A Study on Distortion Estimation Based on Image Gradients

Image noise is a variation of uneven pixel values that occurs randomly. A good estimation of image noise parameters is crucial in image noise modeling, image denoising, and image quality assessment. To the best of our knowledge, there is no single estimator that can predict all noise parameters for multiple noise types. The first contribution of our research was to design a noise data feature extractor that can effectively extract noise information from the image pair. The second contribution of our work leveraged other noise parameter estimation algorithms that can only predict one type of noise. Our proposed method, DE-G, can estimate additive noise, multiplicative noise, and impulsive noise from single-source images accurately. We also show the capability of the proposed method in estimating multiple corruptions.

Ageing transitions in a network of Rulkov neurons

The phenomenon of ageing transitions (AT) in a Erdős–Rényi network of coupled Rulkov neurons is studied with respect to parameters modelling network connectivity, coupling strength and the fractional ratio of inactive neurons in the network. A general mean field coupling is proposed to model the neuronal interactions. A standard order parameter is defined for quantifying the network dynamics. Investigations are undertaken for both the noise free network as well as stochastic networks, where the interneuronal coupling strength is assumed to be superimposed with additive noise. The existence of both smooth and explosive AT are observed in the parameter space for both the noise free and the stochastic networks. The effects of noise on AT are investigated and are found to play a constructive role in mitigating the effects of inactive neurons and reducing the parameter regime in which explosive AT is observed.

Additive Noise Effects on the Stabilization of Fractional-Space Diffusion Equation Solutions

This paper considers a class of stochastic fractional-space diffusion equations with polynomials. We establish a limiting equation that specifies the critical dynamics in a rigorous way. After this, we use the limiting equation, which is an ordinary differential equation, to approximate the solution of the stochastic fractional-space diffusion equation. This equation has never been studied before using a combination of additive noise and fractional-space, therefore we generalize some previously obtained results as special cases. Furthermore, we use Fisher’s and Ginzburg–Landau equations to illustrate our results. Finally, we look at how additive noise affects the stabilization of the solutions.

Statistical Modeling of Energy Harvesting in Hybrid PLC-WLC Channels

This work introduces statistical models for the energy harvested from the in-home hybrid power line-wireless channel in the frequency band from 0 to 100 MHz. Based on numerical analyses carried out over the data set obtained from a measurement campaign together with the use of the maximum likelihood value criterion and the adoption of five distinct power masks for power allocation, it is shown that the log-normal distribution yields the best model for the energies harvested from the free-of-noise received signal and from the additive noise in this setting. Additionally, the total harvested energy can be modeled as the sum of these two statistically independent random variables. Thus, it is shown that the energies harvested from this kind of hybrid channel is an easy-to-simulate phenomenon when carrying out research related to energy-efficient and self-sustainable networks.

Causal Discovery with Confounding Cascade Nonlinear Additive Noise Models

Identification of causal direction between a causal-effect pair from observed data has recently attracted much attention. Various methods based on functional causal models have been proposed to solve this problem, by assuming the causal process satisfies some (structural) constraints and showing that the reverse direction violates such constraints. The nonlinear additive noise model has been demonstrated to be effective for this purpose, but the model class does not allow any confounding or intermediate variables between a cause pair–even if each direct causal relation follows this model. However, omitting the latent causal variables is frequently encountered in practice. After the omission, the model does not necessarily follow the model constraints. As a consequence, the nonlinear additive noise model may fail to correctly discover causal direction. In this work, we propose a confounding cascade nonlinear additive noise model to represent such causal influences–each direct causal relation follows the nonlinear additive noise model but we observe only the initial cause and final effect. We further propose a method to estimate the model, including the unmeasured confounding and intermediate variables, from data under the variational auto-encoder framework. Our theoretical results show that with our model, the causal direction is identifiable under suitable technical conditions on the data generation process. Simulation results illustrate the power of the proposed method in identifying indirect causal relations across various settings, and experimental results on real data suggest that the proposed model and method greatly extend the applicability of causal discovery based on functional causal models in nonlinear cases.