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.

Alleviating the anisotropic microstructural change and boosting the lithium ions diffusion by grain orientation regulation for Ni-rich cathode materials

Generally,layered Ni-rich cathode materials exhibit the morphology of polycrystalline secondary sphere composed of numerous primary particles.While the arrangement of primary particles plays a very important role in the properties of Ni-rich cathodes.The disordered particle arrangement is harmful to the cyclic performance and structural stability,yet the fundamental understanding of disordered structure on the structural degradation behavior is unclarified.Herein,we have designed three kinds of LiNi_(0.83)Co_(0.06)Mn_(0.11)O_(2) cathode materials with different primary particle orientations by regulating the precursor coprecipitation process.Combining finite element simulation and in-situ characterization,the Li^(+)transport and structure evolution behaviors of different materials are unraveled.Specifically,the smooth Li^(+)diffusion minimizes the reaction heterogeneity,homogenizes the phase transition within grains,and mitigates the anisotropic microstructural change,thereby modulating the crack evolution behavior.Meanwhile,the optimized structure evolution ensures radial tight junctions of the primary particles,enabling enhanced Li^(+)diffusion during dynamic processes.Closed-loop bidirectional enhancement mechanism becomes critical for grain orientation regulation to stabilize the cyclic performance.This precursor engineering with particle orientation regulation provides the useful guidance for the structural design and feature enhancement of Ni-rich layered cathodes.

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.

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.

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.

Anisotropic WM conductivity reconstruction based on diffusion tensor magnetic resonance imaging: a simulation study

The present study aims to estimate the in vivo anisotropic conductivities of the White Matter (WM) tissues by means of Magnetic Resonance Electrical Impedance Tomography (MREIT) technique. The realistic anisotropic volume conductor model with different conductivity properties (scalp, skull, CSF, gray matter and WM) is constructed based on the Diffusion Tensor Magnetic Resonance Imaging (DT- MRI) from a healthy human subject. The Radius Basic Function (RBF)-MREIT algorithm of using only one magnetic flux density component was applied to evaluate the eigenvalues of the anisotropic WM with target values set according to the DT-MRI data based on the Wolter’s model, which is more physiologically reliable. The numerical simulations study performed on the five-layer realistic human head model showed that the conductivity reconstruction method had higher accuracy and better robustness against noise. The pilot research was used to judge the feasibility, meaningfulness and reliability of the MREIT applied on the electrical impedance tomography of the complicated human head tissues including anisotropic characteristics.

Usefulness of an Anisotropic Diffusion Method in Cerebral CT Perfusion Study Using Multi-Detector Row CT

Purpose: To present an application of the anisotropic diffusion (AD) method to improve the accuracy of the functional images of perfusion parameters such as cerebral blood flow (CBF), cerebral blood volume (CBV) and mean transit time (MTT) generated from cerebral CT perfusion studies using multi-detector row CT (MDCT). Materials and Methods: Continuous scans (1 sec/rotation ×60 sec) consisting of four 5-mm-thick contiguous slices were acquired after an intravenous injection of iodinated contrast material in 6 patients with cerebrovascular disease using an MDCT scanner with a tube voltage of 80 kVp and a tube current of 200 mA. New image data were generated by thinning out the above original images at an interval of 2 sec or 3 sec. The thinned-out images were then interpolated by linear interpolation to generate the same number of images as originally acquired. The CBF, CBV and MTT images were generated using deconvolution analysis based on singular value decomposition. Results: When using the AD method, the correlation coefficient between the MTT values obtained from the original and thinned-out images was significantly improved. Furthermore, the coefficients of variation of the CBF, CBV and MTT values in the white matter significantly decreased as compared to not using the AD method. Conclusion: Our results suggest that the AD method is useful for improving the accuracy of the functional images of perfusion parameters and for reducing radiation exposure in cerebral CT perfusion studies using MDCT.

Diffusion tensor imaging reveals brain structure changes in dogs after spinal cord injury

Based on the Wallerian degeneration in the spinal cord pathways,the changes in synaptic connections,and the spinal cord-related cellular responses that alter the cellular structure of the brain,we presumed that brain diffusion tensor imaging(DTI)parameters may change after spinal cord injury.However,the dynamic changes in DTI parameters remain unclear.We established a Beagle dog model of T10 spinal cord contusion and performed DTI of the injured spinal cord.We found dynamic changes in DTI parameters in the cerebral peduncle,posterior limb of the internal capsule,pre-and postcentral gyri of the brain within 12 weeks after spinal cord injury.We then performed immunohistochemistry to detect the expression of neurofilament heavy polypeptide(axonal marker),glial fibrillary acidic protein(glial cell marker),and NeuN(neuronal marker).We found that these pathological changes were consistent with DTI parameter changes.These findings suggest that DTI can display brain structure changes after spinal cord injury.

On the Well-Posedness Problem of the Anisotropic Porous Medium Equation with a Variable Diffusion Coefficient

The initial-boundary value problem of an anisotropic porous medium equation■is studied.Compared with the usual porous medium equation,there are two different characteristics in this equation.One lies in its anisotropic property,another one is that there is a nonnegative variable diffusion coefficient a(x,t)additionally.Since a(x,t)may be degenerate on the parabolic boundary∂Ω×(0,T),instead of the boundedness of the gradient|∇u|for the usual porous medium,we can only show that∇u∈L^(∞)(0,T;L^(2)_(loc)(Ω)).Based on this property,the partial boundary value conditions matching up with the anisotropic porous medium equation are discovered and two stability theorems of weak solutions can be proved naturally.

MRS and diffusion tensor image in mild traumatic brain injuries

Objective:To analyze characters of magnetic resonance spectroscopy(MRS) and diffusion tensor imaging(DTI) in the diagnosis of mild trauma brain injuries(MTBI) in frontal lobe and to compare with conventional magnetic resonance imaging(MRI).Methods:A total of 21 patients were selected,who all aged 12-51 years old and had injury within 24 hours.Computer tomography (CT) and the Glasgow Coma Scale were used to evaluate the degree of injury.All patients were diagnosed as MTBI,and 19 had conventional MRI,MRS and DTI.The major parameters of MRS were Probe-P sequence,TE= 144 or 35 ms,and both single voxel spectrum and chemical shift imging were included.The major parameters of DTI were diffusion directions =15,b value = 1000 s/mm^2. Frational anisotropic(FA) map and average ADC map were obtained to evaluate DTI result. Positive deletion ratio was observed and the imaging changes were compared between injured side and normal side.Results:All 21 patients had CT scan and Glasgow scale.A total of 19 patients had conventional MRI.DTI and MRS.Results of CT and conventional MRI showed no significant abnormality in lobe,and Glasgow scale showed mild type.MRS result showed significant decrease in N-acetyl aspartate(NAA) and NAA/creatine(Cr) in 13 cases(68.4%) (P【0.001),and increase in lactic acid(Lac) in 7 cases(36.8%).FA mapping of the frontal lobe displayed significant changes in 7 cases(36.8%),with 5 out of the 7 cases having increase in FA value.And there was no significant difference in average ADC.Conclusions:MRS and DTI might be more sensible than other methods,such as CT and conventional MRI in diagnosis of MTBI.The particular changes were reduced NAA and increased Lac for MRS.and increased FA values for DTI.

Diffusion tensor imaging of the brain in patients with Alzheimer's disease and cerebrovascular lesions

Background:Recent autopsy study showed a high incidence of cerebrovascular lesions in Alzheimer's disease(AD).To assess the impact of cerebrovascular pathology in AD,we used diffusion tensor imaging(DTI) to study AD patients with and without cerebrovascular lesions.Materials and Methods:Conventional and DTI scans were obtained from 10 patients with probable AD,10 AD/V patients(probable AD with cerebrovascular lesions) and ten normal controls.Mean diffusivity(D) and fractional anisotropy(FA) values of some structures involved with AD pathology were measured.Results:D value was higher in AD patients than in controls in hippocampus and the cingulate gyrus.In AD/V patients,increased D value was found in the same structures and also in the thalamus and basal ganglia compared to controls.There was a significant difference of D value between AD and AD/V patients.FA value reduced in the white matter of left inferior temporal gyrus and in the bilateral middle cingulate gyrus in patients with AD/V compared with controls.The MMSE(mini-mental state examination) score significantly correlated with FA value in the right hippocampus(r=0.639,P<0.019),in the right anterior cingulate gyrus(r=0.587,P<0.035) and in left parahippocampal gyrus(r=0.559,P<0.047).Conclusion:Cerebrovascular pathology had stronger impact on the D value than the AD pathology alone did.Elevated D value in thalamic and basal ganglia may contribute to cognitive decline in AD/V patients.Reduced FA values in AD/V patients may indicate that cerebrovascular pathology induced more severe white matter damage than the AD pathology alone did.

Simulation of Nucleation of Anisotropic Si Islands on Reconstructed Si(100)(2x1)Surface

The nucleation of anisotropic Si islands on reconstructed Si(100)(2x1)surface has been studied by computer simulation,in which the anisotropic diffusion rate along different direction of the substrate is included.Some results such as anisotropic islands formed at various substrate temperatures,the number of islands(including single Si dimers)with different anisotropic diffusion are obtained.It is shown that the shape and number of anisotropic Si islands are dependent obviously on the substrate temperature and the anisotropic diffusion.The simulation results are consistent with the experimental observations.

Macroscopic anisotropic Brownian motion is related to the directional movement of a “Universe field”

Brownian motion was discovered by the botanist Robert Brown in 1827, and the theoretical model of Brownian motion has real-world applications in fields such as mathematics, economics, physics and biology. It is the presumably random motion of particles suspended in a liquid or a gas that results from their bombardment by fast-moving atoms or molecules, but the exact mechanism of Brownian motion still remains one of the unresolved mysteries in physics. Here circadian and seasonal changes in long-term macroscopic anisotropic (asymmetric) Brownian motion of a toluidine blue colloid solution in water in two dimensions were identified, suggesting that such an anisotropic Brownian motion may be related to an effect of the directional movement of “Universe field”, and thereby providing new interpretations and potential applications of Brownian motion.

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.

A Novel Method for Solving Time-Dependent 2D Advection-Diffusion-Reaction Equations to Model Transfer in Nonlinear Anisotropic Media

This paper presents a new numerical technique for solving initial and bound-ary value problems with unsteady strongly nonlinear advection diffusion reaction(ADR)equations.The method is based on the use of the radial basis functions(RBF)for the approximation space of the solution.The Crank-Nicolson scheme is used for approximation in time.This results in a sequence of stationary nonlinear ADR equations.The equations are solved sequentially at each time step using the proposed semi-analytical technique based on the RBFs.The approximate solution is sought in the form of the analytical expansion over basis functions and contains free parameters.The basis functions are constructed in such a way that the expansion satisfies the boundary conditions of the problem for any choice of the free parameters.The free parameters are determined by substitution of the expansion in the equation and collocation in the solution domain.In the case of a nonlinear equation,we use the well-known procedure of quasilinearization.This transforms the original equation into a sequence of the linear ones on each time layer.The numerical examples confirm the high accuracy and robustness of the proposed numerical scheme.

Extrapolation Cascadic Multigrid Method for Cell-Centered FV Discretization of Diffusion Equations with Strongly Discontinuous and Anisotropic Coefficients

Extrapolation cascadic multigrid(EXCMG)method with conjugate gradient smoother is very efficient for solving the elliptic boundary value problems with linearfinite element discretization.However,it is not trivial to generalize the vertex-centred EXCMG method to cell-centeredfinite volume(FV)methods for diffusion equations with strongly discontinuous and anisotropic coefficients,since a non-nested hierarchy of grid nodes are used in the cell-centered discretization.For cell-centered FV schemes,the vertex values(auxiliary unknowns)need to be approximated by cell-centered ones(primary unknowns).One of the novelties is to propose a new gradient transfer(GT)method of interpolating vertex unknowns with cell-centered ones,which is easy to implement and applicable to general diffusion tensors.The main novelty of this paper is to design a multigrid prolongation operator based on the GT method and splitting extrapolation method,and then propose a cell-centered EXCMG method with BiCGStab smoother for solving the large linear system resulting from linear FV discretization of diffusion equations with strongly discontinuous and anisotropic coefficients.Numerical experiments are presented to demonstrate the high efficiency of the proposed method.

基于ROAD和小波收缩的MLEM低剂量CT重建算法

针对低剂量CT(Computed Tomography)重建图像质量退化的问题,提出一种基于小波收缩和绝对差值排序各项异性扩散的MLEM(Maximum Likelihood Expectation Maximization)低剂量CT重建算法。算法在每次迭代中首先采用MLEM算法对低剂量CT投影数据进行重建。由于各项异性扩散对噪声敏感,所以算法先对重建后的图像进行小波变换,再在更稳定的低频小波域进行基于绝对差值排序的各项异性扩散处理,对小波高频系数进行软阈值降噪处理。然后将降噪处理后的系数进行小波反变换,得到降噪后的图像。最后使用中值滤波对图像进行处理,从而消除脉冲噪声点。实验结果表明,与其他几种常用重建算法相比,该算法重建的图像信噪比更高,归一化均方误差更小,处理后的图像更清晰,即可以在抑制噪声的同时,较好地保持图像的边缘和细节信息。