Image Denoising Using Total Variation Model Guided by Steerable Filter

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

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.

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.

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.

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.

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.

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.

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.

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 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.

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.

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.

Adaptive total variation denoising based on difference curvature

In medical applications, computed tomography (CT) is widely used to evaluate various sample characteristics. However, image quality of CT reconstruction can be degraded due to artifacts. To propose and test a truncated total variation (truncation TV) model to solve the problem of large penalties for the total variation (TV) model. In this study, a truncated TV image denoising model in the fractional B-spline wavelet domain is developed to obtain the best solution. The method is validated by the analysis of CT reconstructed images of actual biological Pigeons samples. For this purpose, several indices including the peak signal-to-noise ratio (PSNR), structural similarity index (SSIM) and mean square error (MSE) are used to evaluate the quality of images. Comparing to the conventional truncated TV model that yields 22.55, 0.688 and 361.17 in PSNR, SSIM and MSE, respectively, using the proposed fractional B-spline-truncated TV model, the computed values of these evaluation indices change to 24.24, 0.898 and 244.98, respectively, indicating substantial reduction of image noise with higher PSNR and SSIM, and lower MSE. Study results demonstrate that compared with many classic image denoising methods, the new denoising algorithm proposed in this study can more effectively suppresses the reconstructed CT image artifacts while maintaining the detailed image structure.

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.