Start-Tv: A Closed-Form Initialization For Total Variation Models

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.

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.

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.

Truncated total variation in fractional B-spline wavelet transform for micro-CT image denoising.

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.

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Although the Total Variation (TV) model has good performance in the image inpainting including both maintaining damaged images' edge and reducing numerical calculation, it should be improved in the inpainting domain with rich texture. In this paper, an image multi-level-inpainting method based on TV model and texture synthesis scheme is proposed. It is the main research topic to improve the visual result of inpainted images with scratches including rich texture. At the first inpainting level, damaged images are calculated following the TV model, and then the patch-based texture synthesis scheme is used to improve the inpainted results of rich texture domain in the first level. Experimental results prove that the method has better performance in restoring an incomplete 2-D image in every detail that it looks more `complete' and `natural'.

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

Fractional-order derivative is attracting more and more interest from researchers working on image processing because it helps to preserve more texture than total variation when noise is removed. In the existing works, the Grunwald–Letnikov fractional-order derivative is usually used, where the Dirichlet homogeneous boundary condition can only be considered and therefore the full lower triangular Toeplitz matrix is generated as the discrete partial fractional-order derivative operator. In this paper, a modified truncation is considered in generating the discrete fractional-order partial derivative operator and a truncated fractional-order total variation (tFoTV) model is proposed for image restoration. Hopefully, first any boundary condition can be used in the numerical experiments. Second, the accuracy of the reconstructed images by the tFoTV model can be improved. The alternating directional method of multiplier is applied to solve the tFoTV model. Its convergence is also analyzed briefly. In the numerical experiments, we apply the tFoTV model to recover images that are corrupted by blur and noise. The numerical results show that the tFoTV model provides better reconstruction in peak signal-to-noise ratio (PSNR) than the full fractional-order variation and total variation models. From the numerical results, we can also see that the tFoTV model is comparable with the total generalized variation (TGV) model in accuracy. In addition, we can roughly fix a fractional order according to the structure of the image, and therefore, there is only one parameter left to determine in the tFoTV model, while there are always two parameters to be fixed in TGV model.

Compressed sensing for breakthrough Nyquist sampling theorem provides a strong theoretical , making compressive sampling for image signals be carried out simultaneously. In traditional imaging procedures using compressed sensing theory, not only can it reduces the storage space, but also can reduce the demand for detector resolution greatly. Using the sparsity of image signal, by solving the mathematical model of inverse reconfiguration, realize the super-resolution imaging. Reconstruction algorithm is the most critical part of compression perception, to a large extent determine the accuracy of the reconstruction of the image.The reconstruction algorithm based on the total variation (TV) model is more suitable for the compression reconstruction of the two-dimensional image, and the better edge information can be obtained. In order to verify the performance of the algorithm, Simulation Analysis the reconstruction result in different coding mode of the reconstruction algorithm based on the TV reconstruction algorithm. The reconstruction effect of the reconfigurable algorithm based on TV based on the different coding methods is analyzed to verify the stability of the algorithm. This paper compares and analyzes the typical reconstruction algorithm in the same coding mode. On the basis of the minimum total variation algorithm, the Augmented Lagrangian function term is added and the optimal value is solved by the alternating direction method.Experimental results show that the reconstruction algorithm is compared with the traditional classical algorithm based on TV has great advantages, under the low measurement rate can be quickly and accurately recovers target image.

Imaging through turbid medium has many potential applications such as looking through clouds, seeing into seawater and observing through biological tissues. The transmission matrix (TM) method is one of the main imaging technologies that has potential in imaging of large targets. With aid of pre-measured TM, several optimization models are proposed to recover targets from speckle patterns, including ℓ₂ norm optimization model, sparse representation (SR) framework and total variation (TV) model. However, the solution of ℓ₂ norm optimization model contains large reconstruction noise, while the SR framework and TV model are two kinds of compressive sensing strategies, which require that the targets are sparse. In this paper, in order to image non-sparse targets and suppress the reconstruction noise, we apply the maximum entropy method (MEM) model to recover the target images from speckle patterns. Simulation results show that, for non-sparse target, the MEM model has better reconstruction performance under different noise levels compared with the TV model. For example, peak signal-to-noise ratio (PSNR) and correlation coefficient (CC) of images reconstructed by MEM model at SNR=15 dB are comparable with those by TV model at SNR=35 dB.

New discretization of total variation functional for image processing tasks

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.

Non-blind image deblurring method by local and nonlocal total variation 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.