Total Generalized Variation Model Research Articles

A non–convex total generalized variation model for image denoising

We propose an effective regularization model based on second–order total generalized variation for image restoration with mixed Poisson–Gaussian noise. An efficient alternating minimization algorithm is employed to solve the considered model. Finally, provided numerical results show that our proposed model can preserve more details and get higher image visual quality than recent state-of-the-art methods.

Anisotropic total generalized variation model for Poisson noise removal

Anisotropic total generalized variation model for Poisson noise removal

An adaptive total generalized variational model for speckle reduction in ultrasound images

In this paper, we propose an adaptive total generalized variation model for removing the speckle noise in ultrasound image. The existence and uniqueness of the minimizers to the proposed model are established. Furthermore, we design an alternating minimization algorithm to solve numerically the model. By incorporating the generalized cross validation technique, the regularization parameter of the model can be updated during the iterations of the designed algorithm. Finally, experimental results are reported to demonstrate the effectiveness of the proposed method, and its performance is competitive with that of the other testing methods.

A wavelet frame constrained total generalized variation model for imaging conductivity distribution

<p style='text-indent:20px;'>Electrical impedance tomography (EIT) is a sensing technique with which conductivity distribution can be reconstructed. It should be mentioned that the reconstruction is a highly ill-posed inverse problem. Currently, the regularization method has been an effective approach to deal with this problem. Especially, total variation regularization method is advantageous over Tikhonov method as the edge information can be well preserved. Nevertheless, the reconstructed image shows severe staircase effect. In this work, to enhance the quality of reconstruction, a novel hybrid regularization model which combines a total generalized variation method with a wavelet frame approach (TGV-WF) is proposed. An efficient mean doubly augmented Lagrangian algorithm has been developed to solve the TGV-WF model. To demonstrate the effectiveness of the proposed method, numerical simulation and experimental validation are conducted for imaging conductivity distribution. Furthermore, some comparisons are made with typical regularization methods. From the results, it can be found that the proposed method shows better performance in the reconstruction since the edge of the inclusion can be well preserved and the staircase effect is effectively relieved.</p>

Two Variational Models for Image Denoising Using Jacobian of Normals

Variational models with second order regularizers can efficiently overcome the problems of staircasing effects caused by first order models. However, different types of second order regularizers may lead to different properties of feature preserving in restored images. In this paper, we show two variational models with second order regularizers. The first one is bounded Hessian model with Jacobian of normals, which uses bounded Jacobian of image intensity normals as regularizer, it is an extension of classical bounded Hessian (BH) model. The second one is total generalized variation model with Jacobian of normals, which is an extension to total generalized variation (TGV) model by replacing gradients in TGV with normals. The common objective is to improve feature preserving, such as edge, contrast and smoothness preservation. Additionally, their Alternating Direction Method of Multipliers (ADMM) are designed by introducing some proper auxiliary variables, Lagrange multipliers and penalty parameters to decompose the original models into some simple minimization sub-problems to solve. Extensive comparisons demonstrate that the proposed models are superior to the classical models with Hessian and TGV regularizers, especially in edge and corner preservation, smoothness, contrast enhancement. Moreover, the proposed models can be also extended to image inpainting, deblurring, and image enhancement.

Nonconvex Total Generalized Variation Model for Image Inpainting

It is a challenging task to prevent the staircase effect and simultaneously preserve sharp edges in image inpainting. For this purpose, we present a novel nonconvex extension model that closely incorporates the advantages of total generalized variation and edge-enhancing nonconvex penalties. This improvement contributes to achieve the more natural restoration that exhibits smooth transitions without penalizing fine details. To efficiently seek the optimal solution of the resulting variational model, we develop a fast primal-dual method by combining the iteratively reweighted algorithm. Several experimental results, with respect to visual effects and restoration accuracy, show the excellent image inpainting performance of our proposed strategy over the existing powerful competitors.

A Non-Convex L₁-Norm Penalty-Based Total Generalized Variation Model for Reconstruction of Conductivity Distribution

Electrical impedance tomography (EIT) is a potential imaging technique for reconstructing the interior conductivity distribution within an object. The reconstruction is realized by processing the boundary voltage measured from the EIT. Mathematically, the reconstruction of conductivity distribution is a highly nonlinear ill-posed inverse problem as the solution is not unique and is sensitive to the noise, which largely hinders the practical application of the EIT technique. In this paper, a novel modified non-convex ${L}_{1}$ -norm penalty based total generalized variation (NCP-TGV) model is proposed to solve the inverse problem and reconstruct the conductivity distribution. An iteratively reweighted ${L}_{1}$ algorithm is developed to convert the non-convex model to convex function and the Chambolle-Pock primal-dual algorithm is then applied to solve the minimization problem. To demonstrate the performance of the proposed NCP-TGV model in reconstructing the conductivity distribution, extensive numerical simulation and experimental work have been carried out. Additionally, the proposed approach has been validated by comparing its performance with the convex ${L}_{1}$ -norm penalty based total variation (TV) and TGV inverse models. The results indicate that the images reconstructed by the proposed NCP-TGV model show better quality with the advantages of simultaneous reduction of staircase effect and preservation of edge in comparison to the TV and TGV approaches.

Solving Mixed Quasi-variational Inequality for Modified Total Generalized Variation for Image Denoising

Image denoising has always been a hot issue in the field of image processing. In order to better reduce the image noise, a modified total generalized variation model is presented. The theory of mixed quasi-variational inequality is introduced to numerically solve the modified model. Compared with several variational models, experiments demonstrate that the proposed method has better performance in edge-preserving while filtering the noise

Box constrained total generalized variation model and primal-dual algorithm for Poisson noise removal

We consider the image denoising problem under Poisson noise. To further enhance the image denoising effect, a box constraint is incorporated into the total generalized variation (TGV) model by simply projecting all pixel values of the denoised image to lie in a certain interval (e.g., [0, 1] for normalized images and [0, 255] for 8-bit images). Thus, a box constrained TGV model is proposed. Computationally, combining with the dual representation of the second-order TGV regularization, our proposed model is transformed into a minimax problem, and the Chambolle–Pock’s first-order primal-dual algorithm is used to compute the saddle point of the minimax problem. In addition, the convergence of Algorithm 1 is discussed. Numerical experiments demonstrate that our proposed model not only gets better visual effects but also obtains higher signal-to-noise ratio, peak signal-to-noise ratio and structural similarity index than several existing state-of-the-art methods.

A Novel Total Generalized Variation Model for Image Dehazing

In this paper, we propose a new variational model for removing haze from a single input image. The proposed model combines two total generalized variation (TGV) regularizations, which are related to the image intensity and the transmission map, respectively, to build an optimization problem. Actually, TGV functionals are more appropriate for describing a natural color image and its transmission map with slanted plane. By minimizing the energy functional with double-TGV regularizations, we obtain the final haze-free image and the refined transmission map simultaneously instead of the general two-step framework. The existence and uniqueness of solutions to the proposed variational model are further obtained. Moreover, the variational model can be solved in a unified way by realizing a primal–dual method for associated saddle-point problems. A number of experimental results on natural hazy images are presented to demonstrate our superior performance, in comparison with some state-of-the-art methods in terms of the subjective and objective visual quality assessments. Compared with the total variation-based models, the proposed model can generate a haze-free image with less staircasing artifacts in the slanted plane and more details in the remote scene of an input image.

Weighted total generalized variation model for Poisson noise removal

We consider the image denoising problem under Poisson noise. The total generalized variation (TGV)-based method is high efficient in eliminating the staircase effect which often occurs in the total variation-based methods. However, the TGV-based method may produces over-smoothing edges. In order to avoid over-smoothing edges, a weighted total generalized variation (WTGV) model is proposed. Computationally, the WTGV minimization problem is transformed into a saddle-point problem by using the dual technique of optimization. Then, the Chambolle–Pock’s first-order primal–dual algorithm is used to solve the transformed saddle-point problem. At last, compared with several existing state-of-the-art methods, experimental results demonstrate the performance of our proposed method in edges preservation and staircase effect elimination.

Truncated Fractional-Order Total Variation Model for Image Restoration

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.

A new adaptive boosting total generalized variation (TGV) technique for image denoising and inpainting

In this paper we present a new adaptive boosting technique for total generalized variation (TGV) based image denoising and inpainting. Instead of the strengthening and substracting steps in existing boosting techniques, the proposed technique is iteratively operated by two steps: the first step is to take average of restored image with observed image, and updated parameter; the second step is to operate the TGV restoration algorithm with the average and dynamic parameter. For each iteration, as the input contains more correct information, the restoration algorithm can produce signals with more details. We have solved our boosting TGV model by primal-dual method, and applied the boosting TGV technique for gray/color image denoising and inpainting. Our algorithms have been discussed about influence of parameters, computational cost and compared with several typical existing methods. Plenty of experimental results show that our method can produce images with more structures and prevent staircase artifacts effectively.

Fast high-resolution brain metabolite mapping on a clinical 3T MRI by accelerated H-FID-MRSI and low-rank constrained reconstruction.

Epitomizing the advantages of ultra short echo time and no chemical shift displacement error, high-resolution-free induction decay magnetic resonance spectroscopic imaging (FID-MRSI) sequences have proven to be highly effective in providing unbiased characterizations of metabolite distributions. However, its merits are often overshadowed in high-resolution settings by reduced signal-to-noise ratios resulting from the smaller voxel volumes procured by extensive phase encoding and the related acquisition times. To address these limitations, we here propose an acquisition and reconstruction scheme that offers both implicit dataset denoising and acquisition acceleration. Specifically, a slice selective high-resolution FID-MRSI sequence was implemented. Spectroscopic datasets were processed to remove fat contamination, and then reconstructed using a total generalized variation (TGV) regularized low-rank model. We further measured reconstruction performance for random undersampled data to assess feasibility of a compressed-sensing SENSE acceleration scheme. Performance of the lipid suppression was assessed using an ad hoc phantom, while that of the low-rank TGV reconstruction model was benchmarked using simulated MRSI data. To assess real-world performance, 2D FID-MRSI acquisitions of the brain in healthy volunteers were reconstructed using the proposed framework. Results from the phantom and simulated data demonstrate that skull lipid contamination is effectively removed and that data reconstruction quality is improved with the low-rank TGV model. Also, we demonstrated that the presented acquisition and reconstruction methods are compatible with a compressed-sensing SENSE acceleration scheme. An original reconstruction pipeline for 2D H-FID-MRSI datasets was presented that places high-resolution metabolite mapping on 3T MR scanners within clinically feasible limits.

Nonconvex and nonsmooth total generalized variation model for image restoration

In this paper, we propose a nonconvex and nonsmooth total generalized variation (TGV) model for image restoration, which can provide an even sparser representation of the variation of the image function than the traditional TGV model that uses convex l1 norm to measure the variation. New model combines the advantages of nonconvex regularization and TGV regularization, and can preserve image edges well and simultaneously alleviate the staircase effects often arising in the total variation based models. Two different iteratively reweighed algorithms are introduced to numerically solve the proposed nonconvex and nonsmooth TGV model. Numerical results show that the proposed model is effective in edge-preserving and staircase-reduction in image restoration. In addition, compared with several state-of-the-art variational models, the proposed model has the best performance in terms of PSNR and MSSIM values.

InSAR phase filtering using spatially adapted total generalized variation

ABSTRACTPhase filtering is an important processing step in interferometric synthetic aperture radar (InSAR) measurement. It is a difficult task to achieve noise reduction and fringe preservation simultaneously. To solve the dilemma, a new noise reduction scheme for InSAR phase images is introduced based on total generalized variation (TGV). The TGV regularization has been mathematically proven to be able to preserve edges while still imposing high-order smoothness in homogeneous regions. Combined with the characteristics of phase image, a spatially adapted TGV model is used as a regularizer in phase filtering. The regularization parameters are adaptively selected according to the coherence and local phase image features. The presented model is realized in the complex domain in order to avoid the effect of phase wrapping. Experiment results from simulated and real data sets demonstrate the effectiveness of this algorithm.

An Adaptive Total Generalized Variation Model with Augmented Lagrangian Method for Image Denoising

We propose an adaptive total generalized variation (TGV) based model, aiming at achieving a balance between edge preservation and region smoothness for image denoising. The variable splitting (VS) and the classical augmented Lagrangian method (ALM) are used to solve the proposed model. With the proposed adaptive model and ALM, the regularization parameter, which balances the data fidelity and the regularizer, is refreshed with a closed form in each iterate, and the image denoising can be accomplished without manual interference. Numerical results indicate that our method is effective in staircasing effect suppression and holds superiority over some other state-of-the-art methods both in quantitative and in qualitative assessment.