Denoising of Tourist Street Scene Image Based on ROF Model of Second-Order Partial Differential Equation

Although the traditional TV (Total Variation) model owns excellent image denoising ability, there are staircase effect problems for TV model. In this article, two detection operators for staircase effect problem are proposed. The staircase effect problem can be solved effectively by introducing two operators into traditional TV model. On the basis, it proposes an adaptive total variation model for image denoising. When dealing with image edge, it can still use the traditional TV model. Its purpose is to maintain the advantages in edge protection for TV model. When it is in the smooth area of image, linear diffusion is used to avoid the staircase effect.

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

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.

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.

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.

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.

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.

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.

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.

Image segmentation is an important step in automatic fingerprint identification systems. While tremendous progress has been made in rolled and plain fingerprint segmentation, the segmentation of latent fingerprints is still a difficult problem. Features used for rolled and plain fingerprint images fail to work properly on latent images due to the poor quality in ridge information and the presence of multiple types of strong structured noise. In this work, we present an adaptive total variation (TV) model to achieve effective latent fingerprint segmentation. The proposed solution can remove various types of structured noise existing in a single latent image and automatically locate the region of interest (ROI), which contains primarily the latent fingerprint. Then, the following tasks such as fingerprint feature extraction and matching can be conducted in the ROI only. In the proposed TV-based image model, one can adaptively adjust the weight coefficient of the fidelity term in L1-norm depending on the background noise level, which is estimated via TV-based texture analysis. We apply the proposed TV-based segmentation algorithm to the NIST SD27 latent fingerprint database to demonstrate its superior performance.

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.

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.

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