (SSIM) index.