An adaptive noise removal approach for restoration of digital images corrupted by multimodal noise

Data smoothing algorithms are commonly applied to reduce the level of noise and eliminate the weak textures contained in digital images. Anisotropic diffusion algorithms form a distinct category of noise removal approaches that implement the smoothing process locally in agreement with image features such as edges that are typically determined by applying diverse partial differential equation (PDE) models. While this approach is opportune since it allows the implementation of feature-preserving data smoothing strategies, the inclusion of the PDE models in the formulation of the data smoothing process compromises the performance of the anisotropic diffusion schemes when applied to data corrupted by non-Gaussian and multimodal image noise. In this paper we first evaluate the positive aspects related to the inclusion of a multi-scale edge detector based on the generalisation of the Di Zenzo operator into the formulation of the anisotropic diffusion process. Then, we introduce a new approach that embeds the vector median filtering into the discrete implementation of the anisotropic diffusion in order to improve the performance of the noise removal algorithm when applied to multimodal noise suppression. To evaluate the performance of the proposed data smoothing strategy, a large number of experiments on various types of digital images corrupted by multimodal noise were conducted.Keywords — Anisotropic diffusion, vector median filtering, feature preservation, multimodal noise, noise removal

A fourth-order PDE denoising model with an adaptive relaxation method

In this paper, an adaptive relaxation method and a discontinuity treatment of edges are proposed to improve the digital image denoising process by using the fourth-order partial differential equation (known as the YK model) first proposed by You and Kaveh. Since the YK model would generate some speckles into the denoised image, a relaxation method is incorporated into the model to reduce the formation of isolated speckles. An additional improvement is employed to handle the discontinuity on the edges of the image. In order to stop the iteration automatically, a control of the iteration is integrated into the denoising process. Numerical results demonstrate that such modifications not only make the denoised image look more natural, but also achieve a higher value of PSNR

A Total Fractional-Order Variation Model for Image Restoration with Non-homogeneous Boundary Conditions and its Numerical Solution

To overcome the weakness of a total variation based model for image restoration, various high order (typically second order) regularization models have been proposed and studied recently. In this paper we analyze and test a fractional-order derivative based total $\alpha$-order variation model, which can outperform the currently popular high order regularization models. There exist several previous works using total $\alpha$-order variations for image restoration; however first no analysis is done yet and second all tested formulations, differing from each other, utilize the zero Dirichlet boundary conditions which are not realistic (while non-zero boundary conditions violate definitions of fractional-order derivatives). This paper first reviews some results of fractional-order derivatives and then analyzes the theoretical properties of the proposed total $\alpha$-order variational model rigorously. It then develops four algorithms for solving the variational problem, one based on the variational Split-Bregman idea and three based on direct solution of the discretise-optimization problem. Numerical experiments show that, in terms of restoration quality and solution efficiency, the proposed model can produce highly competitive results, for smooth images, to two established high order models: the mean curvature and the total generalized variation.Comment: 26 page

Restoration and enhancement of astronomical images using hybrid adaptive nonlinear complex diffusion-based filter

In this paper, a hybrid and adaptive nonlinear complex diffusion based technique is proposed for restoration and enhancement of astronomical images corrupted with additive noise due to diffractions limit, aberrations in telescope camera lens, atmospheric irregularities which are modelled by Gaussian functions. In addition to additive noise removal, the proposed filter is also capable of removing noisy stars and spike noises due to other numerous stars that may have surrounded an object in the astronomical image such as in nebula images. The proposed scheme is completely adaptive in nature in the sense that it estimates all the required filtering parameters from the observed image itself. The performance of the proposed hybrid scheme is compared with other image restoration techniques such as averaging filter, Gaussian filter, median filter, anisotropic diffusion based filter, local variance based adaptive anisotropic diffusion filter and also the adaptive and hybrid version of anisotropic diffusion filter similar to the proposed one in terms of average SNR and BSNR. The results obtained show the efficacy of the proposed scheme.Defence Science Journal, 2012, 62(6), pp.437-442, DOI:http://dx.doi.org/10.14429/dsj.62.129