TV-based Model Research Articles

Analysis of Different Height Correction Models for Tropospheric Delay Grid Products over the Yunnan Mountains

Accurate tropospheric delays are of great importance for both Global Navigation Satellite System (GNSS)-based positioning and precipitable water vapor monitoring. The gridded tropospheric delay products, including zenith hydrostatic delays (ZHD) and zenith wet delays (ZWD), are the most ideal method for accessing accurate tropospheric delays. The vertical adjustment method is critical for implementing the gridded tropospheric products. In this work, we consider the different models used for grid products and assess their performance over Yunnan mountains with complex topography. We summarize the main results as follows: (1) The products can provide accurate ZHD with mean biases of −2.6 mm and mean Standard Deviation (STD) of 1.5 mm while the ZWD results from grid products show a performance with biases of −0.4 mm and STD of 1.3 cm over the Yunnan area. (2) The Tv-based model shows a better performance than the T0-based model and IGPZWD in rugged areas with large height differences. The grid products can provide hourly ZHD with biases of 3 mm and wet delay with mean biases of within 2 cm and mean STD of below 3 cm in the Yunnan mountains, which exhibit a large height difference of around 1.5 km. (3) The radiosondes results confirm that the Tv-based model has an obvious advantage in calculating ZHD height corrections for differences within 2 km while the T0-model suffers from a loss in accuracy in the case of large height differences. If the site is located more than 1 km below the reference height, the IGPZWD model can provide a better ZWD with a mean bias of 1.5 cm and a mean STD of 1.7 cm. With vertical reduction models, the grid products can provide accurate ZHD and ZWD in real time, even if in complex area.

A Mathematical Algorithm for Improving the Medical Image

In this paper, we present a hybrid model based on total generalized variation (TGV) and shearlet with non-quadratic fidelity data terms for blurred images corrupted by impulsive and Poisson noises. Numerical experiments demonstrate that the proposed can reduce the staircase effect while preserving edges and outperform classical TV-based models in the peak signal-to-noise ratio (PSNR).

A Fractional-Order Fidelity-Based Total Generalized Variation Model for Image Deblurring

Image deblurring is a fundamental image processing task, and research for efficient image deblurring methods is still a great challenge. Most of the currently existing methods are focused on TV-based models and regularization term construction; little efforts are paid to model proposal and correlated algorithms for the fidelity term in fractional-order derivative space. In this paper, we propose a novel fractional-order variational model for image deblurring, which can efficiently address three different blur kernels. The objective functional contains a fractional-order gradient fidelity term and a total generalized variation (TGV) regularization term, and it highlights the ability to preserve details and eliminate the staircase effect. To solve the problem efficiently, we provide two numerical algorithms based on the Chambolle-Pock primal-dual method (PD) and the alternating direction method of multipliers (ADMM). A series of experiments show that the proposed method achieves a good balance between detail preservation and deblurring compared with several existing advanced models.

Edge detection techniques using nonlinear diffusion-based models

An overview of the edge detection techniques based on partial differential equations (PDE) is presented in this work. Nonlinear anisotropic diffusion-based boundary extraction approaches, like the influential Perona- Malik model and some improved variants of it, are described first. Anisotropic diffusion-based detection schemes using the mean curvature motion and nonlinear PDE-based approaches combining anisotropic diffusion to the bilateral filter are then discussed here. Some nonlinear reaction-diffusion-based edge detection methods are described next. Variational edge detection solutions using the total variation (TV) regularization or combining the anisotropic diffusion to the TV-based models are then presented. Directional diffusion-based image edge extraction algorithms are also discussed. Our own contributions in this computer vision domain are finally described.

Enhanced total variation minimization for stable image reconstruction

The total variation (TV) regularization has phenomenally boosted various variational models for image processing tasks. We propose to combine the backward diffusion process in the earlier literature on image enhancement with the TV regularization, and show that the resulting enhanced TV minimization model is particularly effective for reducing the loss of contrast. The main purpose of this paper is to establish stable reconstruction guarantees for the enhanced TV model from noisy subsampled measurements with two sampling strategies, non-adaptive sampling for general linear measurements and variable-density sampling for Fourier measurements. In particular, under some weaker restricted isometry property conditions, the enhanced TV minimization model is shown to have tighter reconstruction error bounds than various TV-based models for the scenario where the level of noise is significant and the amount of measurements is limited. The advantages of the enhanced TV model are also numerically validated by preliminary experiments on the reconstruction of some synthetic, natural, and medical images.

A region fusion based split Bregman method for TV Denoising algorithm

A novel robust image denoising method based Total Variation (TV) model called Region Fusion based Split Bregman (RFSB) method is proposed in this paper. First, the structural characteristics of the edge region and that of the smooth region of the noisy image are analyzed and then separated. Second, split Bregman method is used for calculating two baseline TV-based model, the TV model and TV-penalized least squares functional model, and results of the two models are fused by proposed Region Fusion method. Third, for the fusion denoising result contains a wealth of repetitive redundant information, fast non-local means (FNLM) is introduced for post-processing the denoising result. Our proposed method has three contributions: (i) the use of split Bregman to calculate two baseline TV-based model because of its highly minimization speed; (ii) the proposal of a region fusion method to fuse two baseline models; (iii) the application of the FNLM method as the post-processing. Gray images and color images with different intensities of noise are used to compare our proposed method with other existing classical TV-based method. Experimental results show that Our proposed method has outperformed other TV-based methods in denoising visual effect and objective evaluation for different styles of noised images. The time complexity of our proposed method is about 2% and 50% lower than that of TV and Zhang’s Total Variation (ZTV). Our proposed method shows lower time complexity and does not distort the image information compared with two deep learning algorithm.

A Filtering-Based Framework for Optical Flow Estimation

We present a novel optical flow estimation framework that reinterprets most popular algorithms (e.g., the Horn-Schunck model, PDE-based models, TV-based models, and nonlocal-based models) from an iterative filtering perspective. Different regularizers in the related optical flow estimation algorithms can be achieved by adopting different filtering operations. The key merit of the proposed framework is that a variety of filtering models and corresponding optimization strategies, which are used in image processing, can be directly utilized in the regularization term, leading to a convenient way of designing appropriate optical flow estimation algorithms. Under the proposed filtering framework, we demonstrate easily designing optical flow estimation algorithms with respect to translation consistency, rotation consistency, and divergence consistency constraints by adopting different spatial filters, respectively. We also derive a novel optical flow estimation algorithm with 3D filtering-based model for the regularization term, which makes use of nonlocal self-similarity and sparse characteristic of optical flow field. Benefited from the advantages of patch-based nonlocal sparse regularizer, the derived algorithm can remove outliers while preserving sharp flow edges and important motion details. At present, the proposed algorithm achieves a high ranking on the challenging MPI-Sintel dataset and shows good performance on the Kitti flow 2015 and Middlebury datasets.

An adaptive algorithm for TV-based model of three norms [formula omitted] in image restoration

In this paper, we present an adaptive method for the TV-based model of three norms Lq(q=12,1,2) for the image restoration problem. The algorithm with the L2 norm is used in the smooth regions, where the value of |∇u| is small. The algorithm with the L12 norm is applied for the jumps, where the value of |∇u| is large. When the value of |∇u| is moderate, the algorithm with the L1 norm is employed. Thus, the three algorithms are applied for different regions of a given image such that the advantages of each algorithm are adopted. The numerical experiments demonstrate that our adaptive algorithm can not only keep the original edge and original detailed information but also weaken the staircase phenomenon in the restored images. Specifically, in contrast to the L1 norm as in the Rudin–Osher–Fatemi model, the L2 norm yields better results in the smooth and flat regions, and the L12 norm is more suitable in regions with strong discontinuities. Therefore, our adaptive algorithm is efficient and robust even for images with large noises.

TGV-based multiplicative noise removal approach: Models and algorithms

Abstract Total variation (TV) based models have been used widely in multiplicative denoising problem. However, these models are always accompanied by an unsatisfactory effect named staircase due to the property of BV space. In this paper, we present two high-order variational models based on total generalized variation (TGV) for two kinds of multiplicative noises. The proposed models reduce the staircase while preserving the edges. In the meantime we develop an efficient algorithm which is called Prediction-Correction proximal alternative direction method of multipliers (PADMM) to solve our models. Moreover, we show the convergence of our algorithm under certain conditions. Numerical experiments demonstrate that our high-order models outperform the classical TV-based models in PSNR and SSIM values.

A mesh-free algorithm for ROF model

The total variation (TV) denoising method is a PDE-based technique that preserves the edges well but has undesirable staircase effect in some cases, namely, the translation of smooth regions (ramps) into piecewise constant regions (stairs). This paper introduces a novel mesh-free approach using TV (ROF model) regularization and radial basis function (RBF) for the numerical approximation of TV-based model to remove the additive noise from the measurements. This approach is structured on local collocation and multiquadric radial basis function. These features enable this strategy not only to eliminate noise from images and preserve the edges but also has the advantage to minimize the staircase effect substantially from real and artificial images which cause the image to look blocky. Experimental results demonstrate that the proposed mesh-free approach is robust and performs well in visual improvement as well as peak signal-to-noise ratio compared with the recent partial differential equation (PDE)-based traditional methods.

Primal-dual method to smoothing TV-based model for image denoising

The total variation-based Rudin–Osher–Fatemi model is an effective and popular prior model in the image processing problem. Different to frequently using the splitting scheme to directly solve this model, we propose the primal dual method to solve the smoothing total variation-based Rudin–Osher–Fatemi model and give some convergence analysis of proposed method. Numerical implements show that our proposed model and method can efficiently improve the numerical results compared with the Rudin–Osher–Fatemi model.

A Fast Fixed Point Algorithm for Total Variation Deblurring and Segmentation

In this paper, we propose a fast fixed point algorithm and apply it to total variation (TV) deblurring and segmentation. The TV-based models can be written in the form of a general minimization problem. The novel method is derived from the idea of establishing the relation between solutions of the general minimization problem and new variables, which can be obtained by a fixed point algorithm efficiently. Under gentle conditions it provides a platform to develop efficient numerical algorithms for various image processing tasks. We then specialize this fixed point methodology to the TV-based image deblurring and segmentation models, and the resulting algorithms are compared with the split Bregman method, which is a strong contender for the state-of-the-art algorithms. Numerical experiments demonstrate that the algorithm proposed here performs favorably.

Image recovery via total variation minimization and related problems

We study here a classical image denoising technique introduced by L. Rudin and S. Osher a few years ago, namely the constrained minimization of the total variation (TV) of the image. First, we give results of existence and uniqueness and prove the link between the constrained minimization problem and the minimization of an associated Lagrangian functional. Then we describe a relaxation method for computing the solution, and give a proof of convergence. After this, we explain why the TV-based model is well suited to the recovery of some images and not of others. We eventually propose an alternative approach whose purpose is to handle the minimization of the minimum of several convex functionals. We propose for instance a variant of the original TV minimization problem that handles correctly some situations where TV fails.