Anisotropic Diffusion Research Articles

Numerics with coordinate transforms for efficient Brownian dynamics simulations

Many stochastic processes in the physical and biological sciences can be modelled as Brownian dynamics with multiplicative noise. However, numerical integrators for these processes can lose accuracy or even fail to converge when the diffusion term is configuration-dependent. One remedy is to construct a transform to a constant-diffusion process and sample the transformed process instead. In this work, we explain how coordinate-based and time-rescaling-based transforms can be used either individually or in combination to map a general class of variable-diffusion Brownian motion processes into constant-diffusion ones. The transforms are invertible, thus allowing recovery of the original dynamics. We motivate our methodology using examples in one dimension before then considering multivariate diffusion processes. We illustrate the benefits of the transforms through numerical simulations, demonstrating how the right combination of integrator and transform can improve computational efficiency and the order of convergence to the invariant distribution. Notably, the transforms that we derive are applicable to a class of multibody, anisotropic Stokes-Einstein diffusion that has applications in biophysical modelling.

Design and preliminary tests of an Active Plasma Chamber for ECR Ion Sources

An innovative plasma chamber for Electron Cyclotron Resonance Ion Sources (ECRIS) has been developed at INFN and will soon be installed and tested with the AISHa (Advanced Ion Source for Hadrontherapy) ion source. It consists in inserting a particular liner into the existing chamber, which allows an electrical segmentation of the internal walls of the chamber. The purpose of this system is to reduce the ion losses induced by the anisotropic diffusion mechanism, to improve the plasma confinement and thus to increase the overall performance of the ion source. In fact, in ECRIS plasmas, electrons mostly diffuse along magnetic field lines while ions mostly leak across the same lines. In particular, the inner walls of the plasma chamber are covered with 30 tiles, each one polarized to a proper positive voltage. The tiles are made of Al-6082 and anodized except for the surface directly facing the plasma. The anodizing process makes each tile electrically insulated from the others and from the plasma chamber while preserving the correct operation of the cooling system. The tiles are wrapped by 2 half-cylinders made of Al-6082 acting as shells. Some tiles are equipped of a temperature sensor and machined to allow the wiring of the entire system.In this work the results of the preliminary tests of the thermal and electrical behaviour of the active chamber and the future perspectives are presented.

Diffusion behavior along Nd–Fe–B grain boundaries in different directions and mechanism of coercivity strengthening

In this study, DyF3 powder was sprayed onto the polar and side surfaces of the magnets to determine the anisotropic diffusion mechanism of Dy in the sintered Nd–Fe–B magnet. The coercivity and squareness of the magnet in which the diffusion of Dy is perpendicular to the c-axis (a-magnet) are lower than those of the magnet with the diffusion of Dy parallel to the c-axis (c-magnet). Compared with the c-magnet, the a-magnet has a longer Dy-enrichment region from the diffusion surface, where Dy is enriched in the 2:14:1 grain. By contrast, the Dy concentration in the grain boundaries beyond the Dy enrichment region is lower in the a-magnet. Moreover, the Dy shells beyond the Dy enrichment region in the a-magnet are distributed on the side surfaces of the 2:14:1 grains but not on the polar surfaces. Based on the micromagnetic simulation, the Dy shells on the polar surfaces of the grains are more effective in enhancing coercivity. According to first-principle calculations, Dy migrating through [001] into the Nd vacancy in the Nd2Fe14B crystal has a higher diffusion barrier, thus indicating that the lattice diffusion of Dy parallel to the c-axis is more difficult.

Scale-Aware Edge-Preserving Full Waveform Inversion with Diffusion Filter for Crosshole Sensor Arrays.

Full waveform inversion (FWI) is recognized as a leading data-fitting methodology, leveraging the detailed information contained in physical waveform data to construct accurate, high-resolution velocity models essential for crosshole surveys. Despite its effectiveness, FWI is often challenged by its sensitivity to data quality and inherent nonlinearity, which can lead to instability and the inadvertent incorporation of noise and extraneous data into inversion models. To address these challenges, we introduce the scale-aware edge-preserving FWI (SAEP-FWI) technique, which integrates a cutting-edge nonlinear anisotropic hybrid diffusion (NAHD) filter within the gradient computation process. This innovative filter effectively reduces noise while simultaneously enhancing critical small-scale structures and edges, significantly improving the fidelity and convergence of the FWI inversion results. The application of SAEP-FWI across a variety of experimental and authentic crosshole datasets clearly demonstrates its effectiveness in suppressing noise and preserving key scale-aware and edge-delineating features, ultimately leading to clear inversion outcomes. Comparative analyses with other FWI methods highlight the performance of our technique, showcasing its ability to produce images of notably higher quality. This improvement offers a robust solution that enhances the accuracy of subsurface imaging.

Enhancing image denoising: A novel non-local anisotropic diffusion framework based on Caputo derivatives and Gaussian convolution for the Perona–Malik model

In the field of image restoration, denoising is considered one of the most important techniques. It is a pre-processing approach aims to refine image clarity and enhance its overall quality by effectively reducing noise present in the image. The aim is to obtain good-quality images from a version degraded by additive noise or convolutional noise that introduces blur. As a result, more advanced treatments can be performed on the resulting image. In order to remove Gaussian noise from input images, we propose the following methodology using a fractional differential equation in time-space based on Gaussian convolution, where the integer and fractional order derivatives of Caputo can be discretized using finite difference and L1−approximations. Once the equation is solved numerically, the scheme is applied to grayscale digital images using the presented algorithm. The parameters must be optimized and adjusted. As a result of testing with natural images, we are able to successfully suppress the noise present in the images. Aside from that. Our model demonstrates strong visual quality, as verified by the calculation of indexes such as Peak Signal-To-Noise Ratio (PSNR) and Structural Similarity Index Measure (SSIM). Our denoising technique demonstrates its effectiveness in mitigating noise present in both MRI and X-ray images, resulting in improved image quality and diagnostic accuracy for these vital medical imaging modalities.

Adaptive structure-based full-waveform inversion

In simultaneous-shot full-waveform inversion (FWI), the re-started limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm can be used to suppress crosstalk, but crosstalk cannot be completely eliminated from the inversion results. To further solve the crosstalk problem caused by the interference among individual shots in simultaneous-shot FWI, adaptive structure-based smoothing is applied to the FWI with the restarted L-BFGS algorithm. Structure-based smoothing can mitigate the crosstalk by highlighting structure boundaries. To perform structure-based smoothing, an implicit anisotropic diffusion equation is solved. We carry out a multiscale inversion strategy. Because the FWI results in the low-frequency band contain less structural information and more crosstalk, structure-based smoothing is applied to the frequency band at frequencies higher than the peak frequency to prevent negative effects from the model structure in the low-frequency band. The estimated structural information is iteratively updated during the inversion process. Furthermore, structure-based smoothing is only added to the iterations with invariant encoding to reduce oversmoothing. The invariant encoding means that the shot encoding remains unchanged between iterations. Numerical experiments with an overthrust model indicate that the proposed adaptive structure-based FWI method can effectively suppress artifacts and provide a high-resolution inversion result, even when the encoded data are contaminated with strong noise. Another advantage of the adaptive structure-based FWI method is that no seismic migration needs to be performed, which makes it more efficient for real data.

The very singular solution for the Anisotropic Fast Diffusion Equation and its consequences

We construct the Very Singular Solution (VSS) for the Anisotropic Fast Diffusion Equation (AFDE) in the suitably good exponent range. VSS is a solution that, starting from an infinite mass located at one point as initial datum, evolves as an admissible solution of the corresponding equation everywhere away from the point singularity. It is expected to represent important properties of the fundamental solutions when the initial mass is very big. Here we work in the whole Euclidean space.In this setting we show how the diffusion process distributes mass from the initial infinite singularity with different rates along the different space directions. Indeed, and up to constant factors, there is a simple partition formula for the anisotropic mass expansion, given approximately as the minimum of separate 1-D VSS solutions. This striking fact is a consequence of the improved scaling properties of the special solution, and it has strong consequences.If we consider the family of fundamental solutions for different masses, we prove that they all share the same universal tail behaviour (i.e., for large |x|) as the VSS. Namely, their tail is asymptotically convergent to the unique VSS tail. This means that the VSS partition formula holds also for the fundamental solutions at spatial infinity. With the help of this analysis we study the behaviour of the class of nonnegative finite-mass solutions of the Anisotropic FDE, and prove the Global Harnack Principle (GHP) and the Asymptotic Convergence in Relative Error (ACRE) under a natural assumption on the decay of the initial tail.

A data-driven model for damage evolution of bridge stay cable

Chloride ion concentration is crucial for the reliability of stay cables, particularly when their protective covers are compromised. Previous studies have focused on the corrosion of single wires or cables over time, proposing estimation models that primarily consider corrosion duration while neglecting other significant factors. Addressing this gap, this paper establishes a corrosion damage model for stay cables considering time, temperature, humidity and inclination angle based on the diffusion characteristics of chloride ions. Firstly, We conducted accelerated corrosion experiments on stay cables in different environments to assess the characteristics of the spatial distribution of chloride ion concentrations within the cables and the mass loss characteristics of the wires. Secondly, a three-dimensional diffusion model for chloride ions in stay cables is proposed based on Fick's second law. A pivotal innovation of our research is the application of diverse machine learning techniques to explore how the diffusion coefficient of chloride ions is influenced by factors like time and environmental temperature, leading to the formulation of a sophisticated chloride ion diffusion model. Finally, by amalgamating this diffusion model with the established corrosion law for steel reinforcement, we devised a comprehensive corrosion damage evolution model for the steel wires of stay cables. The result demonstrates the anisotropic diffusion of chloride ions and its substantial correlation with the corrosion damage observed in steel wires. Notably, the PSO-BPNN method emerged as a highly accurate predictor for the diffusion coefficient of chloride ions. The model established in this paper considers a variety of influencing factors and accurately predicts the corrosion damage characteristics of stay cables, which makes an important contribution to improving the reliability of stay cables.

Migration of confined micro-swimmers subject to anisotropic diffusion

Shear-induced migration of elongated micro-swimmers exhibiting anisotropic Brownian diffusion at a population scale is investigated analytically in this work. We analyse the steady motion of confined ellipsoidal micro-swimmers subject to coupled diffusion in a general setting within a continuum homogenisation framework, as an extension of existing studies on macro-transport processes, by allowing for the direct coupling of convection and diffusion in local and global spaces. The analytical solutions are validated successfully by comparison with numerical results from Monte Carlo simulations. Subsequently, we demonstrate from the probability perspective that symmetric actuation does not yield net vertical polarisation in a horizontal flow, unless non-spherical shapes, external fields or direct coupling effects are harnessed to generate steady locomotion. Coupled diffusivities modify remarkably the drift velocity and vertical migration of motile micro-swimmers exposed to fluid shear. The interplay between stochastic swimming and preferential alignment could explain the diverse concentration and orientation distributions, including rheological formations of depletion layers, centreline focusing and surface accumulation. Results of the analytical study shed light on unravelling peculiar self-propulsion strategies and dispersion dynamics in active-matter systems, with implications for various transport problems arising from the fluctuating shape, size and other external or inter-particle interactions of swimmers in confined environments.

Applications of Ni and Ag metallizations at the solder/Cu interfaces in advanced high-power automobile interconnects: An electromigration study

An advanced Pb-free solder interconnect, Cu line/Cu pillar/Ni/Sn1.8Ag/Ag/Cu lead frame/Sn3Ag0.5Cu/Au/Ni(P)/Cu trace, using the flip-chip quad flat no‑lead (FCQFN) packaging technology was designed for high-power automobile applications. An electromigration study revealing the Ni and Ag metallization effects on the interfacial reaction was investigated. Current stressing was conducted at a 2 A direct current at 160 °C until the defined 200 %-electrical-resistance-rise failure occurrence. Electromigration induced a two-stage electrical resistance increase mode in the advanced automobile test vehicle with a mechanism transition time of 585 h, as evidenced by the in situ resistance monitoring. Phase transformation from the constituent phases into the predominant (Cu,Ni)6Sn5 and Cu3Sn intermetallic compounds (IMCs) at the interfaces was proposed to explain the rapid resistance rise in the early-stage electromigration. Void formation and coalescence due to the Kirkendall effect and volume shrinkage during the phase transformation were proposed to explain the following steady resistance increase after the critical current stressing time. Furthermore, the phase transformation and growth of the IMCs behaved divergently at different interfaces and electron flow directions. The rapid phase transformation occurred in the downstream Sn1.8Ag solder interconnect due to the accelerated Ni metallization dissolution and formed a complete IMC joint. The anisotropic diffusion driven by the competitive or synergetic effect between the electron wind force and chemical potential gradient was proposed to explain the asymmetric microstructures after the electromigration experiment. The application of Ag metallization benefited the flip-chip soldering process, and the layer-type Ag3Sn IMC served as a diffusion barrier against Sn/Cu interdiffusion at the solder/Cu lead frame interface during the solid-state electromigration. In contrast, the Ni metallization was designed as a diffusion barrier to hinder interdiffusion and the undesirable Cu3Sn growth at the solder/Cu interface. The findings presented in this study could benefit the solder interconnect design with an appropriate metallization combination against undesirable electromigration failure.

Deep learning with adaptive convolutions for classification of retinal diseases via optical coherence tomography

Optical coherence tomography (OCT) uses interferometry to capture high-resolution cross-sectional images of the retina to diagnose retinal diseases. Convolutional neural networks (CNNs) have become essential for developing efficient computer-aided diagnostic algorithms, but noisy images can hinder their performance. This study introduces an innovative image preprocessing strategy that involves a new method of representing images to reduce image noise and a new adaptive convolution layer. The adaptive convolution layer aims to replace traditional convolution layers for OCT image classification by relying on local’Feature Content’. The proposed image representation is based on Zeckendorf's theorem, which states that every positive integer may be split into a unique sum of distinct, non-adjacent Fibonacci numbers. The proposed approach enables the generation of two separate images, known as the ‘base’ and ‘fine,’ where the ‘base’ image is the denoised image. We assessed our methodology by evaluating against ten filters, comprising a Low-pass filter, Gaussian filter, Wiener filter, Wavelet filter, Guided filter, Lee filter, Frost filter, Kuan filter, Detail Preserving Anisotropic Diffusion (DPAD) filter, and Non-Local Means (NLM) filter. In our study, we found that the proposed filter produced the most favorable results in five of the six no-reference parameters (Blur Percent (BP), Blind/Referenceless Image Spatial Quality Evaluator (BRISQUE), Naturalness Image Quality Evaluator (NIQE), Wavelet Variance (WAVV), Wavelet Variance Radial (WAVR)) used to assess the effectiveness of the proposed image enhancement technique. The OCT dataset utilized in the study was compiled by the University of California San Diego. The proposed adaptive convolution layer and its accompanying activation function were tested using seven OCT image classification CNN architectures. The test architectures comprise OctNET, NT-CNN, AOCT-NET, M-CNN, LightOCT, RetiNet, and DeepOCT. Experiments were conducted to assess the impact of the new preprocessing algorithm and the placement of the adaptive convolution layer as a substitute for the conventional convolution layer. Implementing the proposed approaches resulted in accuracy improvements ranging from 0.44% to 2.44% across architectures. Our findings highlight the efficacy of the proposed indirect noise reduction technique and a texture-sensitive adaptive convolution layer.

Two-Phase Speckle Noise Removal in US Images: Speckle Reducing Improved Anisotropic Diffusion and Optimal Bayes Threshold

Medial images are contaminated by multiplicative speckle noise, which dramatically reduces ultrasound images and has a detrimental impact on a variety of image interpretation tasks. Hence, to overcome this issue, this paper presented a Two-Phase Speckle Reduction approach with Improved Anisotropic Diffusion and Optimal Bayes Threshold termed TPSR-IADOT, which includes the phases like image enhancement and two-level decomposition processes. Initially, the speckle noise is subjected to an image enhancement process where the Speckle Reducing Improved Anisotropic Diffusion (SRAID) filtering process is carried out for the speckle removal process. Afterwards, two-level decomposition takes place which utilizes Discrete Wavelet Transform (DWT) to remove the residual noise. As the speckle noise is mostly present in the high-frequency band, Improved Bayes Threshold will be applied to the high- frequency subbands. Finally, to provide the best outcomes, an optimization algorithm termed Self Improved Pelican Optimization Algorithm (SI-POA) in this work via choosing the optimal threshold value. The efficiency of the proposed method has been validated on an ultrasound image database using Simulink in terms of PSNR, SSIM, SDME and MAPE. Accordingly, from the analysis, it is proved that the proposed TPSR-IADOT attains the PSNR of 40.074, whereas the POA is 38.572, COOT is 38.572, BES is 37.003, PRO is 30.419, WOA is 33.218, RFU-LA is 29.935 and SSI-COA is 39.256, for noise variance[Formula: see text]0.1.

A positivity-preserving edge-centred finite volume scheme for heterogeneous and anisotropic diffusion problems on polygonal meshes

A positivity-preserving edge-centred finite volume scheme for heterogeneous and anisotropic diffusion problems on polygonal meshes

Anisotropic equation based on fractional diffusion tensor for image noise removal

In this paper, we propose an anisotropic diffusion equation based on fractional‐order tensor diffusion applied on noisy images. We start by investigating the existence and uniqueness results of the proposed model. We also provide a discretization scheme based on the finite difference method. In order to prove the efficacy of our proposed approach, we deliver some simulations, which show robustness and remarkable results against noise while preserving edges and corners, compared to some well‐known models in literature. For a fair comparison, we manage to obtain the optimal parameters of every model thanks to PSNR and SSIM. We demonstrate the robustness efficacy of our model against high level of noise.

Correction: An enhanced flux continuity three-dimensional finite element method for heterogeneous and anisotropic diffusion problems on general meshes

Correction: An enhanced flux continuity three-dimensional finite element method for heterogeneous and anisotropic diffusion problems on general meshes

Anisotropic grain boundary diffusion process in textured sintered and hot-deformed Nd-Fe-B magnets

A systematic study of the dependence of the Grain Boundary Diffusion Process (GBDP) on texture using Dy and Dy-Nd-Cu in microcrystalline sintered and nanocrystalline hot deformed Nd-Fe-B magnets was performed. Diffusion parallel or perpendicular to the texture direction, the nominal c-axes orientation in the polycrystals, was investigated. By measuring thin slices from the respective samples, coercivity as a function of (i) magnet thickness and (ii) diffusion depth was obtained showing that GBDP efficiency depends on the diffusion direction, diffusion source as well as the grain morphology originating from the magnet production route. In nanocrystalline hot deformed magnets perpendicular diffusion is superior due to the platelet-like shape of the grains. Microcrystalline sintered magnets consist of equiaxed grains hence the main effects originate in anisotropic lattice diffusion and pole surface hardening. The magnetic properties are correlated with a comprehensive analysis of microstructure, chemistry and magnetization reversal.

Automated diagnosis of acute cerebral ischemic stroke lesions from diffusion-weighted magnetic resonance images in assessment with modified Rankin Scale

Purpose: Automated diagnosis of acute cerebral ischemic stroke lesions (ACISL) is an evolving science. Early detection and exact delineation of ACISL automatically from diffusion-weighted magnetic resonance (DWMR) images are crucial for initiating prompt treatment. Thus, this work aims to determine the appropriate slice out of 60 pieces using multi-fractal analysis (MFA) and to segment the lesions in DWMR images using a hybrid optimization method. Features extracted from the segmented images were clinically correlated with the modified Rankin Scale (mRS). Methods: Thirty-one real-time stroke patients’ images were collected from Rajiv Gandhi Government General Hospital, Chennai, India. Multiple MRI slices were taken from each patient and filtered using an anisotropic diffusion filter (ADF). These filtered images were skull-stripped automatically by the maximum entropy thresholding technique incorporating mathematical morphological operations (MEM). The multi-fractal analysis (MFA) identifies the prominent slice with the significant infarct lesion. An isodata algorithm that integrated differential evolution with the particle swarm optimization method based on Kapur’s (IDPK) and Otsu’s (IDPO) approaches was attempted to segment the ACISL. Finally, the geometric and moment features extracted from the segmented lesions categorized the stroke severity and were correlated with the mRS. Results: The findings of the experimental work confirm that the suggested IDPK approach achieved usual normalized values for image similarity indices such as Sokal-Michener Coefficient (98.51%), Roger-Tanimoto Coefficient (90.16%), Sokel-Sneath-2 (91.04%), and Sorenson Index (90.04%) are superior to IDPO. Statistical significance proved that the segmented lesions’ area (r = 0.820, p < 0.0001) and perimeter (r = 0.928, p < 0.0001) were strongly correlated with the mild and moderate criteria of mRS. Conclusion: The proposed work effectively detected ischemic stroke lesions and their severity within the studied image groups. It could be a promising and potential tool to aid radiologists in validating their diagnosis.

Multi-classification of disease induced in plant leaf using chronological Flamingo search optimization with transfer learning.

Agriculture is imperative research in visual detection through computers. Here, the disease in plants can distress the quality and cultivation of farming. Earlier detection of disease lessens economic losses and provides better crop yield. Detection of disease from crops manually is an expensive and time-consuming task. A new scheme is devised for accomplishing multi-classification of disease using plant leaf images considering the chronological Flamingo search algorithm (CFSA) with transfer learning (TL). The leaf image undergoes pre-processing using Adaptive Anisotropic diffusion to discard noise. Here, the segmentation of plant leaf is done with U-Net++, and trained by the Moving Gorilla Remora algorithm (MGRA). The image augmentation is further applied considering two techniques namely position augmentation and color augmentation to reduce data dimensionality. Thereafter the feature mining is done to produce crucial features. Next, the classification in terms of the first level is considered for classifying plant type and classification in terms of the second level is done to categorize disease using convolutional neural network (CNN)-based TL with LeNet and it undergoes training using CFSA. The CFSA-TL-based CNN with LeNet provided better accuracy of 95.7%, sensitivity of 96.5% and specificity of 94.7%. Thus, this model is better for earlier plant leaf disease detection.

HYPERSPECTRAL IMAGE (HSI)-ASSISTED MULTI-LEVEL CROP CLASSIFICATION WITH SPINALNET-ENABLED FRACTIONAL LIGHT SPECTRUM OPTIMIZER

The accurate categorization of crop kinds with hyperspectral remote sensing imaging (HRSI) represents an imperative adaption in agriculture and is of huge emergence in estimating the yield of crops and monitoring growth. Amidst the deep models, convolutional neural networks (CNNs) tend to be the best technique for hyperspectral image (HSI) classification. However, the classical CNN poses a fixed shape, which poses simulation complexity in modeling huge ranges. To handle the problem, a two-level classification technique is developed for crop classification using HSI. The aim is to design a Spinal Net-assisted multi-level crop classification using HSI. Here, a hyperspectral satellite crop image is taken as input, and the anisotropic diffusion is used for pre-processing. U-Net is applied to segment crops. The feature mining is executed considering spectral-spatial features, and vegetation index features. The hyperspectral crop identification process is engaged with Squeeze Net, which is trained by fractional light spectrum optimizer (FLSO). In this step, if the hyperspectral crop is identified, then the multi-level crop type classification process is carried out using FLSO-based Spinal Net. The FLSO-based Spinal Net provided better accuracy of 92.2%, false positive rate (FPR) of 0.083, and true positive rate (TPR) of 91.7%.

Impact of Anisotropic Cosmic-Ray Transport on the Gamma-Ray Signatures in the Galactic Center

The very high energy (VHE) emission of the central molecular zone (CMZ) is rarely modeled in 3D. Most approaches describe the morphology in 1D or simplify the diffusion to the isotropic case. In this work, we show the impact of a realistic 3D magnetic field configuration and gas distribution on the VHE γ-ray distribution of the CMZ. We solve the 3D cosmic-ray transport equation with an anisotropic diffusion tensor using the approach of stochastic differential equations as implemented in the CRPropa framework. We test two different source distributions for five different anisotropies of the diffusion tensor, covering the range of effectively fieldline-parallel diffusion to isotropic diffusion. Within the tested magnetic field configuration, the anisotropy of the diffusion tensor is close to the isotropic case, and three point sources within the CMZ are favored. Future missions such as the upcoming CTA will reveal more small-scale structures that are not yet included in the model. Therefore, a more detailed 3D gas distribution and magnetic field structure will be needed.