Application of upscaling methods for fluid flow and mass transport in multi-scale heterogeneous media: A critical review

https://research.edgehill.ac.uk/files/46422294/1_s2.0_S1566253521001792_main.pdf

Real-world single image super-resolution: A brief review

Real-World Single Image Super-Resolution: A Brief Review

To avoid the irregularities during the level set evolution, a fractional distance regularized variational model is proposed for image segmentation. We first define a fractional distance regularization term which punishes the deviation of the level set function (LSF) and the signed distance function. Since the fractional derivative of the constant value function outside the starting point is nonzero, the fractional gradient modular of the LSF does not approach infinity where the integer order gradient modular is close to 0. This prevents the sharp reverse diffusion of LSF in flat areas and ensures the smooth evolution of LSF. Then, we use the Grunwald-Letnikov (G-L) fractional derivative to derive the discrete forms of the conjugate of fractional derivatives and fractional divergence. To facilitate the calculation of fractional derivatives and their conjugates, we designed their covering templates. Finally, a numerical solution to the minimization of the energy functional is obtained from these discrete forms and covering templates. Numerical experiments of medical images with different modalities show that the model in this paper can well segment weak images and intensity inhomogeneity images.

/pdf/fractional-distance-regularized-level-set-evolution-with-its-4g215h2jla.pdf

Fractional Distance Regularized Level Set Evolution With Its Application to Image Segmentation

In the present work, we investigate the inverse problem of identifying simultaneously the denoised image and the weighting parameter that controls the balance between two diffusion operators for an...

A high order PDE-constrained optimization for the image denoising problem

The multi-frame super-resolution(SR) aims to recover a high-resolution (HR) image from a degraded low-resolution (LR) sequence. Since the SR problem is considered as an ill-posed one, the regularization techniques are then inevitable. However, the choice of the fidelity and regularization terms is not easy and plays a major role in the quality of the desired HR image. In this paper, we propose a new nonconvex data fitting term and a fractional total variation regularization term for image super-resolution. The proposed model differs from existing image variational SR models where the fidelity term is always derived from the L 1 or L 2 - norm, and the regularization term is based on a widely choice of convex and nonconvex functions. The use of the nonconvex data fitting term can efficiently reduce complex noises such as impulse noise while the fractional order regularization term preserves image features like edges and texture much better. Numerical experiments show that the proposed model can produce competitive results, visually and quantitatively, compared to some available variational SR models.

A nonconvex fractional order variational model for multi-frame image super-resolution

The multiframe image super-resolution (SR) has appeal great care due to its relevant practical applications. Since the SR methods are always considered as ill-posed problems, great interest is therefore investigated to reconstruct an image with less artefacts. In this paper, we propose a high-order partial differential equation (PDE) that preserve singularities and edge continuities while smoothing. This PDE is based on anisotropic diffusion behavior by adding some constraints to the Weickert coherence enhancing diffusion tensor in order to control the diffusion process near edges and avoids tiny corners destruction. In fact, this PDE combine between the diffusion process of Perona–Malik in the flat regions and the anisotropic diffusion of the Weickert model near strong edges. Moreover, the introduction of the high-order derivatives reduces unwanted artifacts such as staircasing. The given experimental results show the effectiveness of the proposed PDE compared to some competitive methods in both visually and quantitatively.

An edge preserving high-order PDE for multiframe image super-resolution

A new multiframe super-resolution based on nonlinear registration and a spatially weighted regularization

In denoising problems, it is always hard to deal with a mixture of two noise densities. In this paper, we introduce a nonlinear constrained-PDE based on the fractional order tensor diffusion to approximate the clean image and also the impulse component in a mixture of Gaussian and impulse noise. Our model offers an ideal compromise between the edge preservation, staircasing creation and the loss of image contrasts. The proposed constrained-PDE is formulated using a variational model that features a L1 data discrepancy encoding the impulse noise and an L2 term of the clean image which is a solution of a high-order PDE. Then, a rigorous analysis of the existence of the solution to the proposed model is checked in a suitable functional framework. In addition, to solve the constrained-PDE, we consider an extension of the Primal-Dual algorithm to nonlinear operators with an accelerate Bregman iteration. Numerical experiments show that the proposed model produces pleasant results in terms of restoration quality and solution efficiency compared to some competitive regularizations.

Aissam Hadri

Papers

A nonconvex fractional order variational model for multi-frame image super-resolution

An edge preserving high-order PDE for multiframe image super-resolution

A new multiframe super-resolution based on nonlinear registration and a spatially weighted regularization

A denoising model adapted for impulse and Gaussian noises using a constrained-PDE

A high order PDE-constrained optimization for the image denoising problem