scholarly journals An Efficient Algorithm for Reconstruction Images Corrupted by Some Multiplicative Noises

2019 ◽  
Vol 5 (2) ◽  
pp. 263-278
Author(s):  
L. Ziad ◽  
O. Oubbih ◽  
F. Sniba
Keyword(s):  
Multiplicative Noise ◽  
Slow Growth ◽  
Mathematical Framework ◽  
Well Posedness ◽  
Multiplicative Noises ◽  
Proposed Model ◽  
Staircase Effect ◽  
Map Estimator ◽  
Denoised Image ◽  
Numerical Approaches

AbstractIn this paper, we propose a novel hybrid model for restoration of images corrupted by multiplicative noise. Using a MAP estimator, we can derive a functional whose minimizer corresponds to the denoised image we want to recover. The energies studied here are inspired by image restoration with non linear variable exponent [1, 2], and it is a combination of fast growth with respect to low gradient and slow growth when the gradient is large. We study a mathematical framework to prove the well posedness of the minimizer problem and we introduce the associated evolution problem, for which we derive numerical approaches. At last, compared experimental results distinctly demonstrate the superiority of the proposed model, in term of removing some muliplicative noise while preserving the edges and reducing the staircase effect.

scholarly journals Quantitative measure of hysteresis for memristors through explicit dynamics

2012 ◽  
Vol 468 (2144) ◽  
pp. 2210-2229 ◽  
Author(s):  
P. S. Georgiou ◽  
S. N. Yaliraki ◽  
E. M. Drakakis ◽  
M. Barahona
Keyword(s):  
Differential Equation ◽  
Analytical Solutions ◽  
Quantitative Measure ◽  
Explicit Solutions ◽  
Mathematical Framework ◽  
Input Output ◽  
Explicit Formulas ◽  
Hewlett Packard ◽  
Lumped Parameter ◽  
Proposed Model

We introduce a mathematical framework for the analysis of the input–output dynamics of externally driven memristors. We show that, under general assumptions, their dynamics comply with a Bernoulli differential equation and hence can be nonlinearly transformed into a formally solvable linear equation. The Bernoulli formalism, which applies to both charge- and flux-controlled memristors when either current or voltage driven, can, in some cases, lead to expressions of the output of the device as an explicit function of the input. We apply our framework to obtain analytical solutions of the i – v characteristics of the recently proposed model of the Hewlett–Packard memristor under three different drives without the need for numerical simulations. Our explicit solutions allow us to identify a dimensionless lumped parameter that combines device-specific parameters with properties of the input drive. This parameter governs the memristive behaviour of the device and, consequently, the amount of hysteresis in the i – v . We proceed further by defining formally a quantitative measure for the hysteresis of the device, for which we obtain explicit formulas in terms of the aforementioned parameter, and we discuss the applicability of the analysis for the design and analysis of memristor devices.

scholarly journals Image Enhancement under Data-Dependent Multiplicative Gamma Noise

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Jidesh Pacheeripadikkal ◽  
Bini Anattu
Keyword(s):  
Anisotropic Diffusion ◽  
Multiplicative Noise ◽  
State Of The Art ◽  
Noise Removal ◽  
Diffusion Term ◽  
Art Restoration ◽  
Locally Adaptive ◽  
Edge Points ◽  
Diffusive Term ◽  
Map Estimator

An edge enhancement filter is proposed for denoising and enhancing images corrupted with data-dependent noise which is observed to follow a Gamma distribution. The filter is equipped with three terms designed to perform three different tasks. The first term is an anisotropic diffusion term which is derived from a locally adaptivep-laplacian functional. The second term is an enhancement term or a shock term which imparts a shock effect at the edge points making them sharp. The third term is a reactive term which is derived based on the maximum a posteriori (MAP) estimator and this term helps the diffusive term to perform a Gamma distributive data-dependent multiplicative noise removal from images. And moreover, this reactive term ensures that deviation of the restored image from the original one is minimum. This proposed filter is compared with the state-of-the-art restoration models proposed for data-dependent multiplicative noise.

scholarly journals Mathematical modelling with experimental validation of viscoelastic properties in non-Newtonian fluids

2020 ◽  
Vol 378 (2172) ◽  
pp. 20190284 ◽  
Author(s):  
C. M. Ionescu ◽  
I. R. Birs ◽  
D. Copot ◽  
C. I. Muresan ◽  
R. Caponetto
Keyword(s):  
Fractional Order ◽  
Experimental Validation ◽  
Model Identification ◽  
Nonlinear Least Squares ◽  
Advanced Materials ◽  
Mathematical Framework ◽  
Nonlinear Identification ◽  
Proposed Model ◽  
Materials Modelling ◽  
Fluid Properties

The paper proposes a mathematical framework for the use of fractional-order impedance models to capture fluid mechanics properties in frequency-domain experimental datasets. An overview of non-Newtonian (NN) fluid classification is given as to motivate the use of fractional-order models as natural solutions to capture fluid dynamics. Four classes of fluids are tested: oil, sugar, detergent and liquid soap. Three nonlinear identification methods are used to fit the model: nonlinear least squares, genetic algorithms and particle swarm optimization. The model identification results obtained from experimental datasets suggest the proposed model is useful to characterize various degree of viscoelasticity in NN fluids. The advantage of the proposed model is that it is compact, while capturing the fluid properties and can be identified in real-time for further use in prediction or control applications. This article is part of the theme issue ‘Advanced materials modelling via fractional calculus: challenges and perspectives’.

scholarly journals Hamiltonian identification for quantum systems: well-posedness and numerical approaches

2007 ◽  
Vol 13 (2) ◽  
pp. 378-395 ◽  
Author(s):  
Claude Le Bris ◽  
Mazyar Mirrahimi ◽  
Herschel Rabitz ◽  
Gabriel Turinici
Keyword(s):  
Quantum Systems ◽  
Well Posedness ◽  
Numerical Approaches

scholarly journals A Fast High-Order Total Variation Minimization Method for Multiplicative Noise Removal

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Xiao-Guang Lv ◽  
Jiang Le ◽  
Jin Huang ◽  
Liu Jun
Keyword(s):  
Total Variation ◽  
Multiplicative Noise ◽  
Noise Removal ◽  
High Order ◽  
Alternating Minimization ◽  
Minimization Method ◽  
Total Variation Minimization ◽  
Alternating Minimization Algorithm ◽  
Staircase Effect ◽  
Multiplicative Noise Removal

Multiplicative noise removal problem has received considerable attention in recent years. The total variation regularization method for the solution of the noise removal problem can preserve edges well but has the sometimes undesirable staircase effect. In this paper, we propose a fast high-order total variation minimization method to restore multiplicative noisy images. The proposed method is able to preserve edges and at the same time avoid the staircase effect in the smooth regions. An alternating minimization algorithm is employed to solve the proposed high-order total variation minimization problem. We discuss the convergence of the alternating minimization algorithm. Some numerical results show that the proposed method gives restored images of higher quality than some existing multiplicative noise removal methods.

scholarly journals On Fixed-Point Smoothing for Descriptor Systems with Multiplicative Noise and Single Delayed Observations

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Xiao Lu ◽  
Xin Dong ◽  
Haixia Wang ◽  
Baoye Song
Keyword(s):  
Fixed Point ◽  
Singular Value Decomposition ◽  
Multiplicative Noise ◽  
Singular Value ◽  
Descriptor Systems ◽  
Multiplicative Noises ◽  
Different Types ◽  
Delayed System ◽  
Reorganized Innovation ◽  
Value Decomposition

Optimal fixed-point smoothing problem for the descriptor systems with multiplicative noises is considered, where instantaneous and delayed observations are available. Standard singular value decomposition is used to give the restricted equivalent delayed system, where the observations also include two different types of measurements. Reorganized innovation lemma and projection theorem are used to give the fixed-point smoother for the restricted equivalent delayed system. The fixed-point smoother is given in terms of recursive Riccati equations.

scholarly journals Multiplicative Noise Removal Based on the Linear Alternating Direction Method for a Hybrid Variational Model

2017 ◽  
Vol 2017 ◽  
pp. 1-10
Author(s):  
Yan Hao ◽  
Jianlou Xu ◽  
Fengyun Zhang ◽  
Xiaobo Zhang
Keyword(s):  
Total Variation ◽  
Multiplicative Noise ◽  
Splitting Method ◽  
Noise Removal ◽  
Variational Model ◽  
Total Variation Regularization ◽  
Alternating Direction ◽  
Staircase Effect ◽  
Multiplicative Noise Removal ◽  
Alternative Direction Method

To preserve the edge, multiplicative noise removal models based on the total variation regularization have been widely studied, but they suffer from the staircase effect. In this paper, to preserve the edge and reduce the staircase effect, we develop a hybrid variational model based on the variable splitting method for multiplicative noise removal; the new model is a strictly convex objective function which contains the total variation regularization and a modified regularization term. We use the linear alternative direction method to find the minimal solution and also give the convergence proof of the proposed algorithm. Experimental results verify that the proposed model can obtain the better results for removing the multiplicative noise compared with the recent method.

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