Turing-Hopf bifurcation of reaction-diffusion neural networks with leakage delay

Image de-noising and enhancement are becoming increasingly widespread. Anisotropic diffusion is one of the greatest techniques that are used to remove noise of the image, while keeping the important information unvaried. Nevertheless, it suffers from many drawbacks such as the image blurring. This work is concerned with a new anisotropic diffusion approach founded on an innovative mathematical function for noise reducing and edge preserving. The entire contribution can be observed from the experimental results which have shown that the new proposed anisotropic scheme is not only able to remove the noise efficiently but also to preserve the content in the denoised image.

An advanced and adaptive mathematical function for an efficient anisotropic image filtering

We propose an ultrasound speckle filtering method for not only preserving various edge features but also filtering tissue-dependent complex speckle noises in ultrasound images. The key idea is to detect these various edges using a phase congruence-based edge significance measure called phase asymmetry (PAS), which is invariant to the intensity amplitude of edges and takes 0 in non-edge smooth regions and 1 at the idea step edge, while also taking intermediate values at slowly varying ramp edges. By leveraging the PAS metric in designing weighting coefficients to maintain a balance between fractional-order anisotropic diffusion and total variation (TV) filters in TV cost function, we propose a new fractional TV framework to not only achieve the best despeckling performance with ramp edge preservation but also reduce the staircase effect produced by integral-order filters. Then, we exploit the PAS metric in designing a new fractional-order diffusion coefficient to properly preserve low-contrast edges in diffusion filtering. Finally, different from fixed fractional-order diffusion filters, an adaptive fractional order is introduced based on the PAS metric to enhance various weak edges in the spatially transitional areas between objects. The proposed fractional TV model is minimized using the gradient descent method to obtain the final denoised image. The experimental results and real application of ultrasound breast image segmentation show that the proposed method outperforms other state-of-the-art ultrasound despeckling filters for both speckle reduction and feature preservation in terms of visual evaluation and quantitative indices. The best scores on feature similarity indices have achieved 0.867, 0.844 and 0.834 under three different levels of noise, while the best breast ultrasound segmentation accuracy in terms of the mean and median dice similarity coefficient are 96.25% and 96.15%, respectively.

Phase Asymmetry Ultrasound Despeckling With Fractional Anisotropic Diffusion and Total Variation

A systematic review on recent developments in nonlocal and variational methods for SAR image despeckling

Despite extensive availability of filters for denoising, speckle noise suppression remains a challenging task. Speckle noise also hinders tasks such as efficient extraction of features, recognition, analysis, detection of edges, etc. Therefore, in this paper, motivated by the impressive performance of time delay regularization in additive noise removal, we develop a class of nonlinear diffusion-based coupled partial differential equation models for multiplicative noise removal. This denoising framework considers separate partial differential equations to handle diffusion function as well as fidelity term. By using a maximum a posteriori regularization approach, we can derive an energy functional and study the associated evolution problem which corresponds to the denoised image we want to recover. We then evaluate the effectiveness of our model with several standard test images and real ultrasound images. Qualitative and quantitative studies confirm that the proposed model is robust in comparison with state-of-the-art approaches. The denoised images have appealing visual characteristics with different levels of noise and textures while preserving the important details of the original image.

A Nonlinear Coupled Diffusion System for Image Despeckling and Application to Ultrasound Images

Speckle noise is a principal and unavoidable source of visual degradation in several real world images obtained from coherent imaging systems such as ultrasound, SAR, and laser. Over the la...

Non-linear Diffusion Models for Despeckling of Images: Achievements and Future Challenges

In this paper we propose and compare the use of two iterative solvers using the Crank–Nicolson finite difference method, to address the task of image denoising via partial differential equations (PDEs) models such as Regularized Perona–Malik equation or C -model and Bazan model (Bilateral-filter-based model). The solvers which are considered in this paper are the Successive-over-Relaxation (SOR) and an advanced solver known as Hybrid Bi-Conjugate Gradient Stabilized (Hybrid BiCGStab) method. From numerical experiments, it is found that the Crank–Nicolson method with hybrid BiCGStab iterative solver produces better results and is more efficient than SOR and already existing, in terms of MSSIM and PSNR.

Iterative solvers for image denoising with diffusion models: A comparative study

For the existing issues of edge blur and uncertainty of parameter selection during image filtering, a novel telegraph total variational PDE model based on edge detector is proposed. We propose image structure tensor as an edge detector to control smoothing process and keep more detail features. The proposed model takes advantages of both telegraph and total variational model, which is edge preserving and robust to noise. Experimental results illustrate the effectiveness of the proposed model and demonstrate that our algorithm competes favorably with state of the-art approaches in terms of producing better denoising results.

Subit K. Jain

Papers

Non-linear Diffusion Models for Despeckling of Images: Achievements and Future Challenges

Iterative solvers for image denoising with diffusion models: A comparative study

A Nonlinear Coupled Diffusion System for Image Despeckling and Application to Ultrasound Images

Edge Detectors Based Telegraph Total Variational Model for Image Filtering

Time-delay-induced instabilities and Hopf bifurcation analysis in 2-neuron network model with reaction–diffusion term