Restoration of blurred images using geometric and chebichef moments / Ahlad Kumar - Ahlad, Kumar (2016)
Blur affects the edges of an image that leads to the degradation of the image quality. Several methods have been developed in both spatial and frequency domains to deblur Gaussian and motion blurred images by using iterative methods to estimate the blur parameters. In this study geometric moments (GM) and Tchebichef moments (TM), from the family of non-orthogonal and orthogonal moments respectively, are utilized for deblurring of images. Here, three methods are proposed for deblurring of images. In the first method, the framework of variational method is formulated in moment domain to implement deblurring of the Gaussian and motion blurred images using Euler-Lagrange identity and alternate minimization (AM) algorithm. It uses an iterative procedure in the form of partial differential equations (PDE) to restore the deblurred GMs. This is addressed for both non-blind and blind methods which use an iterative procedure to restore the deblurred GMs. Then, a reconstruction method using Stirling numbers is used to restore the deblurred image from the deblurred GMs. Three experiments are carried out to demonstrate the effectiveness of the proposed method on the quality of the restored images by considering the effects of the regularization parameter and blur size. In the second method, Gaussian blur estimation problem is modelled as regression problem and is solved using Weighted Geometric moments (WGM) and extreme learning machine (ELM). In particular, WGMs are formulated as linear combination of fundamental basis GMs which are used as feature vectors that can effectively capture the behavior of edges present in an image subjected to Gaussian blur. These feature vectors along with ELM are used in estimating the blur parameters. Once the blur parameters are estimated, the restoration of the degraded image is performed in moment domain using the cascaded digital filters operating as subtractors to perform the task of image reconstruction. Here, two experiments are performed on six publicly available standard databases of images in order to validate the performance of the proposed method. In the first experiment, the cross database analysis of the proposed method for blur estimation is carried out and the results show that the blur parameters can be estimated. In the second experiment, the proposed methods are compared with the five existing methods and the quality of the restored images is evaluated using BRISQUE and SSIM. The results show the proposed method performed well in most cases. In the third method, Tchebichef moments (TM) of low order are selected as features used as inputs to ELM to estimate the Gaussian blur parameters. Once the blur parameters are estimated, image restoration of the proposed method is carried out using split Bregman algorithm. The performance analysis using the proposed TM method is compared with the same five existing methods. It has been observed that TMs based image restoration perform well compared to the five existing methods when evaluated using image quality metrics.