arXiv subjects

Rajendra K. Ray

Publications and source records attributed to Rajendra K. Ray.

At least 19 recordsLinked to original sources

arXiv2026

Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs

Physics-informed neural networks (PINNs) have emerged as a powerful framework for solving forward and inverse partial differential equations (PDEs), but conventional real-valued PINNs (RV-PINNs) often suffer from spectral bias, limited expressivity, and reduced accuracy for high-frequency, oscillatory, and phase-dependent dynamics. In this work, we propose a generalized split complex-valued physics-informed neural network (SCV-PINN), in which network parameters and latent representations are defined in the complex domain. The framework employs split complex-valued activation functions by independently applying standard real-valued activations to the real and imaginary components, providing numerical stability, computational efficiency, and improved approximation capability. This formulation enables simultaneous learning of amplitude and phase information, enhancing the representation of nonlinear and oscillatory systems. Extensive ablation studies evaluate different split activation functions and collocation sampling strategies. The proposed framework is validated on forward and inverse PDE benchmarks including Burgers, Allen-Cahn, Korteweg-de Vries, nonlinear Schrodinger, Helmholtz, Poisson, Kovasznay flow (Re = 20), lid-driven cavity flow (Re = 100), the Lorenz system, inverse Burgers, inverse Navier-Stokes (Re = 100), and a three-dimensional Navier-Stokes Beltrami flow. For the Beltrami benchmark, SCV-PINN achieves a relative L2 error of 4.07 x 10^-5. Numerical results consistently demonstrate lower relative L2 errors and more accurate parameter identification than RV-PINNs and several existing PINN variants. The proposed SCV-PINN provides a robust and generalized extension of standard PINNs for complex-valued, multiscale, oscillatory, high-dimensional, and real-valued nonlinear PDEs.

physics.flu-dyn↗

arXiv2026

Comparative Study of Weighted and Coupled Second- and Fourth-Order PDEs for Image Despeckling in Grayscale, Color, SAR, and Ultrasound

Partial Differential Equation (PDE)-based approaches have gained significant attention in image despeckling due to their strong capability to preserve structural details while suppressing noise. However, conventional second-order PDE models tend to generate blocky artifacts, whereas higher-order models often introduce speckle patterns. To resolve it, this paper proposes and comparatively analyzes two advanced PDE-based frameworks designed for speckle noise suppression while preserving the fine edges. The first model introduces a novel weighted formulation that combines second and fourth-order PDEs through a weighting parameter. The second-order diffusion coefficient employs grayscale and gradient-based indicators, while the fourth-order term is guided solely by a Laplacian-based indicator. The second model constructs a coupled PDE framework, where independent fourth and second-order components are explicitly solved in an iterative manner. In this coupled structure, each diffusion coefficient is defined separately to enhance adaptability in varying image regions. Both models are implemented using the explicit finite difference method. The proposed techniques are extensively evaluated on a variety of datasets, including standard grayscale, color, Synthetic Aperture Radar (SAR), and ultrasound images. Comparative experiments with the existing Telegraph Diffusion Model (TDM) and Fourth-Order Telegraph Diffusion Model (TDFM) demonstrate the superiority of the proposed approaches in reducing speckle noise while effectively preserving fine image structures and edges. Quantitative evaluations using PSNR, SSIM and Speckle Index metrics confirm that the proposed models produce higher image quality and enhanced visual perception. Overall, the presented PDE-based formulations provide a reliable and efficient framework for image despeckling in both natural and medical imaging.

cs.CV↗

arXiv2026

Single Image Defogging Using a Fourth-Order Telegraph PDE Guided by Physical Haze Modeling

In real-world scenarios, image defogging is an inverse problem due to unknown scene depth, atmospheric scattering, and the common absence of ground truth . To resolve the issue, we propose a hybrid defogging model that integrates a fourth-order nonlinear PDE with a physical haze formation model. We used Dark Channel Prior to estimate atmospheric parameters and to generate a guidance image, while the final restoration is performed via a fourth-order PDE-based evolution. A fourth-order PDE of the type telegraph is then evolved, incorporating an edge-adaptive diffusion coefficient and a fidelity term weighted by the transmission map. Fourth-order diffusion effectively suppresses haze while preserving structural details, and the hyperbolic formulation improves numerical stability and convergence behavior. We use relative error norm criteria for the convergence of our PDE. The proposed method is compared with Dark Channel prior, modified Dark Channel prior, and variational-based single-image defogging techniques. When we have ground truth available, we use MSE and SSIM for quantitative evaluation, whereas no-reference metrics, including FADE, Contrast Restoration Index, Average Gradient, and Entropy, are applied to real-world foggy images. Experimental results demonstrate that the proposed hybrid PDE-based method provides comparable visual quality and maintains structural details.

cs.CV↗

arXiv2026

A Coupled Fourth Order Telegraph Diffusion Framework Using Grayscale Indicators for Image Despeckling

Speckle noise severely limits the quality of images acquired from coherent imaging systems such as Synthetic Aperture Radar (SAR) and medical ultrasound. Traditional second-order PDE-based despeckling approaches, although popular, often introduce staircase artifacts and blur fine details. To overcome these limitations, we present a nonlinear, fourth-order coupled hyperbolic-parabolic PDE model that effectively reduces noise while preserving the structure. The framework consists of two evolution equations: one governing fourth-order diffusion for effective speckle reduction and smooth intensity transitions, and another refining an edge indicator to protect textures and structural features. The diffusion coefficient is adaptively constructed using both the image intensity variable u and a grayscale-based indicator function, ensuring structure-aware denoising while avoiding blocky artifacts and preserving fine details. We also prove the existence of a weak solution to the proposed model by applying Schauder fixed-point theorem. A finite-difference scheme with Gauss Seidel iteration is employed for efficient implementation. We compare the proposed model with the existing coupled second-order PDE model (HPCPDE) and the fourth-order telegraph diffusion model (TDFM). The results show that our model consistently outperforms these approaches. Experiments on standard grayscale images, real SAR and ultrasound data, as well as speckle-corrupted color images, demonstrate that the proposed method achieves superior performance over conventional PDE-based techniques in terms of PSNR, MSSIM, and Speckle Index.

eess.IV↗

arXiv2026

An Efficient Wavelet-based Physics Informed Residual Neural Networks for Flow Field Reconstruction with Extremely Sparse Data

This paper introduces wavelet-physics-informed residual neural networks (W-PIRNNs) to study complex fluid flow problems by reconstructing the flow field from highly sparse, supervised data. Our W-PIRNNs fundamentally integrate ResNet and employ the wavelet $W(t) = w_1 \sin(t) + w_2 \cos(t)$ as an activation function. Due to the vanishing and ballooning gradient problems associated with typical PINNs' deep networks, we implemented residual-based skip connections. Our W-PIRNNs, which integrate supervised data with physical principles, demonstrate efficacy even in scenarios of sparse or partial data, enabling the reconstruction of flow fields using merely $0.05\%$ velocity data for training. The wake flow around a circular cylinder served as the test case for our proposed technique, which depends exclusively on velocity data for training. This technique facilitates the precise reconstruction of velocity, pressure, streamlines, and vorticity, requiring fewer epochs and less processing time. Significantly, our proposed W-PIRNNs effectively resolve PDEs in both forward and inverse contexts. Burger's equation served as a test case for both the forward and inverse problem configurations. Our network calculates the diffusion or viscosity coefficient ($\lambda_2$) with an absolute error of $0.065\%$ and the convection coefficient ($\lambda_1$) with an absolute error of $0.002\%$. Furthermore, the Schr\"odinger equation is examined in the forward setting to assess the framework's ability to handle periodic boundary conditions. To the best of our knowledge, W-PIRNNs represent the first method capable of flow reconstruction using highly sparse supervised data, as well as reconstructing streamline and vorticity, and they effectively address both forward and inverse problems with high accuracy.

physics.flu-dyn↗

arXiv2026

A Simple but Efficient Transformer-Based Physics-Informed Neural Network for Incompressible Navier--Stokes Equations

Traditional computational fluid dynamics and physics-informed neural networks (PINNs) often suffer from high computational cost, mesh sensitivity, and reduced accuracy for strongly nonlinear and time-dependent flows. To address these limitations, we propose \textit{PhysicsFormer}, a simple and efficient Transformer-based physics-informed neural network framework for complex fluid flow simulations. The proposed architecture employs encoder--decoder multi-head attention to capture long-range temporal dependencies and enhance spatio-temporal information propagation. Unlike conventional multilayer perceptron-based PINNs, \textit{PhysicsFormer} utilizes pseudo-sequential spatio-temporal representations together with a dynamics-weighted loss formulation to improve convergence, stability, and predictive accuracy. Owing to its lightweight architecture and parallel learning strategy, the proposed framework achieves faster training and lower computational cost than existing Transformer-based PINN models. The performance of the proposed framework is demonstrated on the convection equation, Burgers' equation, lid-driven cavity flow at $Re=100$, and inverse Navier--Stokes and flow reconstruction problems for flow past a circular cylinder at $Re=100$ and $Re=3900$. For the inverse Navier--Stokes problem at $Re=100$, the proposed framework simultaneously reconstructs the flow field and identifies governing equation parameters with nearly $0\%$ absolute error under both clean and noisy data conditions. Furthermore, for the high-Reynolds-number case at $Re=3900$, \textit{PhysicsFormer} accurately reconstructs the velocity and pressure fields using only $25$ spatial measurements per snapshot over $100$ temporal snapshots. The obtained results demonstrate that \textit{PhysicsFormer} provides an accurate, robust, and computationally efficient framework for complex time-dependent fluid flow problems.

physics.flu-dyn↗

arXiv2025

New Fourth-Order Grayscale Indicator-Based Telegraph Diffusion Model for Image Despeckling

Second-order PDE models have been widely used for suppressing multiplicative noise, but they often introduce blocky artifacts in the early stages of denoising. To resolve this, we propose a fourth-order nonlinear PDE model that integrates diffusion and wave properties. The diffusion process, guided by both the Laplacian and intensity values, reduces noise better than gradient-based methods, while the wave part keeps fine details and textures. The effectiveness of the proposed model is evaluated against two second-order anisotropic diffusion approaches using the Peak Signal-to-Noise Ratio (PSNR) and Mean Structural Similarity Index (MSSIM) for images with available ground truth. For SAR images, where a noise-free reference is unavailable, the Speckle Index (SI) is used to measure noise reduction. Additionally, we extend the proposed model to study color images by applying the denoising process independently to each channel, preserving both structure and color consistency. The same quantitative metrics PSNR and MSSIM are used for performance evaluation, ensuring a fair comparison across grayscale and color images. In all the cases, our computed results produce better results compared to existing models in this genre.

cs.CV↗

arXiv2024

New Higher-Order Super-Compact Scheme for Enhanced Three-Dimensional Heat Transfer with Nanofluid and Conducting Fins

This study presents a new higher-order super-compact (HOSC) finite difference scheme for analyzing enhanced heat transfer of three-dimensional (3D) nanofluid natural convection in a cubic cavity. The unique contribution of the present work lies in the extension of the higher-order super-compact finite difference scheme to examine the natural convection of nanofluid in the 3D cavity. This numerical approach achieves fourth-order spatial accuracy and second-order temporal accuracy. `Super-compact' term signifies its efficiency, utilizing 19 grid points at the current time level $(n^{th}$ time level$)$ and just seven grid points at the subsequent time level $((n + 1)^{th}$ time level$)$ around which the finite difference discretization is made. The nanoparticle volume fraction is maintained up to 0.04 (4\%) to ensure the mixture exhibits Newtonian behavior. The newly developed numerical scheme is validated by qualitative and quantitative comparisons with existing benchmark results. The scheme is then applied to investigate fluid flow and heat transfer phenomena in a Cu-water nanofluid-filled cavity over a range of Rayleigh numbers ($10^2 \leq Ra \leq 10^5$). In addition to introducing the new HOSC scheme for the convection of nanofluids, we examine two cases: the natural convection of nanofluid in a simple 3D cavity, and a configuration incorporating two aluminum conducting fins on the heated wall to further enhance the heat transfer rate. Results are presented through isotherms, streamlines, local Nusselt numbers, and average Nusselt numbers for both the considered cases and compared their results. It is found that the addition of nanoparticles or conducting fins does not always lead to enhanced heat transfer rates. Instead, the effectiveness of these enhancements is highly dependent on a range of parameters, which are thoroughly examined and discussed in this work.

physics.flu-dyn↗

arXiv2024

New Higher-Order Super-Compact Finite Difference Scheme to Study Three-Dimensional Natural Convection and Entropy Generation in Non-Newtonian Fluids

This work introduces a new higher-order super-compact (HOSC) implicit finite difference scheme for analyzing three-dimensional (3D) natural convection and entropy generation in non-Newtonian fluids. The proposed scheme achieves fourth-order accuracy in space and second-order accuracy in time while utilizing only seven directly adjacent grid points of the compact stencils at the $(n+1)$ time level, making it highly efficient and super compact. To the best of our knowledge, this is the first higher-order accurate finite difference scheme proposed to study 3D natural convection and entropy generation in non-Newtonian fluids. A time-marching technique is applied, where pressure corrections are addressed using a modified artificial compressibility method. The scheme is applied to the power-law model of non-Newtonian fluids, investigating both shear-thinning and shear-thickening effects on natural convection and entropy generation within a 3D cubic cavity. In the numerical simulations, the Prandtl number remains constant at $Pr = 1.0$, while various Rayleigh numbers ($Ra = 10^2$, $10^3$, $10^4$, $10^5$) and power-law indices ($n = 0.75$, $1.0$, $1.25$) are considered. Results are presented in terms of isotherms, streamlines, Nusselt numbers, Bejan numbers, and local entropy generation rates. The validation of the proposed scheme demonstrates excellent agreement with existing benchmark results. The numerical study reveals that the $n$ and $Ra$ have significant impacts on flow dynamics, heat transfer, and entropy generation. As $Ra$ increases, the maximum value of average Nusselt number ($Nu_{\text{avg}}$) also increases, whereas an opposite trend is observed with $n$ values. Shear-thinning fluids demonstrate the highest convection efficiency compared to Newtonian and shear-thickening fluids at any specific $Ra$.

physics.flu-dyn↗

arXiv2024

Effect of Uniform and Non-uniform wall heating on Three-Dimensional Magneto-Hydrodynamics Natural Convection and Entropy Generation: A computational study using New Higher Order Super Compact Scheme

Current research work deals with the effect of uniform and non-uniform wall heating on magnetohydrodynamic (MHD) natural convection within a three-dimensional (3D) cavity filled with molten lithium. A new Higher-Order Super Compact (HOSC) finite difference scheme is used to analyze the thermal behavior under both heating scenarios. After the quantitative and qualitative validations, the computed results are analyzed for a range of Hartman number ($Ha = 25, 50, 100, 150$) and Rayleigh number ($Ra = 10^3, 10^4, 10^5$) with fixed $Pr=0.065$ (molten lithium). Three distinct heating scenarios, i.e., uniform heating ($T_h = 1$), $y$-dependent non-uniform heating ($T_h = sin(\pi y$)), and a combination of $y$ and $z$-dependent non-uniform heating ($T_h = sin(\pi y)sin(\pi z)$) are investigated on the left wall ($x=0$) of the cubic cavity. It is found that variations in the $Ha$ and $Ra$, along with distinct thermal boundary conditions, exert significant effects on both the temperature distribution and flow field inside the 3D cubical cavity. Specifically, an increase in $Ra$ corresponds to enhanced heat transfer, highlighting the dominance of convection. Conversely, an increase in $Ha$ leads to a reduction in heat transfer due to the deceleration of fluid velocity. The scenario in which walls are uniformly heated exhibits the most significant total entropy generation. It is observed that with an increase in the $Ra$, the Bejan number ($Be$) decreases, which ultimately leads to an increase in total entropy generation. The implementation of the new HOSC scheme in this analysis showcases its effectiveness in capturing the complexities of 3D MHD-driven natural convection and entropy generation. This study offers significant information that might help improve the optimization and design of relevant engineering systems. Thus, our work stands out as genuinely novel and pioneering in its approach.

physics.flu-dyn↗

arXiv2024

A New Higher-Order Super Compact Finite Difference Scheme to Study Three-Dimensional Non-Newtonian Flows

This work introduces a new higher-order accurate super compact (HOSC) finite difference scheme for solving complex unsteady three-dimensional (3D) non-Newtonian fluid flow problems. As per the author's knowledge, the proposed scheme is the first ever developed finite difference scheme to solve three-dimensional non-Newtonian flow problem. Not only that, the proposed method is fourth-order accurate in space variables and second-order accurate in time. Also, the proposed scheme utilizes only seven directly adjacent grid points, at the $(n+1)^{th}$ time level, around which the finite difference discretization is made. The governing equations are solved using a time-marching methodology, and pressure is calculated using a pressure-correction strategy based on the modified artificial compressibility method. Using the power-law viscosity model, we tackle the benchmark problem of a 3D lid-driven cavity, systematically analyzing the varied rheological behavior of shear-thinning ($n=0.5$), shear-thickening $(n=1.5)$, and Newtonian $(n=1.0)$ fluids across different Reynolds numbers $(Re= 1, 50, 100, 200)$. Both Newtonian and non-Newtonian results are carefully investigated in terms of streamlines, velocity variation, pressure distributions, and viscosity contours, and the computed results are validated with the existing benchmark results. The findings demonstrate excellent agreement with the existing results. This extensive analysis, using the new HOSC scheme, not only increases our understanding of non-Newtonian fluid behavior but also provides a robust foundation for future research and practical applications.

physics.flu-dyn↗

arXiv2024

A Novel Gaussian filter-based Pressure Correction Technique with Super Compact Scheme for Unsteady 3D Incompressible, Viscous Flows

This work deals with a novel Gaussian filter-based pressure correction technique with a super compact higher order finite difference scheme for solving unsteady three-dimensional (3D) incompressible, viscous flows. This pressure correction technique offers significant advantages in terms of optimizing computational time by taking minimum iterations to reach the required accuracy, making it highly efficient and cost-effective. Pressure fields often exhibit highly nonlinear behavior, and employing the Gaussian filter can help to enhance their reliability by reducing noise and uncertainties. On the other hand, the super compact scheme uses minimum grid points to produce second-order accuracy in time and fourth-order accuracy in space variables. The main focus of this study is to enhance the accuracy and efficiency and minimize the computational cost of solving complex fluid flow problems. The super compact scheme utilizes 19 grid points at the known time level (i.e., $n^{th}$ time level) and only seven grid points from the unknown time level (i.e., $n + 1$ time level). By employing the above strategies, it becomes possible to notably decrease computational expenses while maintaining the accuracy of the computational scheme for solving complex fluid flow problems. We have implemented our methodology across three distinct scenarios: the 3D Burger's equation having analytical solution, and two variations of the lid-driven cavity problem. The outcomes of our numerical simulations exhibit a remarkable concordance, aligning exceptionally well with both the analytical benchmarks and previously validated numerical findings for the cavity problems.

math.NA↗

arXiv2023

Impact of a Cold Control Plate on Fluid Flow and Heat Transfer across an Isothermally Heated Rotary Oscillating Circular Cylinder

The main objective of this paper is to study the effect of a cold, vertical, arc-shaped control plate on the flow characteristics and forced convective heat transfer mechanism across a rotary oscillating, isothermally heated circular cylinder. Two-dimensional, unsteady, incompressible, laminar, and viscous flow of a Newtonian, constant property fluid is considered across the cylinder. The simulations are performed with an in-house code for various gap ratios between the control plate and the cylinder ($0\leq d/R_0 \leq 3$), maximum angular velocity ($0.5\leq \alpha_m \leq 4$) and frequency ratio of oscillation ($f/f_0=0.5,\ 3$) at Prandtl number $0.7$ and Reynolds number $150$. Here, $d$ denotes the gap between the surface of the cylinder and the leading surface of the control plate, $R_0$ denotes the radius of the cylinder, $f$ is the frequency of oscillation and $f_0$ is the frequency of natural vortex shedding. $d/R_0=0$ corresponds to the no plate case. Heat transfer and vortex shedding phenomena are discussed in relation to one another. A significant increase in heat transmission is observed for all $\alpha_m$ with the gap ratio of $d/R_0=0.5$ and $f/f_0=0.5$. The heat absorption on the surface of the control plate decreases to zero with increasing gap ratio when $\alpha_m=0.5$ and $f/f_0=0.5$ but never becomes zero when $\alpha_m=4$ and $f/f_0=3$. Additionally, when compared to the no plate case with $(\alpha_m,\ f/f_0)=(0.5,\ 0.5)$, the maximum peak of the drag coefficient is decreased by $9.877\%$ for the gap ratio of $d/R_0=3$. For $\alpha_m=4$ and $f/f_0=3$, the smallest gap ratio of $d/R_0=0.5$ is found to significantly increase the lift coefficient relative to other cases.

physics.flu-dyn↗

arXiv2023

Impact of an Arc-shaped Control Plate on Flow and Heat Transfer around a Isothermally Heated Rotating Circular Cylinder

The main objective of this paper is to study the flow characteristics of a rotating, isothermally heated circular cylinder with a vertical arc-shaped control plate placed downstream. Stream function-Vorticity ($\psi-\omega$) formulation of two dimensional (2-D) Navier-Stokes (N-S) equations is considered as the governing equation and the simulations are performed for different distances of the control plate ($0.5$, $1$, $2$, $3$), rotational rates ($0.5$, $1$, $2.07$, $3.25$) at Prandtl number $0.7$ and Reynolds number $150$. The governing equations are discretized using the Higher Order Compact (HOC) scheme and the system of algebraic equations, arising from HOC discretization, is solved using the Bi-Conjugate Gradient Stabilized approach. Present computed results show that the vortex shedding plane is shifted upward from the centerline of the flow domain by the cylinder's rotational motion. The structure of the wake varies based on the plate's position. The size of vortices is greatly reduced when the control plate is set at $d/R_0=3$ and the rotational rate is very high. At greater rotational rates, the impact of varied positions of the arc-shaped control plate is very significant. The rotation of the cylinder and the location of the plate can be used to lower or enhance the values of drag and lift coefficients as well as the heat transfer from the surface of the cylinder. The maximum value of the drag coefficient, which is about $3$, is achieved for $d/R_0=2$ and $\alpha=3.25$.

physics.flu-dyn↗

arXiv2019

Mathematical Modelling of Streamwise Velocity Profile in Open Channels Using Tsallis Entropy

This study derived the vertical distribution of streamwise velocity in wide open channels by maximizing Tsallis entropy, in accordance with the maximum entropy principle, subject to the total probability rule and the conservation of mass, momentum, and energy. Entropy maximizing leads to a highly nonlinear differential equation for velocity which was transformed into a relatively weaker nonlinear equation and then solved analytically using a non-perturbation approach that yielded a series solution. The convergence of the series solution was proved using both theoretical and numerical procedures. For the assessment of velocity profile, the Lagrange multipliers and the entropy index were obtained by solving a system of nonlinear equations by Gauss-Newton method after approximating the constraint integrals using Gauss-Legendre quadrature rule. The derived velocity profile was validated for some selected sets of experimental and field data and also compared with the existing velocity profile based on Tsallis entropy. The incorporation of the above constraints and the effect of entropy index were found to improve the velocity profile for experimental as well as field data. The methodology reported in this study can also be employed for addressing other open channel flow problems, such as sediment concentration and shear stress distribution.

physics.comp-ph↗

arXiv2019

On the Role of Tsallis Entropy Index for Velocity Modelling in Open Channels

Following the work on Shannon entropy together with the principle of maximum entropy, Luo & Singh (J. Hydrol. Eng., 2011, 16(4): 303-315) and Singh & Luo (J. Hydrol. Eng., 2011, 16(9): 725-735) explored the concept of non-extensive Tsallis entropy for modelling velocity in open channels. Later, the idea was extended by Cui & Singh (J. Hydrol. Eng., 2013, 18(3): 331-339; 2014, 19(2): 290-298) by hypothesizing an accurate cumulative distribution function (CDF). However, these studies estimated the entropy index through a data-fitting procedure and the values of the index were different for different studies. The present study investigates the role of Tsallis entropy index for modelling velocity in open channels using the method of moments, based on conservation of mass and momentum. It is found that the entropy index depends on the normalized mean velocity and the momentum coefficient. In addition to the physical meaning of the index, it is also found that the modified velocity profile significantly improves for both wide and narrow channels, as shown by small predicted velocity errors. The proposed approach may be further employed for other open channel flow problems, such as sediment concentration, and shear stress distribution.

physics.flu-dyn↗

arXiv2019

On the Development of a Coupled Non-linear Telegraph-Diffusion Model for Image Restoration

In this work, we propose a telegraph coupled partial differential equation (TCPDE) based model for image restoration. New framework interpolates between a couple of non-linear telegraph equation and a parabolic equation. Proposed strategy can be applied to significantly preserve the oscillatory and texture pattern in an image, even in low signal-to-noise ratio. First, we prove that the present model has a unique global weak solution using Banach's fixed point theorem. Then apply our model over a set of gray-level images to illustrate the superiority of the proposed model over the recently developed hyperbolic-parabolic PDE based models as well as coupled diffusion-based model.

math.AP↗

arXiv2019

Well-posedness study of a non-linear hyperbolic-parabolic coupled system applied to image speckle reduction

In this article, we consider a non-linear hyperbolic-parabolic coupled system based on telegraph diffusion framework applied to image despeckling. A separate equation is used to calculate the edge variable, which improves the quality of the despeckled images. A well-posedness result of the proposed coupled system is settled via Schauder's fixed point theorem. Numerical experiments are reported to illustrate the effectiveness of the proposed model, with recently developed models, over a set of gray level test images contaminated by speckle noise.

math.AP↗