A Framework for Image Denoising Using First and Second Order Fractional Overlapping Group Sparsity (HF-OLGS) Regularizer

Denoising images subjected to Gaussian and Poisson noise has attracted attention in many areas of image processing. This paper introduces an image denoising framework using higher order fractional overlapping group sparsity prior to sparser image representation constraint. The proposed prior has a capability of avoiding staircase effects in both edges and oscillatory patterns (textures). We adopt the alternating direction method of multipliers for optimizing the proposed objective function by converting it into a constrained optimization problem using variable splitting approach. Finally, we conduct experiments on various degraded images and compare our results with those of several state-of-the-art methods. The numerical results show that the proposed fractional order image denoising framework improves the peak signal to noise ratio of an image by preserving the textures and eliminating the staircases effects. This leads to visually pleasant restored images which exhibit a higher value of Structural SIMilarity score when compared to that of other methods

Restoration of blurred images using geometric and chebichef moments / Ahlad Kumar

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

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