Total Variation Model Research Articles

Dark Channel Constraint and Alternated Direction Multiplier Optimization of Turbulence Degraded Image Blind Restoration

In order to improve the effect of turbulence degraded image restoration, aiming at the problem that the fuzzy solution is easy to be obtained by using the prior information constraint of gradient distribution under the framework of maximum a posteriori probability of blind restoration algorithm, this paper proposes a dark channel constraint and alternated direction multiplier optimization of turbulence degraded image blind restoration method.First, based on the idea of multi-scale, a dark channel prior constraint is imposed on the image and non-negative constraints and energy constraints are imposed on the point spread function at each level.Then, the kernel and image of the current scale are estimated by alternating iterations of coordinate descent method. When the maximum scale is reached, the final estimated blur kernel is obtained.Last, combined with the total variational model, the image details are quickly restored using the alternate direction optimization method. The experimental results show that the prior information constraint used in the proposed algorithm is advantageous to obtain a clear solution, and can converge to the global optimal solution in the total variational model, which can effectively suppress the artifacts produced in the image restoration process and recover a better target image detail.

Deshadowing of Urban Airborne Imagery Based on Object-Oriented Automatic Shadow Detection and Regional Matching Compensation

With the increase of the spatial resolution of aerial images, the shadow problem is more prominent. The shadows affect the applications such as object recognition, image dense matching, and object classification. Existing shadow detection methods can acquire results with high accuracy, but usually need much manual intervention and the traditional stretch models generally lead to color distortion and undercompensation. Therefore, we propose an object-oriented automatic shadow detection method without manual intervention and a shadow compensation method by regional matching. In the proposed method, pixel-based soft shadow detection, which uses Gaussian mixture model to simulate the gray distribution and refines soft shadow map with guiled filtering, is combined with image segmentation result to obtain accurate shadow regions with complete shape and no hole. Then shadow regions are compensated, with less loss of details and brightness imbalance, referring to their optimal homogeneous nonshadow region obtained by regional matching based on Bag-of-Words. The total variation model is used to decrease the noise amplified by the pixel-based stretch and boundary effect in the result. Experiments are performed on three publicly available high-resolution aerial images to demonstrate the superiority of our proposed methods. It shows that the proposed method can accurately detect shadows from urban high-resolution aerial images with an overall rate of over 88%. The compensation results display excellent visual effects compared with the state-of-the-art methods, consistent with the true color of ground objects.

Anisotropic Total Fractional Order Variation Model in Seismic Data Denoising

Anisotropic Total Fractional Order Variation Model in Seismic Data Denoising

Investigating the Influence of Box-Constraints on the Solution of a Total Variation Model via an Efficient Primal-Dual Method

In this paper, we investigate the usefulness of adding a box-constraint to the minimization of functionals consisting of a data-fidelity term and a total variation regularization term. In particular, we show that in certain applications an additional box-constraint does not effect the solution at all, i.e., the solution is the same whether a box-constraint is used or not. On the contrary, i.e., for applications where a box-constraint may have influence on the solution, we investigate how much it effects the quality of the restoration, especially when the regularization parameter, which weights the importance of the data term and the regularizer, is chosen suitable. In particular, for such applications, we consider the case of a squared L 2 data-fidelity term. For computing a minimizer of the respective box-constrained optimization problems a primal-dual semi-smooth Newton method is presented, which guarantees superlinear convergence.

Latent Fingerprint Segmentation Based on Ridge Density and Orientation Consistency

Latent fingerprints are captured from the fingerprint impressions left unintentionally at the surfaces of the crime scene. They are often used as an important evidence to identify criminals in law enforcement agencies. Different from the widely used plain and rolled fingerprints, the latent fingerprints are usually of poor quality consisting of complex background with a lot of nonfingerprint patterns and various noises. Latent fingerprint segmentation is an important image processing step to separate fingerprint foreground from background for more accurate and efficient feature extraction and matching. Traditional methods are usually based on the local features such as gray scale variance and gradients, which are sensitive to noise and cannot work well for latent images. This paper proposes a latent fingerprint segmentation method based on combination of ridge density and orientation consistency, which are global and local features of fingerprints, respectively. First, a texture image is obtained by decomposition of latent image with a total variation model. Second, we propose to detect the ridge segments from the texture image, and then compute the density of ridge segments and ridge orientation consistency to characterize the global and local fingerprint patterns. Finally, fingerprint segmentation is performed by combining the ridge density and orientation consistency for latent images. The proposed method has been evaluated on NIST SD27 latent fingerprint database. Experimental results and comparison demonstrate the promising performance of the proposed method.

A Novel Total Variation Model for Low-Dose CT Image Denoising

Low-dose computed tomography (LDCT) images are polluted by mottle noise and streak artifacts. To improve LDCT images quality, this paper proposes a novel total variation (NTV) model. A weighted coefficient of the regularization term of NTV model is constructed by standard deviation, gray-level probability and gradient magnitude to smooth LDCT images adaptively, since the standard deviation and the gray-level probability of detail region are higher than that of the noisy background, and the gradient magnitude of edges is higher than that of the noisy background. Besides, to preserve details and edges effectively, the fidelity term of the proposed NTV model is constructed by the block-matching 3d filter because it performs well in details and edges preservation. The experiments are performed on the computer simulated phantom and the actual phantom. Compared with several other competitive methods, both subjective visual effect and objective evaluation criteria show that the proposed NTV model can improve LDCT images quality more effectively such as noise and artifacts suppression, details, and edges preservation.

A Variational Approach to Image Inpainting and Text Removal

A commonly occurring problem in image processing is the reconstruction of missing data, generally referred to as image inpainting and can be viewed as a 2D interpolation problem. In this paper we present an approach based on variational model to solve the inpainting problem. Previously the total variation model has been successfully used to solve inpainting problems. We introduce a variant of total variation model that includes a parameter q that controls the degree of smoothness of the reconstruction. The corresponding Euler-Lagrange equation is derived and the corresponding boundary value problem solved. Test examples show that the method works well.

基于总变分模型的改进图像修复算法

基于总变分模型的改进图像修复算法

Anomaly Detection for Hyperspectral Images Based on Anisotropic Spatial-Spectral Total Variation and Sparse Constraint

A novel anomaly detection method for hyperspectral images (HSIs) is proposed based on anisotropic spatial-spectral total variation and sparse constraint. HSIs are assumed to be not only smooth in spectral dimension but also piecewise smooth in spatial dimension. The proposed method adopts the anisotropic spatial-spectral total variation model which combines 2D spatial total variation and 1D spectral variation to explore the spatial-spectral smooth property of HSIs. Meanwhile, the sparse property of anomalies is exploited for its low probability in the image. To utilize both the spatial and spectral information of HSIs, we preserve the original cubic form of HSIs and divide the HSIs into three 3D arrays, each representing the background, the anomaly, and the noise respectively. By using anisotropic spatial-spectral total variation regularization on the background component and sparse constraint on the anomaly component, this anomaly detection problem has therefore been formulated as a constraint optimization problem whose solution has been derived by alternately using Split Bregman Method and Go Decomposition (GoDec) Method. Experimental results on hyperspectral datasets illustrate that our proposed method has a better detection performance than state-of-the-art hyperspectral anomaly detection methods.

The total variation constrained data divergence minimization model for image reconstruction and its Chambolle-Pock solving algorithm

Image reconstruction is an important inverse problem to reconstruct images from its transform. The two main reconstruction methods are the analytic method and the iterative method. The analytic method, for example, the filtered backprojection algorithm, needs complete projection data, so it is not competent to accurately reconstruct an image from sparse data. Thus the iterative method combined with optimization techniques has received more and more attention. The optimization-based iterative image reconstruction algorithm may accurately reconstruct images by the use of compressed sensing, low rank matrix and other sparse optimization techniques. Among them, the total variation (TV) minimization model is a simple but effective optimization model. The traditional, constrained TV model employs the data fidelity term as the constraint term and the TV regularization term as the objective function. In the present work, we study a novel, TV constrained, data divergence minimization (TVcDM) model and its solver. We derive in detail the Chambolle-Pock (CP) algorithm for solving the TVcDM model, verify the correctness of the model and its solver, analyze the convergence behavior of the algorithm, evaluate the sparse reconstruction ability of the TVcDM-CP algorithm and finally analyze the influence of the model parameters on reconstruction and the effect of algorithm parameters on convergence rate. The studies show that the TVcDM model may accurately reconstruct images from sparse-view projections. The TVcDM-CP algorithm may ensure convergence but the vibration phenomena may be observed in the convergence process. The model parameter, TV tolerance, has important influence on reconstruction quality, i. e. too big a value introduces noise whereas too small a value may smoothen the image details. Also, the studies reveal that different algorithm-parameter selections may lead to different convergence rates. The TVcDM-CP algorithm may be tailored and applied to other computed tomography scanning configurations and other imaging modalities. The necessary key work is just to design the corresponding system matrix and select the optimal model parameters and algorithm parameters according to the insights gained in the work.

Improved BM3D denoising method

Block matching 3D denoising (BM3D) is an excellent single-image denoising method. However, it still needs to be improved for solving practical problems. In this study, the authors attempt to improve the method of BM3D. First, one of the problems of BM3D is that some of its references cannot perform self-adaption when the noise intensity of the images is changed. Therefore, they propose a method using total variation (TV) to calculate the image noise intensity and make the references perform self-adaption. Second, finding similar blocks in the BM3D method is a time-consuming procedure. To solve this problem, they analyse the relationship between the numbers of similar blocks and denoising effect, improve the process of searching for similar blocks, and reduce the running time. Third, through the experiment they find that the denoising effect of BM3D method in the domain of complex texture is unsatisfactory. Thus, they proposed a hybrid denoising method for the complex texture area, using the new TV model and BM3D method together to restore the image. Their experimental results show that the improved BM3D method performs better than the original BM3D method.

Region covariance based total variation optimization for structure-texture decomposition

With conventional structure-preserving filters, it is not always easy to remove texture details and preserve important structures from images of high complexity. To enhance the performance of structure-texture decomposition, a new method based on region covariance of simple image features and total variation optimization is proposed in this paper. We first identify texture from structure by patch-based covariance, which shows highly discriminative power for textures. Then, a total variation model built on the joint covariance and gradient is used for structure-preserving smoothing. To overcome the inherent limitation of covariance descriptor in locating main structures, patch shifting based on the variation of the region covariance is introduced. We compare our approach with state-of-the-art structure-preserving decomposition methods and the results show that our approach outperforms them in removing unimportant texture details while preserving main structures. Even for images containing the mixture of high-contrast textures with obscure boarders between them, our approach still can improve the decomposition at few extra cost of computation. Besides better decomposition results and robustness for various types of images, the simplicity of our approach make it easy to implement and adaptable to other applications.

Hybrid image restoration model with adaptive weight parameter

It is a difficult issue in image restoration to eliminate noise while avoiding the staircase effect and preserving edges. The anisotropic diffusion model proposed by Perona and Malik (PM) and the total variation model presented by Rudin, Osher, and Fatemi (ROF) are widely used to restore an image. However, the well-known defect of the two classic models is that they tend to cause the staircase effect. We propose a well-balanced anisotropic diffusion (WBAD) model by considering an adaptive balance parameter. The balance can be made in a selective way, meaning that it will alternate between the PM diffusion and ROF diffusion in accordance with the image features. The proposed WBAD model can preserve edges well while reducing noise, but it also causes less staircasing effect in the less smooth regions because it acts like the PM diffusion in these regions. Considering that the fourth-order PDEs can reduce the staircasing effect, we introduce a hybrid image restoration model based on an adaptive weight parameter to take advantage of the WBAD model and the fourth-order model. The experimental results illustrate that our algorithm can effectively remove noise and preserve edges. The higher values of peak signal-to-noise ratio and MSSIM highlight the better performance of our hybrid image restoration model.

Nonlocal Gradient Sparsity Regularization for Image Restoration

Total variation (TV) regularization is widely used in image restoration to exploit the local smoothness of image content. Essentially, the TV model assumes a zero-mean Laplacian distribution for the gradient at all pixels. However, real-world images are nonstationary in general, and the zero-mean assumption of pixel gradient might be invalid, especially for regions with strong edges or rich textures. This paper introduces a nonlocal (NL) extension of TV regularization, which models the sparsity of the image gradient with pixelwise content-adaptive distributions, reflecting the nonstationary nature of image statistics. Taking advantage of the NL similarity of natural images, the proposed approach estimates the image gradient statistics at a particular pixel from a group of nonlocally searched patches, which are similar to the patch located at the current pixel. The gradient data in these NL similar patches are regarded as the samples of the gradient distribution to be learned. In this way, more accurate estimation of gradient is achieved. Experimental results demonstrate that the proposed method outperforms the conventional TV and several other anchors remarkably and produces better objective and subjective image qualities.

Significant Anatomy Detection Through Sparse Classification: A Comparative Study.

We present a comparative study for discriminative anatomy detection in high dimensional neuroimaging data. While most studies solve this problem using mass univariate approaches, recent works show better accuracy and variable selection using a sparse classification model. Two types of image-based regularization methods have been proposed in the literature based on either a Graph Net (GN) model or a total variation (TV) model. These studies showed increased classification accuracy and interpretability of results when using image-based regularization, but did not look at the accuracy and quality of the recovered significant regions. In this paper, we theoretically prove bounds on the recovered sparse coefficients and the corresponding selected image regions in four models (two based on GN penalty and two based on TV penalty). Practically, we confirm the theoretical findings by measuring the accuracy of selected regions compared with ground truth on simulated data. We also evaluate the stability of recovered regions over cross-validation folds using real MRI data. Our findings show that the TV penalty is superior to the GN model. In addition, we showed that adding an l2 penalty improves the accuracy of estimated coefficients and selected significant regions for the both types of models.

Introducing diffusion tensor to high order variational model for image reconstruction

Second order total variation (SOTV) models have advantages for image reconstruction over their first order counterparts including their ability to remove the staircase artefact in the reconstructed image. However, such models tend to blur the recovered image when discretised for a numerical solution [1–5]. To overcome this drawback, we introduce a novel tensor weighted second order (TWSO) variational model for image reconstruction. Specifically, we develop a new regulariser for the original SOTV model that uses the Frobenius norm of the product of the Hessian matrix and a diffusion tensor, which has the duel effects of sharpening edges and introducing anisotropy to the model. We then efficiently solve the proposed model by breaking the original problem into several closed-form subproblems using the alternating direction method of multipliers. The proposed method is compared with state-of-the-art approaches such as the tensor-based anisotropic diffusions, total generalised variation, and Euler's elastica. We validate the TWSO model using extensive experiments on numerous images from the Berkeley BSDS500. We also show that our method effectively reduces both the staircase and blurring effects and outperforms existing approaches for image inpainting and denoising applications.

Optimal Selection of the Regularization Function in a Weighted Total Variation Model. Part I: Modelling and Theory

A weighted total variation model with a spatially varying regularization weight is considered. Existence of a solution is shown, and the associated Fenchel predual problem is derived. For automatically selecting the regularization function, a bilevel optimization framework is proposed. In this context, the lower-level problem, which is parameterized by the regularization weight, is the Fenchel predual of the weighted total variation model and the upper-level objective penalizes violations of a variance corridor. The latter object relies on a localization of the image residual as well as on lower and upper bounds inspired by the statistics of the extremes.

A Mixed Non‐local Prior Model for Image Super‐resolution Reconstruction

Generating high-resolution image from a set of degraded low-resolution images is a challenge problem in image processing. Due to the ill-posed nature of Super-resolution (SR), it is necessary to find an effective image prior model to make it well-posed. For this purpose, we propose a mixed non-local prior model by adaptively combining the non-local total variation and non-local H1 models, and establish a multi-frame SR method based on this mixed non-local prior model. The unknown Highresolution (HR) image, motion parameters and hyperparameters related to the new prior model and noise statistics are determined automatically, resulting in an unsupervised super-resolution method. Extensive experiments demonstrate the effectiveness of the proposed SR method, which can not only preserve image details better but also suppress noise better.

Adaptive Bregmanized total variation model for mixed noise removal

To solve the problem of the staircase effect and removing mixed noise, including Gaussian and salt and pepper noise, which can occur during image formation and transmission, a total variation-based denoising model using an edge detection function is proposed. Moreover, an improved split Bregman iteration method is used to solve the nonlinear problem. The results of comparative experiments demonstrate that the proposed model removes Gaussian and salt and pepper noise while maintaining detailed features.

Optimal Selection of the Regularization Function in a Weighted Total Variation Model. Part II: Algorithm, Its Analysis and Numerical Tests

Based on the weighted total variation model and its analysis pursued in Hintermuller and Rautenberg 2016, in this paper a continuous, i.e., infinite dimensional, projected gradient algorithm and its convergence analysis are presented. The method computes a stationary point of a regularized bilevel optimization problem for simultaneously recovering the image as well as determining a spatially distributed regularization weight. Further, its numerical realization is discussed and results obtained for image denoising and deblurring as well as Fourier and wavelet inpainting are reported on.