3D robust anisotropic diffusion filtering algorithm for sparse view neutron computed tomography 3D image reconstruction

The most critical part of a neutron computed tomography(NCT) system is the image processing algorithm,which directly affects the quality and speed of the reconstructed images.Various types of noise in the system can degrade the quality of the reconstructed images.Therefore,to improve the quality of the reconstructed images of NCT systems,efficient image processing algorithms must be used.The anisotropic diffusion filtering(ADF) algorithm can not only effectively suppress the noise in the projection data,but also preserve the image edge structure information by reducing the diffusion at the image edges.Therefore,we propose the application of the ADF algorithm for NCT image reconstruction.To compare the performance of different algorithms in NCT systems,we reconstructed images using the ordered subset simultaneous algebraic reconstruction technique(OS-SART) algorithm with different regular terms as image processing algorithms.In the iterative reconstruction,we selected two image processing algorithms,the Total Variation and split Bregman solved total variation algorithms,for comparison with the performance of the ADF algorithm.Additionally,the filtered back-projection algorithm was used for comparison with an iterative algorithm.By reconstructing the projection data of the numerical and clock models,we compared and analyzed the effects of each algorithm applied in the NCT system.Based on the reconstruction results,OS-SART-ADF outperformed the other algorithms in terms of denoising,preserving the edge structure,and suppressing artifacts.For example,when the 3D Shepp–Logan was reconstructed at 25 views,the root mean square error of OS-SART-ADF was the smallest among the four iterative algorithms,at only 0.0292.The universal quality index,mean structural similarity,and correlation coefficient of the reconstructed image were the largest among all algorithms,with values of 0.9877,0.9878,and 0.9887,respectively.

Medical Image Fusion Based on Anisotropic Diffusion and Non-Subsampled Contourlet Transform

The synthesis of visual information from multiple medical imaging inputs to a single fused image without any loss of detail and distortion is known as multimodal medical image fusion.It improves the quality of biomedical images by preserving detailed features to advance the clinical utility of medical imaging meant for the analysis and treatment of medical disor-ders.This study develops a novel approach to fuse multimodal medical images utilizing anisotropic diffusion(AD)and non-subsampled contourlet transform(NSCT).First,the method employs anisotropic diffusion for decomposing input images to their base and detail layers to coarsely split two features of input images such as structural and textural information.The detail and base layers are further combined utilizing a sum-based fusion rule which maximizes noise filtering contrast level by effectively preserving most of the structural and textural details.NSCT is utilized to further decompose these images into their low and high-frequency coefficients.These coefficients are then combined utilizing the principal component analysis/Karhunen-Loeve(PCA/KL)based fusion rule independently by substantiating eigenfeature reinforcement in the fusion results.An NSCT-based multiresolution analysis is performed on the combined salient feature information and the contrast-enhanced fusion coefficients.Finally,an inverse NSCT is applied to each coef-ficient to produce the final fusion result.Experimental results demonstrate an advantage of the proposed technique using a publicly accessible dataset and conducted comparative studies on three pairs of medical images from different modalities and health.Our approach offers better visual and robust performance with better objective measurements for research development since it excellently preserves significant salient features and precision without producing abnormal information in the case of qualitative and quantitative analysis.

Anisotropic diffusion of volatile pollutants at air-water interface

The volatile pollutants that spill into natural waters cause water pollution. Air pollution arises from the water pollution because of volatilization. Mass exchange caused by turbulent fluctuation is stronger in the direction normal to the air-water interface than in other directions due to the large density difference between water and air. In order to explore the characteristics of anisotropic diffusion of the volatile pollutants at the air-water interface, the relationship between velocity gradient and mass transfer rate was established to calculate the turbulent mass diffusivity. A second-order accurate smooth transition differencing scheme （STDS） was proposed to guarantee the boundedness for the flow and mass transfer at the air-water interface. Simulations and experiments were performed to study the trichloroethylene （C2HC13） release. By comparing the anisotropic coupling diffusion model, isotropic coupling diffusion model, and non-coupling diffusion model, the features of the transport of volatile pollutants at the air-water interface were determined. The results show that the anisotropic coupling diffusion model is more accurate than the isotropic coupling diffusion model and non-coupling diffusion model. Mass transfer significantly increases with the increase of the air-water relative velocity at a low relative velocity. However, at a higher relative velocity, an increase in the relative velocity has no effect on mass transfer.

Solid-liquid transition induced by the anisotropic diffusion of colloidal particles

We numerically study the phase behaviors of colloids with anisotropic diffusion in two dimensions. It is found that the diffusion anisotropy of colloidal particles plays an important role in the phase transitions. A strong diffusion anisotropy induces the large vibration of particles, subsequently, the system goes into a disordered state. In the presence of the strong-coupling, particles with weak diffusion anisotropy can freeze into hexagonal crystals. Thus, there exists a solid-liquid transition. With the degree of diffusion anisotropy increasing, the transition points are shifted to the strongercoupled region. A competition between the degree of diffusion anisotropy and coupling strength widens the transition region where the heterogeneous structures coexist, which results in a broad-peak probability distribution curve for the local order parameter. Our study may be helpful for the experiments related to the phase behavior in statistical physics, materials science and biophysical systems.

Discrete Maximum Principle and a Delaunay-Type Mesh Condition for Linear Finite Element Approximations of Two-Dimensional Anisotropic Diffusion Problems

A Delaunay-type mesh condition is developed for a linear finite element approximation of two-dimensional anisotropic diffusion problems to satisfy a discrete maximum principle.The condition is weaker than the existing anisotropic non-obtuse angle condition and reduces to the well known Delaunay condition for the special case with the identity diffusion matrix.Numerical results are presented to verify the theoretical findings.

Anisotropic diffusion filtering for ultrasound speckle reduction

Speckle noise has long been known as a limiting factor for the quality of an ultrasound B-mode image.In this study,anisotropic diffusion filtering is proposed as an effective method for ultrasound speckle reduction.This article provides a brief description of anisotropic diffusion filtering proposed by Perona and Malik,and compares its speckle filtering effects with other filtering methods including median,moving average,and frequency domain Gaussian low-pass.In this study,multiple filters are implemented in Matlab.For each filter,three different types of noisy images with speckle noise are tested.The results show that anisotropic filter can reduce the noise more effectively and meanwhile preserve the boundaries of the objects.In addition,this filter has more controllable filtering parameters and is independent on the information of the noise.

3D Anisotropic Diffusion on GPUs by Closed-Form Local Tensor Computations

We present an efficient implementation of volumetric anisotropic image diffusion filters on modern programmable graphics processing units(GPUs),where the mathematics behind volumetric diffusion is effectively reduced to the diffusion in 2D images.We hereby avoid the computational bottleneck of a time consuming eigenvalue decomposition in R3.Instead,we use a projection of the Hessian matrix along the surface normal onto the tangent plane of the local isodensity surface and solve for the remaining two tangent space eigenvectors.We derive closed formulas to achieve this and prevent the GPU code from branching.We show that our most complex volumetric anisotropic diffusion filters gain a speed up of more than 600 compared to a CPU solution.

Fractional-order difference curvature-driven fractional anisotropic diffusion equation for image super-resolution

Image super-resolution methods-based existing edge indicating operators—namely Gauss curvature,mean curvature and gradient-cannot effectively identify the edges,ramps and flat regions and suffer from the loss of fine textures.To address these issues,this paper presents a fractional anisotropic diffusion equation based on a new edge indicator,named fractional-order difference curvature,which can characterize the intensity variations in images.We introduce the frequency-domain definition for fractional-order derivative by the Fourier transform,which is easy to implement numerically.The new edge indicator is better than the existing edge indicating operators in distinguishing between ramps and edges and can better handle the fine textures.Comparative results for natural images validate that the proposed method can yield a visually pleasing result and better values of MSSIM and PSNR.

Discrete Maximum Principle for the Weak Galerkin Method for Anisotropic Diffusion Problems

A weak Galerkin discretization of the boundary value problem of a general anisotropic diffusion problem is studied for preservation of the maximum principle.It is shown that the direct application of the M-matrix theory to the stiffness matrix of the weak Galerkin discretization leads to a strong mesh condition requiring all of the mesh dihedral angles to be strictly acute(a constant-order away from 90 degrees).To avoid this difficulty,a reduced system is considered and shown to satisfy the discrete maximum principle under weaker mesh conditions.The discrete maximum principle is then established for the full weak Galerkin approximation using the relations between the degrees of freedom located on elements and edges.Sufficient mesh conditions for both piecewise constant and general anisotropic diffusion matrices are obtained.These conditions provide a guideline for practical mesh generation for preservation of the maximum principle.Numerical examples are presented.

DiscreteMaximumPrinciple Based on Repair Technique for Finite Element Scheme of Anisotropic Diffusion Problems

In this paper,we construct a global repair technique for the finite element scheme of anisotropic diffusion equations to enforce the repaired solutions satisfying the discrete maximum principle.It is an extension of the existing local repair technique.Both of the repair techniques preserve the total energy and are easy to be implemented.The numerical experiments show that these repair techniques do not destroy the accuracy of the finite element scheme,and the computational cost of the global repair technique is cheaper than the local repair technique when the diffusion tensors are highly anisotropic.

A Nominally Second-Order Cell-Centered Finite Volume Scheme for Simulating Three-Dimensional Anisotropic Diffusion Equations on Unstructured Grids

We present a finite volume based cell-centered method for solving diffusion equations on three-dimensional unstructured grids with general tensor conduction.Our main motivation concerns the numerical simulation of the coupling between fluid flows and heat transfers.The corresponding numerical scheme is characterized by cell-centered unknowns and a local stencil.Namely,the scheme results in a global sparse diffusion matrix,which couples only the cell-centered unknowns.The space discretization relies on the partition of polyhedral cells into sub-cells and on the partition of cell faces into sub-faces.It is characterized by the introduction of sub-face normal fluxes and sub-face temperatures,which are auxiliary unknowns.A sub-cellbased variational formulation of the constitutive Fourier law allows to construct an explicit approximation of the sub-face normal heat fluxes in terms of the cell-centered temperature and the adjacent sub-face temperatures.The elimination of the sub-face temperatures with respect to the cell-centered temperatures is achieved locally at each node by solving a small and sparse linear system.This system is obtained by enforcing the continuity condition of the normal heat flux across each sub-cell interface impinging at the node under consideration.The parallel implementation of the numerical algorithm and its efficiency are described and analyzed.The accuracy and the robustness of the proposed finite volume method are assessed by means of various numerical test cases.

A Nonlinear Finite Volume Element Method Satisfying Maximum Principle for Anisotropic Diffusion Problems on Arbitrary Triangular Meshes

A nonlinear finite volume element scheme for anisotropic diffusion problems on general triangular meshes is proposed.Starting with a standard linear conforming finite volume element approximation,a corrective term with respect to the flux jumps across element boundaries is added to make the scheme satisfy the discrete maximum principle.The new scheme is free of the anisotropic non-obtuse angle condition which is a severe restriction on the grids for problems with anisotropic diffusion.Moreover,this manipulation can nearly keep the same accuracy as the original scheme.We prove the existence of the numerical solution for this nonlinear scheme theoretically.Numerical results and a grid convergence study are presented for both continuous and discontinuous anisotropic diffusion problems.

Image restoration using total variation and anisotropic diffusion equation

This paper proposes a new model for the image restoration which combines the total variation minimization with the“pure”anisotropic diffusion equation of Alvarez and Morel.According to the introduction of new diffusion term,this model can not only remove noise but also enhance edges and keep their locality.And it can also keep textures and large-scale fine features that are not characterized by edges.Due to these favorable characteristics,the processed images turn much clearer and smoother,meanwhile,their significant details are kept,which results in appealing vision.

Anisotropic fourth-order diffusion regularization for multiframe super-resolution reconstruction

A novel rcgularization-based approach is presented for super-resolution reconstruction in order to achieve good tradeoff between noise removal and edge preservation. The method is developed by using L1 norm as data fidelity term and anisotropic fourth-order diffusion model as a regularization item to constrain the smoothness of the reconstructed images. To evaluate and prove the performance of the proposed method, series of experiments and comparisons with some existing methods including bi-cubic interpolation method and bilateral total variation method are carried out. Numerical results on synthetic data show that the PSNR improvement of the proposed method is approximately 1.0906 dB on average compared to bilateral total variation method, and the results on real videos indicate that the proposed algorithm is also effective in terms of removing visual artifacts and preserving edges in restored images.

A diffusion method based on polar coordinate for ultrasound images denoising

The paper presents a novel anisotropic diffusion approach to the problem of ultrasound images denoising based on the polar-coordinate representation.Local gradients based on the polar coordinate are introduced and they are more suitable for ultrasound images than horizontal gradients and vertical gradients commonly used in anisotropic diffusion methods.Moreover,an adaptive adjustment scheme for the threshold parameter in conduction functions is presented according to the incident angle of the ultrasonic beam with respect to the organ surface.Furthermore,based on the structure matrix,an edge-adaptive diffusion model is introduced,which can selectively preserve the edge from the blurring or smooth noise.Experimental results of real ultrasound images show the validity of the presented approach,which takes the physical imaging mechanism of ultrasonic devices into account.

Stirring by anisotropic squirming

We consider a fluid stirred by the locomotions of squirmers through it and generalize the stochastic hydrodynamic model proposed by Thiffeault and Childress,Phys.Lett.A(2010)and Lin et al.,J.Fluid Mech.(2011)to the case in which the swimmers move in anisotropically random directions.A non-diagonal effective diffusivity tensor is derived with which the diffusive preference of a passive particle along any given direction can be computed to provide more details of the phenomena beyond scalar statistics.We further identify a fraction from the orthogonal decomposition of the drift-induced particle displacement to distinguish the underlying nonlinear mixing mechanism for different types of swimmers.Numerical simulations verify the analytical results with explicit examples of prescribed,anisotropic stirring motions.We also connect our formulation to several measures used in clinical medical research such as diffusion tensor imaging where anisotropic diffusion has a significant consequence.

An Ophthalmic Evaluation of Central Serous Chorioretinopathy

Nowadays in the medicalfield,imaging techniques such as Optical Coherence Tomography(OCT)are mainly used to identify retinal diseases.In this paper,the Central Serous Chorio Retinopathy(CSCR)image is analyzed for various stages and then compares the difference between CSCR before as well as after treatment using different application methods.Thefirst approach,which was focused on image quality,improves medical image accuracy.An enhancement algorithm was implemented to improve the OCT image contrast and denoise purpose called Boosted Anisotropic Diffusion with an Unsharp Masking Filter(BADWUMF).The classifier used here is tofigure out whether the OCT image is a CSCR case or not.150 images are checked for this research work(75 abnormal from Optical Coherence Tomography Image Retinal Database,in-house clinical database,and 75 normal images).This article explicitly decides that the approaches suggested aid the ophthalmologist with the precise retinal analysis and hence the risk factors to be minimized.The total precision is 90 percent obtained from the Two Class Support Vector Machine(TCSVM)classifier and 93.3 percent is obtained from Shallow Neural Network with the Powell-Beale(SNNWPB)classifier using the MATLAB 2019a program.

A Thermal Analogue of the Zel’Dovich Effect

We analyze in this work anisotropic heat conduction induced by a harmonically oscillating laser source incident on rotating conductors, exploiting an analogy with an effect discovered long ago, called the Zel’dovich effect. We re-covered the main results of a recently published paper that predicts the translational Doppler frequency shift of a thermal wave induced on a sample moving with uniform rectilinear motion. We extend then this framework to take into account the frequency shift of a thermal field propagating on a rotating platform. We show that it coincides with the rotational frequency shift which has been recently observed on surface acoustic waves and hydrodynamic surface waves, called rotational superradiance. Finally, we use an analogy with the Tolman effect to deduce a simple estimate of the average temperature gradient induced by rotation, showing the existence of a new cooling effect associated with heat torque transfer.

AN IMAGE MAGNIFICATION ALGORITHM USING THE GVF CONSTRAINT MODEL

An image magnification method with a Gradient Vector Flow(GVF)constraint-basedanisotropic diffusion model is proposed in this letter.A Low-Resolution(LR)image is first magnifiedusing bilinear interpolation,and then an iterative image restoration method,with the use of an ani-sotropic diffusion model and a Gaussian moving-average constraint,is applied to the magnified image.The estimated GVF of a High-Resolution(HR)image can be used to remove the jagged effect and topreserve the textural structure in the image.Meanwhile,the use of the Gaussian moving-average LRmodel can provide a data fidelity constraint,which renders a magnified image closer to the ideal HRversion.Experimental results show that the proposed method can improve the quality of magnifiedimages in terms of both objective and subjective criteria.

AN APPROACH TO SUPPRESS SPECKLE NOISE AND ENHANCE EDGE

Anisotropic diffusion has good effect on reducing noise and preserving edge, but it may lose some details due to the blocky effect and can not suppress speckle effectively. The Laplacian factor is used to process the observed image which is considered as a piecewise planar image, so the Fourth Order Anisotropic Diffusion （FOAD） can avoid the blocky effect. The edge is preserved and enhanced by the Line Edge Detector （LED） based on stick technique and hypothesis test optimizing method. An approach called the Fourth Order Anisotropic Diffusion and Edge Enhancing （FOADEE）, where the LED is combined with the FOAD, is presented. For quantitative evaluation and comparison with the LED, the FOAD and the FOADEE, two parameters as measure of the noise suppression and edge preservation are introduced. It is proved that the novel method can not only suppress speckle prominently but also preserve even enhance edge and useful details effectively by applying it to the phantoms and tissue images.