Dark channel prior based blurred image restoration method using total variation and morphology

The blurred image restoration method can dramatically highlight the image details and enhance the global contrast, which is of benefit to improvement of the visual effect during practical ap- plications. This paper is based on the dark channel prior principle and aims at the prior information absent blurred image degradation situation. A lot of improvements have been made to estimate the transmission map of blurred images. Since the dark channel prior principle can effectively restore the blurred image at the cost of a large amount of computation, the total variation （TV） and image morphology transform （specifically top-hat transform and bottom- hat transform） have been introduced into the improved method. Compared with original transmission map estimation methods, the proposed method features both simplicity and accuracy. The es- timated transmission map together with the element can restore the image. Simulation results show that this method could inhibit the ill-posed problem during image restoration, meanwhile it can greatly improve the image quality and definition.

Novel image restoration model coupling gradient fidelity term based on adaptive total variation

A novel image restoration model coupling with a gradient fidelity term based on adaptive total variation is proposed in this paper. In order to choose proper parameters, the selection criteria were analyzed theoretically, and a simple scheme to demonstrate its validity was adopted experimentally. To make fair comparisons of performances of three models, the same numerical algorithm was used to solve partial differential equations. Both the international standard test image on Lena and HR image of CBERS-02B of Dalian city were used to verify the performance of the model. Experimental results illustrate that the new model not only preserved the edge and important details but also alleviated the staircase effect effectively.

Adaptive Parameter Selection for Total Variation Image Deconvolution

In this paper,we propose a discrepancy rule-based method to automatically choose the regularization parameters for total variation image restoration problems. The regularization parameters are adjusted dynamically in each iteration.Numerical results are shown to illustrate the performance of the proposed method.

Total Variation Constrained Non-Negative Matrix Factorization for Medical Image Registration

This paper presents a novel medical image registration algorithm named total variation constrained graphregularization for non-negative matrix factorization(TV-GNMF).The method utilizes non-negative matrix factorization by total variation constraint and graph regularization.The main contributions of our work are the following.First,total variation is incorporated into NMF to control the diffusion speed.The purpose is to denoise in smooth regions and preserve features or details of the data in edge regions by using a diffusion coefficient based on gradient information.Second,we add graph regularization into NMF to reveal intrinsic geometry and structure information of features to enhance the discrimination power.Third,the multiplicative update rules and proof of convergence of the TV-GNMF algorithm are given.Experiments conducted on datasets show that the proposed TV-GNMF method outperforms other state-of-the-art algorithms.

Reference-driven method for MR image reconstruction based on wavelet sparsity and nonlocal total variation

A novel reference-driven method for MR image reconstruction based on wavelet sparsity and nonlocal total variation（NLTV）is proposed.Utilizing the sparsity of the difference image between the target image and the motion-compensated reference image in wavelet transform domain,the proposed method does not need to estimate contrast changes and therefore increases computational efficiency.Additionally,NLTV regularization is applied to preserve image details and features without blocky effects.An efficient alternating iterative algorithm is used to estimate motion effects and reconstruct the difference image.Experimental results demonstrate that the proposed method can significantly reduce sampling rate or improve the quality of the reconstructed image alternatively.

A Compton scattering image reconstruction algorithm based on total variation minimization

Compton scattering imaging is a novel radiation imaging method using scattered photons.Its main characteristics are detectors that do not have to be on the opposite side of the source,so avoiding the rotation process.The reconstruction problem of Compton scattering imaging is the inverse problem to solve electron densities from nonlinear equations,which is ill-posed.This means the solution exhibits instability and sensitivity to noise or erroneous measurements.Using the theory for reconstruction of sparse images,a reconstruction algorithm based on total variation minimization is proposed.The reconstruction problem is described as an optimization problem with nonlinear data-consistency constraint.The simulated results show that the proposed algorithm could reduce reconstruction error and improve image quality,especially when there are not enough measurements.

Water Gauge Image Denoising Model Based on Improved Adaptive Total Variation

As an important part of water level warning in water conservancy projects,often due to the influence of environmental factors such as light and stains,the acquired water gauge images have sticky,broken and bright spot conditions,which affect the identification of water gauges.To solve this problem,a water gauge image denoising model based on improved adaptive total variation is proposed.Firstly,the regular term exponent in the adaptive total variational equation is changed to an inverse cosine function;secondly,the differential curvature is used to distinguish the image noise points and increase the smoothing strength at the noise points;finally,according to the characteristics of the gradient mode and adaptive gradient threshold after Gaussian filtering,the New model can adaptively denoise in the smooth area and protect the edge area,so as to have the characteristics of both edge-preserving denoising.The experimental results show that the new model has a great improvement in image vision,higher iteration efficiency and an average increase of 1.6 dB in peak signal-to-noise ratio,and an average increase of 9%in structural similarity,which is more beneficial to practical applications.

Adaptive Image Zooming Algorithm Combining Total Variation Minimization and a Second-order Functional

An image zooming algorithm by using partial differential equations(PDEs) is proposed here. It combines the second-order PDE with a fourth-order PDE. The combined algorithm is able to preserve edges and at the same time avoid the blurry effect in smooth regions. An adaptive function is used to combine the two PDEs. Numerical experiments illustrate advantages of the proposed model.

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.

Primal-dual algorithms for total variation based image restoration under Poisson noise Dedicated to Professor Lin Qun on the Occasion of his 80th Birthday

We consider the problem of restoring images corrupted by Poisson noise. Under the framework of maximum a posteriori estimator, the problem can be converted into a minimization problem where the objective function is composed of a Kullback-Leibler(KL)-divergence term for the Poisson noise and a total variation(TV) regularization term. Due to the logarithm function in the KL-divergence term, the non-differentiability of TV term and the positivity constraint on the images, it is not easy to design stable and efficiency algorithm for the problem. Recently, many researchers proposed to solve the problem by alternating direction method of multipliers(ADMM). Since the approach introduces some auxiliary variables and requires the solution of some linear systems, the iterative procedure can be complicated. Here we formulate the problem as two new constrained minimax problems and solve them by Chambolle-Pock's first order primal-dual approach. The convergence of our approach is guaranteed by their theory. Comparing with ADMM approaches, our approach requires about half of the auxiliary variables and is matrix-inversion free. Numerical results show that our proposed algorithms are efficient and outperform the ADMM approach.

HOMOTOPY CURVE TRACKING FOR TOTAL VARIATION IMAGE RESTORATION

The total variation （TV） minimization problem is widely studied in image restora- tion. Although many alternative methods have been proposed for its solution, the Newton method remains not usable for the primal formulation due to no convergence. A previous study by Chan, Zhou and Chan [15] considered a regularization parameter continuation idea to increase the domain of convergence of the Newton method with some success but no robust parameter selection schemes. In this paper, we consider a homotopy method for the same primal TV formulation and propose to use curve tracking to select the regular- ization parameter adaptively. It turns out that this idea helps to improve substantially the previous work in efficiently solving the TV Euler-Lagrange equation. The same idea is also considered for the two other methods as well as the deblurring problem, again with improvements obtained. Numerical experiments show that our new methods are robust and fast for image restoration, even for images with large noisy-to-signal ratio.Mathematics subject classification： 65N06, 65B99.

New Time Dependent Pretreat Models Based on Total Variational Image Restoration

In this paper, we propose new pretreat models for total variation （TV） minimization problems in image deblurring and denoising. Specially, blur operator is considered as useful information in restoration. New models in form is equivalent to pretreat the initial value by image blur operator. We successfully get a new （L. Rudin, S. Osher, and E. Fatemi） ROF model, a new level set motion model and a new anisotropic diffusion model respectively. Numerical experiments demonstrate that, under the same stopping rule, the proposed methods significantly accelerate the convergence of the toothed, save computation time and get the same restored effect.

Research on Spatially Adaptive High-Order Total Variation Model for Weak Fluorescence Image Restoration

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.

Wavelet inverse scale space for image restoration

This paper proposes a model for image restoration by combining the wavelet shrinkage and inverse scale space （ISS） method. The ISS is applied to the wavelet representation to modify the retained wavelet coefficients, and the coefficients smaller than the threshold are set to zero. The curvature term of the ISS can remove the edge artifacts and preserve sharp edges. For the multiscale interpretation of the ISS and the multiscale property of the wavelet representation, small details are preserved. This paper illustrates that the wavelet ISS model can be deduced from the wavelet based on a total variation minimization problem. A stopping criterion is obtained from this minimization in the sense of the Bregman distance in the wavelet domain. Numerical examples show the improvement for the image denoising with the proposed method in the sense of the signal to noise ratio and with fewer details remained in the residue.

Overview of Digital Image Restoration

Image restoration is an image processing technology with great practical value in the field of computer vision.It is a computer technology that estimates the image information of the damaged area according to the residual image information of the damaged image and carries out automatic repair.This article firstly classify and summarize image restoration algorithms,and describe recent advances in the research respectively from three aspects including image restoration based on partial differential equation,based on the texture of image restoration and based on deep learning,then make the brief analysis of digital image restoration of subjective and objective evaluation method,and briefly summarize application of digital image restoration technique in the future and prospects,provide direction for the research on image after repair.

Algorithm for reconstructing compressed sensing color imaging using the quaternion total variation

A new method for reconstructing the compressed sensing color image by solving an optimization problem based on total variation in the quaternion field is proposed, which can effectively improve the reconstructing ability of the color image. First, the color image is converted from RGB （red, green, blue） space to CMYK （cyan, magenta, yellow, black） space, which is assigned to a quaternion matrix. Meanwhile, the quaternion matrix is converted into the information of the phase and amplitude by the Euler form of the quatemion. Secondly, the phase and amplitude of the quatemion matrix are used as the smoothness constraints for the compressed sensing （CS） problem to make the reconstructing results more accurate. Finally, an iterative method based on gradient is used to solve the CS problem. Experimental results show that by considering the information of the phase and amplitude, the proposed method can achieve better performance than the existing method that treats the three components of the color image as independent parts.

UFC-Net with Fully-Connected Layers and Hadamard Identity Skip Connection for Image Inpainting

Image inpainting is an interesting technique in computer vision and artificial intelligence for plausibly filling in blank areas of an image by referring to their surrounding areas.Although its performance has been improved significantly using diverse convolutional neural network(CNN)-based models,these models have difficulty filling in some erased areas due to the kernel size of the CNN.If the kernel size is too narrow for the blank area,the models cannot consider the entire surrounding area,only partial areas or none at all.This issue leads to typical problems of inpainting,such as pixel reconstruction failure and unintended filling.To alleviate this,in this paper,we propose a novel inpainting model called UFC-net that reinforces two components in U-net.The first component is the latent networks in the middle of U-net to consider the entire surrounding area.The second component is the Hadamard identity skip connection to improve the attention of the inpainting model on the blank areas and reduce computational cost.We performed extensive comparisons with other inpainting models using the Places2 dataset to evaluate the effectiveness of the proposed scheme.We report some of the results.

Multiquadric Radial Basis Function Approximation Scheme for Solution of Total Variation Based Multiplicative Noise Removal Model

This article introduces a fastmeshless algorithm for the numerical solution nonlinear partial differential equations(PDE)by Radial Basis Functions(RBFs)approximation connected with the Total Variation(TV)-basedminimization functional and to show its application to image denoising containing multiplicative noise.These capabilities used within the proposed algorithm have not only the quality of image denoising,edge preservation but also the property of minimization of staircase effect which results in blocky effects in the images.It is worth mentioning that the recommended method can be easily employed for nonlinear problems due to the lack of dependence on a mesh or integration procedure.The numerical investigations and corresponding examples prove the effectiveness of the recommended algorithm regarding the robustness and visual improvement as well as peak-signal-to-noise ratio(PSNR),signal-to-noise ratio(SNR),and structural similarity index(SSIM)corresponded to the current conventional TV-based schemes.

Parallel variable-density spiral imaging using nonlocal total variation reconstruction

The relatively long scan time is still a bottleneck for both clinical applications and research of magnetic resonance imaging. To reduce the data acquisition time, we propose a novel fast magnetic resonance imaging method based on parallel variable-density spiral acquisition, which combines undersampling optimization and nonlocal total variation reconstruction. The undersampling optimization promotes the incoherence of resultant aliasing artifact via the ＂worst-case＂ residual error metric, and thus accelerates the data acquisition. Moreover, nonlocal total variation reconstruction is utilized to remove such an incoherent aliasing artifact and so improve image quality. The feasibility of the proposed method is demonstrated by both numerical phantom simulation and in vivo experiment. The experimental results show that the proposed method can achieve high acceleration factor and effectively remove an aliasing artifact from data undersampling with well-preserved image details. The image quality is better than that achieved with the total variation method.

Improved simultaneous multislice magnetic resonance imaging using total variation regularization

Controlled aliasing in parallel imaging results in higher acceleration （CAIPIRINHA） for simultaneous multislice imaging has been proposed recently, which combines multiband excitation and phase cycling techniques to reduce scan time and improve subsequent imaging reconstruction. In this work, the total variation （TV） regularization method is used to further improve CAIPIRINHA. The TV regularization uses an edge-preserving prior, which establishes a relationship between neighboring pixels for image reconstruction. It reduces artifacts and suppresses noise amplification simultaneously. The results are presented with a standard eight-channel head coil with an acceleration factor of 4, where the TV-regularized CAIPIRINHA generates an improved reconstruction as compared with a typical nonregularized CAIPIRINHA.