Multiplicative Noise Removal Problem Research Articles

Fractional-order diffusion coupled with integer-order diffusion for multiplicative noise removal

The problem of multiplicative noise removal has attracted much attention in recent years. Unlike additive noise, multiplicative noise destroys almost all information of an image; therefore, it is more difficult to remove them from corrupted images. In this paper, we propose a denoising model of fractional-order diffusion coupled with integer-order diffusion for multiplicative gamma noise, which takes advantage of both texture-preserving property of fractional-order diffusion and edge-preserving property of integer-order diffusion. We explore the mutual mechanism of two diffusion equations in the diffusion process, i.e., mutual transfer of texture and edge information respectively from two filtering images, and mutual regularization on the diffusion coefficients in both equations. We design an alternating numerical scheme based on semi-implicit finite difference and discrete Fourier transform for solving the coupled diffusion system. The proposed model is tested on some commonly-used images and is compared with six state-of-the-art models, qualitatively and quantitatively. Experimental results show the superiority of the proposed model in reducing multiplicative gamma noise while preserving textures and edges.

Total generalized variation denoising of speckled images using a primal-dual algorithm

In this paper, multiplicative noise removal problem is considered. Multiplicative noise is also commonly referred to as speckle. We propose a total generalized variation (TGV) based model which involves the multilook M for multiplicative noise removal. The objective function of our proposed model is strictly convex. Computationally, by using the dual representation of the second-order TGV regularization, our proposed model is transformed into a minimax problem. A first-order primal-dual algorithm is developed to solve the minimax problem and the convergence of the proposed algorithm is strictly proved. At last, compared with several existing methods, experimental results demonstrate the effectiveness of the proposed method, in terms of signal-to-noise ratio, peak signal-to-noise ratio and mean absolute-deviation error.

A convex nonlocal total variation regularization algorithm for multiplicative noise removal

This study proposes a nonlocal total variation restoration method to address multiplicative noise removal problems. The strictly convex, objective, nonlocal, total variation effectively utilizes prior information about the multiplicative noise and uses the maximum a posteriori estimator (MAP). An efficient iterative multivariable minimization algorithm is then designed to optimize our proposed model. Finally, we provide a rigorous convergence analysis of the alternating multivariable minimization iteration. The experimental results demonstrate that our proposed model outperforms other currently related models both in terms of evaluation indices and image visual quality.

Multiplicative Noise Removal Based on the Smooth Diffusion Equation

The multiplicative noise removal problem is of momentous significance in various image processing applications. In this paper, a nonlinear diffusion equation with smooth solution is proposed to remove multiplicative Gamma noise. The diffusion coefficient takes full advantage of two features of multiplicative noise image, namely, gradient information and gray level information, which makes the model has the ability to remove high level noise effectively and protect the edges. The existence of the solution has been analyzed by Schauder’s fixed-point theorem. Some other theoretical properties such as the maximum principle are also presented in the paper. In the numerical aspect, the explicit finite difference method, fast explicit diffusion method, additive operator splitting method and Krylov subspace spectral method are employed to implement the proposed model. Experimental results show that the fast explicit diffusion method achieves a better trade-off between computational time and denoising performance, and the Krylov subspace spectral method gets better restored results in the visual aspect. In addition, the capability of the proposed model for denoising is illustrated by comparison with other denoising models.

Multiplicative Noise Removal for Texture Images Based on Adaptive Anisotropic Fractional Diffusion Equations

Multiplicative noise removal problems have attracted much attention in recent years. Unlike additive noise removal problems, multiplicative noise destroys almost all information of the original ima...

Variational total curvature model for multiplicative noise removal

The multiplicative noise removal problem has received considerable attention recently. To solve this problem, various variational models have been proposed, which minimise an energy functional composed of the data term and the regularisation term. Regarding the regularisation term, a first-order model is frequently used to remove multiplicative noise, which may cause staircase effect and loss of contrast in the output image. In this study, the authors use a second-order model, the total curvature (TC), to solve the above problem. The TC model has the benefit of removing the staircase effect and maintaining image edges, contrasts and corners. The augmented Lagrange method is utilised to solve the proposed TC model by introducing auxiliary variables, Lagrange multipliers and using alternating optimisation strategy. In each loop of optimisation, the fast Fourier transform, generalised soft threshold formulas, projection method and gradient descent method are integrated effectively. The experimental results show that the TC model can effectively remove staircase effect and preserve smoothness, via comparison with the first-order model (total variation regularisation and Perona-Malik regularisation). Furthermore, the TC model is better than another second-order model based on bounded Hessian regularisation in preserving contrast and corner.

Root-transformation based multiplicative denoising model and its statistical analysis

Abstract This paper focuses on the problem of multiplicative noise removal. Based on the statistical properties of the noise distribution, a quadratic penalty term which well models the priori distribution of the mth root of the noise is introduced to the denoising scheme. The new model enjoys the merit of its unconditional convexity, and the global optimum is easily obtainable by convex optimization algorithms. Moreover, an accurate estimated root order m can better reflect the statistical characteristics of the noise, resulting in a significant promotion on the performance. To solve the proposed model efficiently, a modified alternating direction method of multipliers is introduced. In the experiments, the influence of the parameter m is explicitly discussed, the denoising performance of the proposed model is compared with several state-of-the-art variational methods. The results confirm the superiority of the proposed method over others.

Multiplicative Noise Removal Based on Unbiased Box-Cox Transformation

AbstractMultiplicative noise removal is a challenging problem in image restoration. In this paper, by applying Box-Cox transformation, we convert the multiplicative noise removal problem into the additive noise removal problem and the block matching three dimensional (BM3D) method is applied to get the final recovered image. Indeed, BM3D is an effective method to remove additive Gaussian white noise in images. A maximum likelihood method is designed to determine the parameter in the Box-Cox transformation. We also present the unbiased inverse transform for the Box-Cox transformation which is important. Both theoretical analysis and experimental results illustrate clearly that the proposed method can remove multiplicative noise very well especially when multiplicative noise is heavy. The proposed method is superior to the existing methods for multiplicative noise removal in the literature.

Sparse analysis model based multiplicative noise removal with enhanced regularization

The multiplicative noise removal problem for a corrupted image has recently been considered under the framework of regularization based approaches, where the regularizations are typically defined on sparse dictionaries and/or total variation (TV). This framework was demonstrated to be effective. However, the sparse regularizers used so far are based overwhelmingly on the synthesis model, and the TV based regularizer may induce the stair-casing effect in the reconstructed image. In this paper, we propose a new method using a sparse analysis model. Our formulation contains a data fidelity term derived from the distribution of the noise and two regularizers. One regularizer employs a learned analysis dictionary, and the other regularizer is an enhanced TV by introducing a parameter to control the smoothness constraint defined on pixel-wise differences. To address the resulting optimization problem, we adapt the alternating direction method of multipliers (ADMM) framework, and present a new method where a relaxation technique is developed to update the variables flexibly with either image patches or the whole image, as required by the learned dictionary and the enhanced TV regularizers, respectively. Experimental results demonstrate the improved performance of the proposed method as compared with several recent baseline methods, especially for relatively high noise levels.

Multiplicative noise removal via adaptive learned dictionaries and TV regularization

Multiplicative noise removal is a key issue in image processing problem. While a large amount of literature on this subject are total variation (TV)-based and wavelet-based methods, recently sparse representation of images has shown to be efficient approach for image restoration. TV regularization is efficient to restore cartoon images while dictionaries are well adapted to textures and some tricky structures. Following this idea, in this paper, we propose an approach that combines the advantages of sparse representation over dictionary learning and TV regularization method. The method is proposed to solve multiplicative noise removal problem by minimizing the energy functional, which is composed of the data-fidelity term, a sparse representation prior over adaptive learned dictionaries, and TV regularization term. The optimization problem can be efficiently solved by the split Bregman algorithm. Experimental results validate that the proposed model has a superior performance than many recent methods, in terms of peak signal-to-noise ratio, mean absolute-deviation error, mean structure similarity, and subjective visual quality.

Adaptive Multiplicative Noise Removal Model Using Pixel Related Smoothing Term

Multiplicative noise removal problems have attracted much attention in recent years. In this paper, we propose a new adaptive multiplicative noise removal algorithm based on variational method. By analysis the shortcoming of Euler- Lagrange equation, we find that these traditional variational models are not fitted for multiplicative noise very well. The amount of multiplicative noise is relative with the pixel value. That is to say, areas with large pixel value should be smoothed much than areas with small pixel value. So we modified the Euler-Lagrange equation by changing the balance parameter to the pixel related one, then we deduce our modified energy equation. The balance of fidelity term and regular- ization term in our changed model can be changed in different areas with different gray value. Thus in iterating procedure, our method can change the degree of noise removing in different areas with different noise level adaptively. It can also preserve the edges and remove the noise very well. The results show the outperforming effect of our method.

A Variational Model for Removing Multiple Multiplicative Noises

The problem of multiplicative noise removal has been widely studied in recent years. Many methods have been used to remove it, but the final results are not very excellent. The total variation regularization method to solve the problem of the noise removal can preserve edge well, but sometimes produces undesirable staircasing effect. In this paper, we propose a variational model to remove multiplicative noise. An alternative algorithm is employed to solve variational model minimization problem. Experimental results show that the proposed model can not only effectively remove Gamma noise, but also Rayleigh noise, as well as the staircasing effect is significantly reduced.

An effective dual method for multiplicative noise removal

The problem of multiplicative noise removal has been widely studied recently, but most models focus on the unconstrained problems. These models require knowing the prior level of noise beforehand, however, the information is not obtained in some case and the regularization parameters are not easy to be adjusted. Thus, in the paper, we mainly study an optimization problem with total variation constraint, and propose two new denoising algorithms which compute the projection on the set of images whose total variation is bounded by a constant. In the first algorithm, we firstly give the dual formula of our model, then compute the dual problem using alternating direction method of multipliers. Experimental results show that our method is simple and efficient to filter out the multiplicative noise when the prior of noise is unknown.

Multiplicative Noise Removal by a Fast Hybrid Total Variation Minimization Method

The multiplicative noise removal problem from laser imaging, synthetic aperture radar and ultrasound imaging has received considerable attention in recent years. In this paper, we propose a fast hybrid total variation minimization method to restore multiplicative noisy images. The proposed method can reduce the staircase effect and preserve edges in the restored images. An alternating minimization algorithm is employed to solve the proposed total variation minimization problem. We discuss the convergence of the alternating minimization algorithm. Numerical experiments are given to illustrate the performance of the proposed method.

A Convex Adaptive Total Variation Model Based on the Gray Level Indicator for Multiplicative Noise Removal

This paper focuses on the problem of multiplicative noise removal. Using a gray level indicator, we derive a new functional which consists of the adaptive total variation term and the global convex fidelity term. We prove the existence, uniqueness, and comparison principle of the minimizer for the variational problem. The existence, uniqueness, and long-time behavior of the associated evolution equation are established. Finally, experimental results illustrate the effectiveness of the model in multiplicative noise reduction. Different from the other methods, the parameters in the proposed algorithms are found dynamically.

A Fast High-Order Total Variation Minimization Method for 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.

Fast algorithm for multiplicative noise removal

In this work, we consider a variational restoration model for multiplicative noise removal problem. By using a maximum a posteriori estimator, we propose a strictly convex objective functional whose minimizer corresponds to the denoised image we want to recover. We incorporate the anisotropic total variation regularization in the objective functional in order to preserve the edges well. A fast alternating minimization algorithm is established to find the minimizer of the objective functional efficiently. We also give the convergence of this minimization algorithm. A broad range of numerical results are given to prove the effectiveness of our proposed model.

A New Total Variation Method for Multiplicative Noise Removal

Multiplicative noise removal problems have attracted much attention in recent years. Unlike additive noise removal problems, the noise is multiplied to the orginal image, so almost all information of the original image may disappear in the observed image. The main aim of this paper is to propose and study a strictly convex objective function for multiplicative noise removal problems. We also incorporate the modified total variation regularization in the objective function to recover image edges. We develop an alternating minimization algorithm to find the minimizer of such an objective function efficiently and also show the convergence of the minimizing method. Our experimental results show that the quality of images denoised by the proposed method is quite good.

A Variational Approach to Removing Multiplicative Noise

This paper focuses on the problem of multiplicative noise removal. We draw our inspiration from the modeling of speckle noise. By using a MAP estimator, we can derive a functional whose minimizer corresponds to the denoised image we want to recover. Although the functional is not convex, we prove the existence of a minimizer and we show the capability of our model on some numerical examples. We study the associated evolution problem, for which we derive existence and uniqueness results for the solution. We prove the convergence of an implicit scheme to compute the solution.