A non-local vectorial total variational model for multichannel SAR image speckle suppression

Abstract This paper aims at the multichannel synthetic aperture radar （SAR） image speckle reduc- tion. This paper proposes a novel energy minimized regularization model for multichannel image denoising, which is an extension of the non-local total variational model for gray-scale image. It contains two terms, namely the vectorial data fidelity term and the non-local vectorial total variation term. The latter is constructed by high-dimensional non-local gradient that contains the structure information of the multichannel image. The existence and the uniqueness of the solution of the model are proved. A fixed point iterative algorithm is designed to acquire the solution of this model. The convergence property of this algorithm is proved as well. This model is applied to the multipolarimetric and multi-temporal RAI）ARSAT-2 images despeckling. The result shows that this model performs better than the original vectorial total variational model on texture preserving.

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.

Adaptive Reversible Visible Watermarking Based on Total Variation for BTC-Compressed Images

Few previous Reversible Visible Watermarking(RVW)schemes have both good transparency and watermark visibility.An adaptive RVW scheme that integrates Total Variation and visual perception in Block Truncation Coding(BTC)compressed domain,called TVB-RVW is proposed in this paper.A new mean image estimation method for BTC-compressed images is first developed with the help of Total Variation.Then,a visual perception factor computation model is devised by fusing texture and luminance characteristics.An adaptive watermark embedding strategy is used to embed the visible watermark with the effect of the visual perception factor in the BTC domain.Moreover,a lossless embedding method of the encrypted visible watermark is exploited to deter illegal watermark removal.The visible watermark can be removed since the visual perception factor and the estimated mean image remain unchanged before and after watermark embedding.Extensive experiments validate the superiority of the proposed algorithm over previous RVW schemes in BTC in terms of the visual quality of watermarked images and watermark visibility,and it can achieve a good balance between transparency and watermark visibility.

Compressive near-field millimeter wave imaging algorithm based on Gini index and total variation mixed regularization

A compressive near-field millimeter wave(MMW)imaging algorithm is proposed.From the compressed sensing(CS)theory,the compressive near-field MMW imaging process can be considered to reconstruct an image from the under-sampled sparse data.The Gini index(GI)has been founded that it is the only sparsity measure that has all sparsity attributes that are called Robin Hood,Scaling,Rising Tide,Cloning,Bill Gates,and Babies.By combining the total variation(TV)operator,the GI-TV mixed regularization introduced compressive near-field MMW imaging model is proposed.In addition,the corresponding algorithm based on a primal-dual framework is also proposed.Experimental results demonstrate that the proposed GI-TV mixed regularization algorithm has superior convergence and stability performance compared with the widely used l1-TV mixed regularization algorithm.

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.

A High Order Accurate Bound-Preserving Compact Finite Difference Scheme for Two-Dimensional Incompressible Flow

For solving two-dimensional incompressible flow in the vorticity form by the fourth-order compact finite difference scheme and explicit strong stability preserving temporal discretizations,we show that the simple bound-preserving limiter in Li et al.(SIAM J Numer Anal 56:3308–3345,2018)can enforce the strict bounds of the vorticity,if the velocity field satisfies a discrete divergence free constraint.For reducing oscillations,a modified TVB limiter adapted from Cockburn and Shu(SIAM J Numer Anal 31:607–627,1994)is constructed without affecting the bound-preserving property.This bound-preserving finite difference method can be used for any passive convection equation with a divergence free velocity field.

Image reconstruction based on total-variation minimization and alternating direction method in linear scan computed tomography

Linear scan computed tomography （LCT） is of great benefit to online industrial scanning and security inspection due to its characteristics of straight-line source trajectory and high scanning speed. However, in practical applications of LCT, there are challenges to image reconstruction due to limited-angle and insufficient data. In this paper, a new reconstruction algorithm based on total-variation （TV） minimization is developed to reconstruct images from limited-angle and insufficient data in LCT. The main idea of our approach is to reformulate a TV problem as a linear equality constrained problem where the objective function is separable, and then minimize its augmented Lagrangian function by using alternating direction method （ADM） to solve subproblems. The proposed method is robust and efficient in the task of reconstruction by showing the convergence of ADM. The numerical simulations and real data reconstructions show that the proposed reconstruction method brings reasonable performance and outperforms some previous ones when applied to an LCT imaging problem.

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.

Image decomposition and staircase effect reduction based on total generalized variation

Total variation （TV） is widely applied in image process-ing. The assumption of TV is that an image consists of piecewise constants, however, it suffers from the so-cal ed staircase effect. In order to reduce the staircase effect and preserve the edges when textures of image are extracted, a new image decomposition model is proposed in this paper. The proposed model is based on the to-tal generalized variation method which involves and balances the higher order of the structure. We also derive a numerical algorithm based on a primal-dual formulation that can be effectively imple-mented. Numerical experiments show that the proposed method can achieve a better trade-off between noise removal and texture extraction, while avoiding the staircase effect efficiently.

Image haze removal via multiscale fusion and total variation

In foggy weather, images of outdoor scene are usually characterized with poor visibility as well as faint color saturation. The degraded hazy images may have substantial negative impact on most computer vision systems. Thus image haze removal is of the practical significance in engineering. This paper proposes a fast and effective single image haze removal algorithm on the basis of the physics imaging model. To extract the global atmospheric light accurately, we exploit multiple prior rules underlying hazy images, and put forward a novel measurement to judge the likelihood that a pixel is regarded as the global atmospheric light. In addition, the rough transmission map is estimated through a multiscale fusion process based on the Laplace pyramid transform, and refined by a total variation model. Experimental results demonstrate the proposed method outperforms most of the state-of-the-art algorithms in terms of the dehazing quality, and achieves a trade-off between the computational efficiency and haze removal capability.

Adaptive variational models for image decomposition combining staircase reduction and texture extraction

New models for image decomposition are proposed which separate an image into a cartoon, consisting only of geometric objects, and an oscillatory component, consisting of textures or noise. The proposed models are given in a variational formulation with adaptive regularization norms for both the cartoon and texture parts. The adaptive behavior preserves key features such as object boundaries and textures while avoiding staircasing in what should be smooth regions. This decomposition is computed by minimizing a convex functional which depends on the two variables u and v, alternatively in each variable. Experimental results and comparisons to validate the proposed models are presented.

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.

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.

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.

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.

Weighted Variational Minimization Model for Wavelet Domain Inpainting with Primal-Dual Method

To preserve the edges and details of the image,a new variational model for wavelet domain inpainting was proposed which contained a non-convex regularizer. The non-convex regularizer can utilize the local information of image and perform better than those usual convex ones. In addition, to solve the non-convex minimization problem,an iterative reweighted method and a primaldual method were designed. The numerical experiments show that the new model not only gets better visual effects but also obtains higher signal to noise ratio than the recent method.

Relationship between the Interannual Variations of Total Ozone in the Northern Hemisphere and the QBO of Basic Flow in the Tropical Stratosphere

The harmonic analyses of monthly mean total ozone in the atmosphere over the Northern Hemisphere for 26 years (1960-1985) are made by using the Fourier expansion. The analysed results show that there is obviously a quasi-biennial oscillation (QBO) in the interannual variations of the amplitudes of total ozone. Generally, the amplitudes of wavenumber 1 and 2 during the westerly of the equatorial QBO are larger than those during the easterly. In the early winter, the amplitude of wavenumber 1 during the easterly phase is larger, and in the late winter, it is larger during the westerly phase. These are in good agreement with the observational distributions.