In this paper, we present an innovative mechanism for image restoration problems in which the image is corrupted by a mixture of additive white Gaussian noise (AWGN) and impulse noise (IN). Mixed noise removal is much more challenging problem in contrast to the problems where either only one type of noise model (either Gaussian or impulse) is involved. Several well-known and efficient algorithms exist to effectively remove either Gaussian noise or Impulse noise, independently. However, in practice, noise may occur as a mixture of such noise models. Thus, the existing techniques devised to handle individual types of noise may not perform well. Moreover, the complexity of the problem hinges on the fact that the removal of either type of noise from the given image affects the noise statistics in the residual image. Therefore, a rigorous mechanism is required which not only infers altered noise statistics but also removes the residual noise in an effective manner. In this regard, an innovative approach is introduced to restore the underlying image in three key steps. Firstly, the intensity values, affected by impulsive noise, are identified by analyzing noise statistics with the help of adaptive median filtering. The identified intensity values are then aggregated by exploiting nonlocal data redundancy prior. Thus the first step enables the remaining noise to follow the zero mean Gaussian distribution in the median filtered image. Secondly, we estimate Gaussian noise in the resulting image, which acts as a key parameter in the subsequent singular value thresholding process for rank minimization. Finally, a reduced rank optimization applied to the pre-processed image obtained in the first step. The experimental results indicate that the proposed AMNLRA (Adaptive Median based Non-local Low Rank Approximation) approach can effectively tackle mixed noise complexity as compared to numerous state of the art algorithms.

This research aims at providing the theoretical effects of the unsteady MHD stagnation point flow of heat and mass transfer across a stretching and shrinking surface in a porous medium including internal heat generation/absorption, thermal radiation, and chemical reaction. The fundamental principles of the similarity transformations are applied to the governing partial differential equations (PDEs) that lead to ordinary differential equations (ODEs). The transformed ODEs are numerically solved by the shooting algorithm implemented in MATLAB, and verification is done from MATLAB built-in solver bvp4c. The numerical data produced for the skin friction coefficient, the local Nusselt number, and the local Sherwood number are compared with the available result and found to be in a close agreement. The impact of involved physical parameters on velocity, temperature, concentration, and density of motile microorganisms profiles is scrutinized through graphs. It is analyzed that the skin friction coefficient enhances with increasing values of an unsteady parameter , magnetic parameter , and porosity parameter . In addition, we observe that the density of a motile microorganisms profile enhances larger values of the bioconvection Lewis number and Peclet number and decreases with the increasing values of an unsteady parameter .

In this paper, an innovative hybridized deep learning framework (EN-CNN) is presented for image noise reduction where the noise originates from heterogeneous sources. More specifically, EN-CNN is applied to the benchmark natural images affected by a mixture of additive white gaussian noise (AWGN) and impulsive noise (IN). Reduction of mixed noise (AWGN and IN) is relatively more involved as compared to removing simply one type of noise. In fact, mitigating the impact of a mixture of multiple noise types becomes exceedingly challenging due to simultaneous presence of different noise statistics. Although, various effective deep learning approaches such as [1] and the classical state-of-the-art approaches like WNNM [2] have been used to suppress AWGN noise only, the same techniques are not suitable in case of mixed noise. In this context, EN-CNN can not only infer changed noise statistics but can also effectively eliminate residual noise. Firstly, EN-CNN employs the classical method of neighborhood filtering followed by non-local low rank estimation to respectively reduce IN noise and estimate the residual noise characteristics after reducing IN noise. As a result of this step, we obtain a pre-processed image with residual noise statistics. Secondly, convolutional neural network (CNN) is applied to the pre-processed image based on the noise statistics inferred in the first step. This two pronged strategy, in conjunction with the deep learning mechanism, effectively handles the mixed noise suppression. As a result, the suggested framework yields promising results as compared to various state-of-the-art approaches.

In this paper, we turn our attention to the mathematical model to simulate steady, hydromagnetic, and radiating nanofluid flow past an exponentially stretching sheet. A numerical modeling technique, simplified finite difference method (SFDM), has been applied to the flow model that is based on partial differential equations (PDEs) which is converted to nonlinear ordinary differential equations (ODEs) by using similarity variables. For the resultant algebraic system, the SFDM uses the tridiagonal matrix algorithm (TDMA) in computing the solution. The effectiveness of numerical scheme is verified by comparing it with solution from the literature. However, where reference solution is not available, one can compare its numerical results with the results of MATLAB built-in package bvp4c. The velocity, temperature, and concentration profiles are graphed for a variety of parameters, i.e., Prandtl number, Grashof number, thermal radiation parameter, Darcy number, Eckert number, Lewis number, and Brownian and thermophoresis parameters. The significant effects of the associated emerging thermophysical parameters, i.e., skin friction coefficient, local Nusselt number, and local Sherwood numbers are analyzed and discussed in detail. Numerical results are compared from the available literature and found a close agreement with each other. It is found that the Eckert number upsurges the velocity curve. However, the dimensionless temperature declines with the Grashof number. It is also shown that the SFDM gives good results when compared with the results obtained from bvp4c and results from the literature.

The aim of this work is to investigate the influence of Arrhenius activation energy and variable thermal conductivity with EMHD fluid flow over a nonlinearly radiating stretching sheet in a porous medium. The main objective of this research is to study the effects of variable electromagnetohydrodynamic (EMHD) on fluid flow motion. The significance of the combined effects of electric and magnetic fields is useful where one can create a strong Lorentz force for industry applications. The fundamental laws, that is, conservation of mass, momentum, and energy equations, are given in the form of partial differential equations (PDEs). The current fluid flow problem is not similar, which means that the presented solution is local. The introduction of nonsimilarity variables transforms PDEs into a set of coupled ODEs. The resultant ODEs are not only solved computationally by MATLAB built-in solver bvp4c but the solution is also obtained with other numerical schemes that include the shooting method and the finite element method (FEM). In applying FEM, we choose the Galerkin method in which the weight function is equal to the shape function. The aforementioned numerical methods are implemented and programmed in MATLAB. Graphs illustrate the effects of various parameters on the velocity, temperature, concentration, and microorganism profiles. Physical parameters measure the roughness of the sheet (skin friction coefficient), heat transfer rate at the sheet (local Nusselt number), the mass transfer rate of the concentration gradient (local Sherwood number), and transfer rate of microorganisms at the sheet (density of motile microorganism). The skin friction coefficient increases for higher values of (K_p) and magnetic parameters (M). The local Sherwood number decreases for different values of activation energy. An excellent agreement of FEM results with other numerical methods, shooting method, and bvp4c has been achieved. Moreover, for particular cases, the current results have a good agreement with the published work.