SOME FRACTIONAL ORDER DIFFUSION MODELS FOR SINGLE IMAGE FOG REMOVAL AND DENOISING

Abstract

This thesis presents new algorithms that endow with improved elucidation to the problem of image restoration. In particular, ve di erent algorithms are presented to deal with the two subproblems of image restoration namely `defogging' and `denoising'. All these ve algorithms utilize a fractional-order generalization of integer order derivatives in the image space during an implementation of di usion ltering. Several experimental results are presented in the form of qualitative and quantitative evaluations to support the algorithms proposed in the thesis. A detailed comparison study of some existing approaches has been carried out to highlight the applicability and the virtue of the proposed algorithms. The proposed algorithms have many applications in di erent areas such as video surveillance, tra c monitoring, healthcare imaging, remote sensing, etc. The thesis starts with a general introduction of the image defogging and image denoising problems. The motivation of the proposed work is also expressed. A brief inspection of the existing techniques related to image denoising and defogging is summed up in rst chapter. Then two di erent algorithms are presented to deal with the problem of image defogging/dehazing. Each of these algorithms uses a fractional-order anisotropic di usion model to have a re ned airlight map for restoring fog a ected degraded images. First algorithm di uses each channel of the airlight map separately and nally these channels are fused to get a re ned airlight map. In the second algorithm, a cross-channel term is added to balance the inter-channel di usion for i ii avoiding the di used/blended bands. This helps restore images having more than one channel in a better and improved way. Apart from the inter-channel regularization term, the intensity and direction of the anisotropic di usion are controlled by a factor p, which gives better results. To extend the study of the thesis to image denoising problem, two di erent algorithms are proposed for removing additive noise from the degraded images. The third algorithm makes use of fractional quaternion wavelet transform (FrQWT). For ltering the noisy components in FrQWT domain, hard and semi-soft thresholdings are used. Finally, a phase regularization step is implemented before applying the inverse FrQWT. It is worth to mention here that the proposed wavelet image denoising in the FrQWT domain gives impressive results in case of additive white Gaussian noise. The fourth algorithm uses anisotropic di usion and wavelet transformbased subspace decomposition. This method is directionally sensitive for better edge preservation. Moreover, fractional derivatives based convolution lters are implemented in di erent wavelet subbands of the noisy image which makes algorithm suitable for parallel computing. Finally, a new di usion coe cient known as `tansig' function of fractional order gradients is proposed to improve the accuracy and convergence of the earlier algorithms. This method is applicable for image defogging as well as image denoising problems. The thesis is concluded based on the work presented in the earlier chapters. Likewise, a brief description of the scope for further study is given.