An Algorithm for Image Denoising Based on Adaptive Total Variation

The noise pollution in tourist street view images is caused by various reasons. A major challenge that researchers have been facing is to find a way to effectively remove noise. Although in the past few decades people have proposed many methods of denoising tourist street scene images, the research on denoising technology of tourist street scene images is still not outdated. There is no doubt that it has become a basic and important research topic in the field of digital image processing. The evolutionary diffusion method based on partial differential equations is helpful to improve the quality of noisy tourist street scene images. This method can process tourist street scene images according to people’s expected diffusion behavior. The adaptive total variation model proposed in this paper is improved on the basis of the total variation model and the Gaussian thermal diffusion model. We analyze the classic variational PDE-based denoising model and get a unified variational PDE energy functional model. We also give a detailed analysis of the diffusion performance of the total variational model and then propose an adaptive total variational diffusion model. By improving the diffusion coefficient and introducing a curvature operator that can distinguish details such as edges, it can effectively denoise the tourist street scene image, and it also has a good effect on avoiding the step effect. Through the improvement of the ROF model, the loyalty term and regular term of the model are parameterized, the adaptive total variation denoising model of this paper is established, and a detailed analysis is carried out. The experimental results show that compared with some traditional denoising models, the model in this paper can effectively suppress the step effect in the denoising process, while protecting the texture details of the edge area of the tourist street scene image. In addition, the model in this paper is superior to traditional denoising models in terms of denoising performance and texture structure protection.

Total variation has been used as a popular and effective image prior model in the regularization-based image processing fields. However, as the total variation model favors a piecewise constant solution, the processing result under high noise intensity in the flat regions of the image is often poor, and some “pseudo-edges” are produced. In this paper, we develop a regional spatially adaptive total variation (RSATV) model. Firstly, the spatial information is extracted based on each pixel, and then two filtering processes are respectively added to suppress the effect of “pseudo-edges”. After that, the spatial information weight is constructed and classified with kmeans clustering, and the regularization strength in each region is controlled by the clustering center value. The experimental results, on both simulated and real datasets, show that the proposed approach can effectively reduce the “pseudo-edges” of the total variation regularization in the flat regions, and maintain the partial smoothness of the highresolution image. More importantly, compared with the traditional pixel-based spatial information adaptive approach, the proposed region-based spatial information adaptive total variation model can better avoid the effect of noise on the spatial information extraction, and maintains robustness with changes in the noise intensity in the super-resolution process. Index Terms—Super-resolution, total variation, regional spatially adaptive, majorization-minimization

Traditional total variation model leads to an undesirable staircase effect and is hard to eliminate high frequency noises in image restoration. In this paper, to solve this problem, a novel image restoration model based on adaptive total variation is proposed. A gradient fidelity term is coupled with adaptive total variation model. In order to choose proper parameters, the parameter selection criteria are analyzed theoretically, and a simple scheme to demonstrate its validity is adopted experimentally. To make fair comparisons of performances of three models, the same numerical algorithm is used to solve partial differential equations. Experimental results illustrate that the new model not only preserves the edge and important details but also alleviates the staircase effect effectively.

Traditional total variation model often leads to an undesirable staircase effect. In this paper, a new image restoration model based on adaptive total variation is proposed to solve the problem. It couples adaptive total variation model with a gradient fidelity term. The validity of the model and uniqueness of the solution are demonstrated theoretically. In the algorithm processing, a more reasonable Laplace operator solution is used to keep better rotational invariance. Experimental results illustrate the coupled model not only preserves the edge and some important details but also avoids the staircase effect in smooth regions effectively.

Denoising algorithms such as Total Variation model modify smooth areas in images into piecewise constant patches and small scale details and textures present in the original image are not preserved satisfactorily by these processes. In this paper, we present an algorithm based on an adaptive Total Variation norm of the gradient of the image, with a family of local constraints for efficient denoising of natural images. In fact, natural images consist of smooth and textured regions. Staircase effect is reduced in smooth areas by using a modified Total Variation functional. The set of local constraints, one for each pixel in the image are able to preserve most of the fine details and textures in the images. Visual and quantitative results of proposed method are presented and are compared with results of existing methods.

In this paper, we introduce two novel total variation models to deal with speckle noise in ultrasound image in order to retain the fine details more effectively and to improve the speed of energy diffusion during the process. Firstly, two new convex functions are introduced as regularization term in the adaptive total variation model, and then, the diffusion performances of Hypersurface Total Variation (HYPTV) model and Logarithmic Total Variation (LOGTV) model are analyzed mathematically through the physical characteristics of local coordinates. We have shown that the larger positive parameter in the model is set, the greater energy diffusion speed appears to be, but it will cause the image to be too smooth that required adequate attention. Numerical experimental results show that our proposed LOGTV model for speckle noise removal is superior to traditional models, not only in visual effect but also in quantitative measures.

By analyzing three important denoising models: the harmonical model, the TV (total variation) model and the generalized TV model, we have proposed an adaptive one which is named `adaptive TV image denoising model'. On the basis of SNR of noisy images, this model can pretreat them with Gaussian filter, so as to overcome the staircase effect in the TV model. Then by utilizing the gradient information of every pixel point of the image, we can adaptively select the most appropriate denoising scheme. The results of numerical experiments show that this method can preserve significant image details while removing the noise. Compared with other variational denoising methods, especially at high noise levels, the method achieves at least about 1.0dB gain for Peak Signal to the Noise Ratio (as PSNR for short) measurement.

Total variation model of image denoising is easy to influence the gradient and lose the details of image. Due to these weaknesses, many adaptive total variation (ATV) models of image denoising have been proposed to eliminate the Gaussian noisy additive in the image. This paper implements the model through a numerical solution, where the gradient descent method is used to derive the partial differential equation (PDE) corresponding to the ATV model. First, based on Euler-Lagrange equation, a detailed derivation process for Partial Differential Equation is used to calculate the ATV model. Then, based on gradient descent method, a numerical calculation of the model is derived from the PDE using the Direct Difference Method. Finally, several different λ parameters are compared to produce different image denoising effects and the appropriate parameter λ value is determined. Experimental results prove that our proposed numerical calculation can effectively realize the ATV denoising model.

Image denoising is an important technology for image preprocessing. In recent years, the image denoising technology based on total variation (TV) has been rapidly developed. However, However, although it can preserve image details well, which generates obvious staircase effects. This is due to the traditional TV-based image denoising technology only applies the gradient information and ignored the local variance of the image. In order to suppress staircase effect, in this paper, a novel image denoising approach based on TV model and weighting function is proposed. First, the theory mechanism of staircase effect brought by the traditional TV model is analyzed. Second, the effects of weighting function on edge regions, flat regions, and gradation and detail regions are also analyzed. Third, based on the above analysis, an improved TV model is proposed. Finally, the image denoising approach is implemented by an iterative algorithm. The experimental results show that, compared with various state-of-the-art models denoising models, the proposed image denoising approach can effectively suppress the staircase effect of the traditional TV model in most cases, preserve the image details, and improve the image denoising performance.

Several methods based on Total Variation (TV) have been proposed for Hyperspectral Image (HSI) denoising. However, the TV terms of these methods just use various l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> norms and penalize image gradient magnitudes, having a negative influence on the preprocessing of HSI denoising and further HSI classification task. In this paper, a novel l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> Total Variation (l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> TV) is first introduced and analyzed for the HSI noise removal framework to preserve more information for classification. We propose a novel Tensor low-rank constraint and l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> Total Variation (TLR-l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> TV) model in this paper. l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> TV directly controls the number of non-zero gradients and focuses on recovering the sharp image edges. The spectral-spatial information among all bands is exploited uniformly for removing mixed noise, which facilitates the subsequent classification after denoising. Including the Weighted Sum of Weighted Nuclear Norm (WSWNN) and the Weighted Sum of Weighted Tensor Nuclear Norm (WSWTNN), we propose two TLR-l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> TV-based algorithms, namely WSWNN-l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> TV and WSWTNN-l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> TV. The Alternating Direction Method of Multipliers (ADMM) and the Augmented Lagrange Multiplier (ALM) are employed to solve the l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> TV model and TLR-l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> TV model, respectively. In both simulated and real data, the proposed models achieve superior performances in mixed noise removal of HSI. Especially, HSI classification accuracy is improved more effectively after denoising by the proposed TLR-l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> TV method.

Confocal laser scanning microscopy (CLSM) has emerged as one of the most advanced fluorescence cell imaging techniques in the field of biomedicine. However, fluorescence cell imaging is limited by spatial blur and additive white noise induced by the excitation light. In this paper, a spatially adaptive high-order total variation (SA-HOTV) model for weak fluorescence image restoration is proposed to conduct image restoration. The method consists of two steps: optimizing the deconvolution model of the fluorescence image by the generalized Lagrange equation and alternating direction method of multipliers (ADMM); using spatially adaptive parameters to balance the image fidelity and the staircase effect. Finally, an comparison of SA-HOTV model and Richardson-Lucy model with total variation (RL-TV model) indicates that the proposed method can preserve the image details ultimately, reduce the staircase effect substantially and further upgrade the quality of the restored weak fluorescence image.

Following the traditional total variational denoising model in removing medical image noise with blurred image texture details, among other problems, an adaptive medical image fractional-order total variational denoising model with an improved sparrow search algorithm is proposed in this study. This algorithm combines the characteristics of fractional-order differential operators and total variational models. The model preserves the weak texture region of the image improvement based on the unique amplitude-frequency characteristics of the fractional-order differential operator. The order of the fractional-order differential operator is adaptively determined by the improved sparrow search algorithm using both the sine search strategy and the diversity variation processing strategy, which can greatly improve the denoising ability of the fractional-order differential operator. The experimental results reveal that the model not only achieves the adaptivity of fractional-order total variable differential order, but also can effectively remove noise, preserve the texture structure of the image to the maximum extent, and improve the peak signal-to-noise ratio of the image; it also displays favorable prospects for applications in medical image denoising.

Total variation is used as a popular and effective image prior model in the regularization-based image processing fields. However, as the total variation model favors a piecewise constant solution, the processing result under high noise intensity in the flat regions of the image is often poor, and some pseudoedges are produced. In this paper, we develop a regional spatially adaptive total variation model. Initially, the spatial information is extracted based on each pixel, and then two filtering processes are added to suppress the effect of pseudoedges. In addition, the spatial information weight is constructed and classified with k-means clustering, and the regularization strength in each region is controlled by the clustering center value. The experimental results, on both simulated and real datasets, show that the proposed approach can effectively reduce the pseudoedges of the total variation regularization in the flat regions, and maintain the partial smoothness of the high-resolution image. More importantly, compared with the traditional pixel-based spatial information adaptive approach, the proposed region-based spatial information adaptive total variation model can better avoid the effect of noise on the spatial information extraction, and maintains robustness with changes in the noise intensity in the super-resolution process.

The problem for image restoration is usually reduced to a constraint optimization problem. Different choice of optimization operator leads to various restoration models, e.g. least squares model and original total variation (TV) model. The TV model and its modified version can efficiently preserve the edge of the restored image well, but there exist obvious staircases in smooth area of the restored image. To reduce those staircases, we propose a new modified TV model, by adding a constraint term for smooth area protection as a penalty function. The numerical experiment shows our model can not only preserve the edge as well as TV model, but also efficiently reduce the staircase appearing in the smooth areas. Furthermore, It is shown that the restored image by our model has higher signal-to-noise ratio, less mean square error and better visual effect than those by the least squares model and by the TV models.

Image denoising is an essential pre-processing step in medical imaging systems. In this paper, a new adaptive total variation based image regularization algorithm using structure tensor matrices is proposed to eliminate the Rician noise present in the magnetic resonance images. In the proposed algorithm a regularization term based on a variable exponent is used. The variable exponent as well as the regularization parameter in the energy functional both depend on the edge stopping function value. The edge stopping function value is based on the trace of structure tensor matrix. In the noisy inner region the value of the variable exponent becomes two that is in the inner region square of the gradient that is used as a regularization term. So the adaptive model behaves like a Tikhonov model and strong smoothing takes place in the flat inner region. At the object boundaries the variable exponent’s value becomes one that is simply a gradient of an image that is used as a regularizing term. So the model behaves like a Rudin-Osher-Fatemi model and the edges are preserved well. The weight of the fidelity term in the functional is also adaptively selected depending on whether a pixel belongs to an edge or the inner region. The weight of the fidelity term is set to a large value at the edges and the small value is in the inner region. The algorithm is found to be very efficient in removing Rician noise present in the brain’s magnetic resonance images compared to the other variable exponent based adaptive total variation models such as Chen model, Erik model, Chambolle model and Qiang Chen total variation model using difference curvature both qualitatively as well as quantitatively.