In this paper Total variation is utilized as a prominent and effectual image prior model in the regularization based image processing fields. Nonetheless, as the total variation model supports a piecewise steady solution, this process comes under high intensity noise in the level areas of the picture is often poor, and a few pseudo edges are formed. In this work we develop a spatially adaptive total variation model. At first, the spatial information is extracted supported each and every pixel, and at that point 2 filtering process are added to restrain the impact of pseudo edges. In addition of this, the spatial info weight is built and classified with k-means clustering, and also the regularization strength in every region is controlled by center value of the cluster. The exploratory results, on both simulated and genuine datasets, demonstrate that the proposed methodology can adequately diminish the pseudo edges of the total variation regularization in the flat areas, and keep up the partial smoothness of the HR images. If we compare the traditional pixel based spatial information adaptive methodology, the proposed region based spatial information adaptive variation model can effectively reduce the effect of noise on the spatial data extraction and maintain strength with changes in the noise intensity in the SR process.

The traditional median filter can handle the image salt and pepper noise better. However, when the noise intensity is large, it is often necessary to enlarge the filter window to ensure the denoising effect, but the enlarged window may also cause excessive smoothing of the image, loss of texture details, and blurred edges. In view of the strong edge preservation characteristics of variational model denoising, we propose a salt and pepper noise removal method based on the edge-adaptive total variational model. Firstly, the image is segmented into edge regions and non-edge regions by edge detection operators. Secondly, the salt and pepper noise of the image is processed using the median filter and adaptive total variation model, respectively. Lastly, the non-edge regions processed by the median filter and the edge regions processed by the adaptive total variation model are extracted for splicing. The experimental results show that the method cannot only effectively remove salt and pepper noise, but also effectively protect the main edge details of the image.

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.

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.

Recently, low-rank regularization has achieved great success in tensor completion. However, only considering the global low-rankness is not sufficient, especially for a low sampling rate (SR). Total variation (TV) is introduced into low-rank tensor completion (LRTC) problem to promote the local smoothness by incorporating the first-order derivatives information. However, TV usually leads to undesirable staircase effects. To alleviate these staircase effects, we suggest a first- and second-order TV-based parallel matrix factorization model for LRTC problem, which integrates the local smoothness and global low-rankness by simultaneously exploiting the first- and second-order derivatives information. To solve the proposed model, an efficient proximal alternating optimization (PAO)-based algorithm is developed with theoretical guarantee. Moreover, we suggest a regularization parameter selection strategy to automatically update two regularization parameters, which is able to take advantage of the best properties of each of the two regularization terms. Extensive experiments on different tensor data show the superiority of the proposed method over other methods, particularly for extremely low SRs.

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.

We propose an adaptive total variation (TV) model by introducing the steerable filter into the TV‐based diffusion process for image filtering. The local energy measured by the steerable filter can effectively characterize the object edges and ramp regions and guide the TV‐based diffusion process so that the new model behaves like the TV model at edges and leads to linear diffusion in flat and ramp regions. This way, the proposed model can provide a better image processing tool which enables noise removal, edge‐preserving, and staircase suppression.

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.

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.

The amount of noise included in a hyperspectral image limits its application and has a negative impact on hyperspectral image classification, unmixing, target detection, and so on. In hyperspectral images, because the noise intensity in different bands is different, to better suppress the noise in the high-noise-intensity bands and preserve the detailed information in the low-noise-intensity bands, the denoising strength should be adaptively adjusted with the noise intensity in the different bands. Meanwhile, in the same band, there exist different spatial property regions, such as homogeneous regions and edge or texture regions; to better reduce the noise in the homogeneous regions and preserve the edge and texture information, the denoising strength applied to pixels in different spatial property regions should also be different. Therefore, in this paper, we propose a hyperspectral image denoising algorithm employing a spectral-spatial adaptive total variation (TV) model, in which the spectral noise differences and spatial information differences are both considered in the process of noise reduction. To reduce the computational load in the denoising process, the split Bregman iteration algorithm is employed to optimize the spectral-spatial hyperspectral TV model and accelerate the speed of hyperspectral image denoising. A number of experiments illustrate that the proposed approach can satisfactorily realize the spectral-spatial adaptive mechanism in the denoising process, and superior denoising results are produced.

The vectorial total variation model and algorithm are studied for multi-channel SAR image denoising.After introducing the vectorial total variation model,an accelerative fix-point iterative algorithm was proposed and its convergence was proved.By improving the filter coefficient of the fix-point iterative process,an adaptive vectorial total variation model was developed for multi-channel SAR image denoising,whose iterative algorithm and convergence theorem were present.The performance of denoising and resolution preservation of our models was tested by multi-polarimetric,multi-temporal RADARSAT-2 images,in addition to the validation of the convergence and the convergent speed of the proposed algorithms.

Image Restoration Employing a Local Structural Adaptive Total Variation Model

In this letter, a novel adaptive total variation (ATV) model is proposed for image inpainting. The classical TV model is a partial differential equation (PDE)-based technique. While the TV model can preserve the image edges well, it has some drawbacks, such as staircase effect in the inpainted image and slow convergence rate. By analyzing the diffusion mechanism of TV model and introducing a new edge detection operator named difference curvature, we propose a novel ATV inpainting model. The proposed ATV model can diffuse the image information smoothly and quickly, namely, this model not only eliminates the staircase effect but also accelerates the convergence rate. Experimental results demonstrate the effectiveness of the proposed scheme.

The adaptive fidelity model and adaptive total variation(ATV) model are analyzed,and the strongpoint and disadvantage of the variational method models are compared according to experiments.The ATV model and texture preserving adaptive fidelity model are combined to deduce a gradient descent flow,and the result proved that it can remove noise effectively applying to remote sensing images,at the same time,the textures of the images are preserved.Finally,improved research tasks needed by remote sensing image noise removal based on partial differential equation are discussed.

Total variation, adaptive total variation and nonconvex smoothly clipped absolute deviation penalty for denoising blocky images

该文提出了一种新的结合非下采样Contourlet变换(NSCT)和自适应全变差模型的图像去噪方法。首先通过NSCT对含噪图像进行分解，根据高斯比例混合(GSM)模型建立图像模型；然后利用贝叶斯估计进行图像去噪，重构后得到初次去噪图像；最后，结合自适应全变差模型对初次去噪图像进行重构滤波，得到最终的去噪图像。实验结果表明，该方法可以有效地消除图像中的Gibbs伪影及噪声，在去噪图像峰值信噪比(PSNR)和边缘保持性能上都优于已有的算法。