Multiplicative Noise Removal Research Articles

Image Denoising via Improved Dictionary Learning with Global Structure and Local Similarity Preservations

We proposed a new efficient image denoising scheme, which leads to four important contributions. The first is to integrate both reconstruction and learning based approaches into a single model so that we are able to benefit advantages from both approaches simultaneously. The second is to handle both multiplicative and additive noise removal problems. The third is that the proposed approach introduces a sparse term to reduce non-Gaussian outliers from multiplicative noise and uses a Laplacian Schatten norm to capture the global structure information. In addition, the image is represented by preserving the intrinsic local similarity via a sparse coding method, which allows our model to incorporate both global and local information from the image. Finally, we propose a new method that combines Method of Optimal Directions (MOD) with Approximate K-SVD (AK-SVD) for dictionary learning. Extensive experimental results show that the proposed scheme is competitive against some of the state-of-the-art denoising algorithms.

Optimization model for multiplicative noise and blur removal based on Gaussian curvature regularization.

In this paper, we focus on the restoration of images that are simultaneously blurred and corrupted by multiplicative noise. First, we introduce a variational restoration model consisting of the convex data-fitting term and the Gaussian curvature of the image as a regularizer to remove multiplicative Gamma noise because it is able to eliminate staircase effects while preserving sharp edges, textures, and other fine structures of the image. We then propose computing the minimizers of our restoration functionals by applying the augmented Lagrange multiplier method with splitting techniques. The numerical results in this paper show that our method has the potential to outperform other approaches in multiplicative noise removal with simultaneous deblurring.

Multiplicative noise and blur removal by Framelet Expansion and Variable Decomposition

Multiplicative noise and blur removal by Framelet Expansion and Variable Decomposition

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.

TGV-based multiplicative noise removal approach: Models and algorithms

Abstract Total variation (TV) based models have been used widely in multiplicative denoising problem. However, these models are always accompanied by an unsatisfactory effect named staircase due to the property of BV space. In this paper, we present two high-order variational models based on total generalized variation (TGV) for two kinds of multiplicative noises. The proposed models reduce the staircase while preserving the edges. In the meantime we develop an efficient algorithm which is called Prediction-Correction proximal alternative direction method of multipliers (PADMM) to solve our models. Moreover, we show the convergence of our algorithm under certain conditions. Numerical experiments demonstrate that our high-order models outperform the classical TV-based models in PSNR and SSIM values.

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.

An Exp Model with Spatially Adaptive Regularization Parameters for Multiplicative Noise Removal

This article proposes a total variation (TV) based model with local constraints for heavy multiplicative noise removal. The local constraint involves multiple local windows rather than one local window as in Chen and Cheng (IEEE Trans Image Process 21(4):1650–1662, 2012), and the proposed model is an extension model of Lu et al. (Appl Comput Harmon Anal 41(2):518–539, 2016) that incorporates a spatially adaptive regularization parameter, which enables us to handle heavy multiplicative noise as well as to sufficiently denoise in homogeneous regions while preserving small details and edges. In addition, convergence analysis such as the existence and uniqueness of a solution for our model is also provided. We also derive an optimization algorithm from the first-order optimality characterization of our model. Furthermore, we utilize a proximal linearized alternating direction algorithm for efficiently solving our subproblem. Numerical results are shown to validate the effectiveness of our model, with comparisons with several existing TV based models.

Multiplicative noise removal via combining total variation and wavelet frame

ABSTRACTTotal variation (TV) regularization has been proved effective for cartoon images restoration however it produces staircase effects, and properly wavelet frames were confirmed to provide a more smoothing approximation to the original image. In this paper, a new model for multiplicative noise removal was proposed, which combines wavelet frame-based regularization and TV regularization. A modified proximal linearized alternating direction method is developed to solve the proposed model, considering that adding a new regularization term to the TV model would yield more parameters, which will result in computational difficulties. For the new model, the existence of solution and the convergence property of the proposed algorithm are proved. Numerical experiments have proved that the proposed model has a superior performance in terms of the peak signal-to-noise ratio and the relative error values for non-piecewise constant images when compared with some state-of-the-art multiplicative noise removal models.

A doubly degenerate diffusion equation in multiplicative noise removal models

In this paper, we consider the Neumann problem of a doubly degenerate diffusion equation which is proposed to deal with multiplicative noise. We prove the existence and the extremum principle of weak solutions for the problem.

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.

A New Variational Approach for Multiplicative Noise and Blur Removal.

This paper proposes a new variational model for joint multiplicative denoising and deblurring. It combines a total generalized variation filter (which has been proved to be able to reduce the blocky-effects by being aware of high-order smoothness) and shearlet transform (that effectively preserves anisotropic image features such as sharp edges, curves and so on). The new model takes the advantage of both regularizers since it is able to minimize the staircase effects while preserving sharp edges, textures and other fine image details. The existence and uniqueness of a solution to the proposed variational model is also discussed. The resulting energy functional is then solved by using alternating direction method of multipliers. Numerical experiments showing that the proposed model achieves satisfactory restoration results, both visually and quantitatively in handling the blur (motion, Gaussian, disk, and Moffat) and multiplicative noise (Gaussian, Gamma, or Rayleigh) reduction. A comparison with other recent methods in this field is provided as well. The proposed model can also be applied for restoring both single and multi-channel images contaminated with multiplicative noise, and permit cross-channel blurs when the underlying image has more than one channel. Numerical tests on color images are conducted to demonstrate the effectiveness of the proposed model.

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

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.

Multiplicative noise removal with a sparsity-aware optimization model

Restoration of images contaminated by multiplicative noise (also known as speckle noise) is a key issue in coherent image processing. Notice that images under consideration are often highly compressible in certain suitably chosen transform domains. By exploring this intrinsic feature embedded in images, this paper introduces a variational restoration model for multiplicative noise reduction that consists of a term reflecting the observed image and multiplicative noise, a quadratic term measuring the closeness of the underlying image in a transform domain to a sparse vector, and a sparse regularizer for removing multiplicative noise. Being different from popular existing models which focus on pursuing convexity, the proposed sparsity-aware model may be nonconvex depending on the conditions of the parameters of the model for achieving the optimal denoising performance. An algorithm for finding a critical point of the objective function of the model is developed based on coupled fixed-point equations expressed in terms of the proximity operator of functions that appear in the objective function. Convergence analysis of the algorithm is provided. Experimental results are shown to demonstrate that the proposed iterative algorithm is sensitive to some initializations for obtaining the best restoration results. We observe that the proposed method with SAR-BM3D filtering images as initial estimates can remarkably outperform several state-of-art methods in terms of the quality of the restored images.

Digital Path Approach Despeckle Filter for Ultrasound Imaging and Video.

We propose a novel filtering technique capable of reducing the multiplicative noise in ultrasound images that is an extension of the denoising algorithms based on the concept of digital paths. In this approach, the filter weights are calculated taking into account the similarity between pixel intensities that belongs to the local neighborhood of the processed pixel, which is called a path. The output of the filter is estimated as the weighted average of pixels connected by the paths. The way of creating paths is pivotal and determines the effectiveness and computational complexity of the proposed filtering design. Such procedure can be effective for different types of noise but fail in the presence of multiplicative noise. To increase the filtering efficiency for this type of disturbances, we introduce some improvements of the basic concept and new classes of similarity functions and finally extend our techniques to a spatiotemporal domain. The experimental results prove that the proposed algorithm provides the comparable results with the state-of-the-art techniques for multiplicative noise removal in ultrasound images and it can be applied for real-time image enhancement of video streams.

Higher order operator splitting methods for an image de-noising model

This paper is concerned with fast iterative methods with development of Euler-Lagrange equation which results from the minimization of Rudin-Osher-Fatemi (ROF) model. There are many applications of image de-noising in field of medical and astronomy. We can classify the image de-noising models into additive and multiplicative noise removal models. In case of additive noise, we have an image u corrupted with additive Gaussian noise η, the main task is to recover u from the image formation model u0 = u+η. This paper mainly focus on additive noise removal. Here semi-implicit (SIM), additive operator splitting (AOS) and additive multiplicative operator splitting (AMOS) type schemes are developed. The quality in AOS is, it treats with all coordinate axes in an equal manner. We develop a new AMOS scheme for the solution of Euler-Lagrange equation arisen from minimization of image additive noise removal model. Comparison of AMOS with SIM and AOS is also presented. Experimental results shows that by using AMOS, additive noisy image can be de-noised with best results. Numerical examples are given to show gain in CPU timing and fast convergence of AMOS-based algorithm. https://doi.org/10.28919/jmcs/3312

Measurement of the unsteady lift of thick airfoils in incompressible turbulent flow

The unsteady lift spectrum for airfoils in turbulent flow has been measured in a water tunnel experiment. The results provide validation data for analytical models that account for the effect of airfoil thickness on the high frequency gust response. A series of four airfoils with elliptical leading edge profiles and thickness-to-chord ratios ranging from 8% to 16% were tested in grid-generated turbulence. The turbulent velocity spectrum was measured using Laser Doppler Velocimetry, and was found to be reasonably well approximated by an isotropic, homogeneous turbulence model. The unsteady force measurement setup and calibration procedure were designed to minimize the effect of system resonances, and contamination from facility vibration was reduced using a multiple coherence noise removal technique. Measurements of the unsteady lift spectrum were made at six speeds over the Reynolds number range 0.5–1.6million, and the results were collapsed into a non-dimensional force spectrum for the non-dimensional frequency range 1<fc/U∞<10. The experimental results agree very well with theory and confirm the importance of accounting for thickness to avoid overprediction of the forces in the high frequency range.

Multiplicative Noise and Blur Removal by Framelet Decomposition and -Based L-Curve Method.

This paper proposes a framelet-based convex optimization model for multiplicative noise and blur removal problem. The main idea is to employ framelet expansion to represent the original image and use the variable decomposition to solve the problem. Because of the nature of multiplicative noise, we decompose the observed data into the original image variable and the noise variable to obtain the resulting model. The original image variable is represented by framelet, and it is determined by using l1-norm in the selection and shrinkage of framelet coefficients. The noise variable is measured by using the mean and the variance of the underlying probability distribution. This framelet setting can be applied to analysis, synthesis, and balanced approaches, and the resulting optimization models are convex, such that they can be solved very efficiently by the alternating direction of a multiplier method. An another contribution of this paper is to propose to select the regularization parameter by using the l1-based L-curve method for these framelet based models. Numerical examples are presented to illustrate the effectiveness of these models and show that the performance of the proposed method is better than that by the existing methods.

Multiplicative noise removal using primal–dual and reweighted alternating minimization

Multiplicative noise removal is an important research topic in image processing field. An algorithm using reweighted alternating minimization to remove this kind of noise is proposed in our preliminary work. While achieving good results, a small parameter is needed to avoid the denominator vanishing. We find that the parameter has important influence on numerical results and has to be chosen carefully. In this paper a primal–dual algorithm is designed without the artificial parameter. Numerical experiments show that the new algorithm can get a good visual quality, overcome staircase effects and preserve the edges, while maintaining high signal-to-noise ratio.

A hybrid optimization method for multiplicative noise and blur removal

The main contribution of this paper is to propose a new hybrid optimization method for the multiplicative noise and blur removal problem. A degraded image can often be recovered efficiently by minimizing an objective function which consists of a data-fidelity term and a regularization term. In the paper, we apply the quadratic penalty function method combined with the alternating direction method to minimize the corresponding objective function. Numerical experiments are presented to demonstrate the effectiveness of the proposed method. Experimental results illustrate the state-of-the-art performance of the proposed method to handle multiplicative noise and blur removal problem.