变分框架下的多尺度图像恢复与重建

变分图像分解,通过极小化能量泛函将图像分解为不同的特征分量,可以被应用到图像的恢复和重建.提出了变分框架下的多尺度图像恢复和重建的思想.基于这种思想,首先提出了一个单参数的（BV,G,E）三元变分分解模型,并且理论分析了参数与不同特征分量的尺度的关系.然后将此模型的参数选为一个二进制序列,得到多尺度的（BV,G,E）变分分解.该多尺度变分分解可以将图像分解为一序列图像结构、纹理和噪声.证明了此多尺度分解的收敛性并且基于对偶理论和交替迭代算法给出了其数值求解方法.最后将提出的多尺度的（BV,G,E）变分分解应用到图像恢复和重建,实验结果证实了理论分析的正确性,显示了将此模型进行图像多尺度恢复和重建的有效性,和与一些其他分解模型相比较的优越性.     

Non-local total bounded variation scheme for multiple-coil magnetic resonance image restoration

In this paper, we design a variational model for restoring multiple-coil magnetic resonance images (MRI) corrupted by non-central Chi distributed noise. The energy functional corresponding to the restoration problem is derived using the maximum a posteriori (MAP) estimator. Optimizing this functional yields the solution, which corresponds to the restored version of the image. The non-local total bounded variation prior is being used as the regularization term in the functional derived using the MAP estimation process. Further, the split-Bregman iteration scheme is being followed for fast numerical computation of the model. The results are compared with the state of the art MRI restoration models using visual representations and statistical measures.     

Variational Image Restoration and Decomposition in Shearlet Smoothness Spaces

We present the shearlet-based variational model for image restoration and decomposition.The new model can be seen as generalizations of Daubechies-Teschke's model.By using regularization term in shearlets smoothness spaces,and writing the problem in a shearlet framework,we obtain elegant shearlet shrinkage schemes.Furthermore,the model allows us to incorporate general bounded linear blur operators into the problem.The experiments on denoising,deblurring and decomposition of images show that our algorithm is very efficient.     

Variational Numerical Methods for Solving Nonlinear Diffusion Equations Arising in Image Processing

In this paper we give a general, robust, and efficient approach for numerical solutions of partial differential equations (PDEs) arising in image processing and computer vision. The well-established variational computational techniques, namely, finite element, finite volume, and complementary volume methods, are introduced on a common base to solve nonlinear problems in image multiscale analysis. Since they are based on principles like minimization of energy (finite element method) or conservation laws (finite and complemetary volume methods), they have strong physical backgrounds. They allow clear and physically meaningful derivation of difference equations that are local and easy to implement. The variational methods are combined with semi-implicit discretization in scale, which gives favorable stability and efficiency properties of computations. We show here L_∞-stability without any restrictions on scale steps. Our approach leads finally to solving linear systems in every discrete scale level, which can be done efficiently by fast preconditioned iterative solvers. We discuss such computational schemes for the regularized (in the sense of F. Catté et al., SIAM J. Numer. Anal.129, 1992, 182–193) Perona–Malik anisotropic diffusion equation (P. Perona and J. Malik, IEEE Trans. Pattern Anal. Mach. Intell.12, 1990, 629–639) and for nonlinear degenerate diffusion equation of mean curvature flow type studied by L. Alvarez et al. (SIAM J. Numer. Anal.129, 1992, 845–866).     

A primal-dual gradient method for image decomposition based on (<Emphasis Type="Italic">BV</Emphasis>, <Emphasis Type="Italic">H</Emphasis><Superscript>−1</Superscript>)

The main aim of this paper is to accelerate the image decomposition model based on (BV, H ⁻¹). It is solved with a particularly effective primal-dual gradient descent algorithm. The algorithm works on the primal-dual formulation and exploits the information of the primal and dual variables simultaneously. It converges significantly faster than some popular existing methods in numerical experiments. This approach is to some extent related to projection type methods for solving variational inequalities.     

Image decomposition combining staircase reduction and texture extraction

This paper proposes a natural and efficient way to achieve staircase reduction in texture extraction models of image processing. Moreover, we propose a precise framework for this amalgamation. In a sense, we utilize the best of both worlds: (I) the use of higher order derivatives through a variant of the Chambolle–Lions inf convolution energy (an image decomposition model in itself) along with (II) approximations to Meyer’s G and E norms including the H⁻¹ negative norm for ameliorating staircasing in image decomposition and restoration problems.     

泊松噪声模糊图像的边缘保持变分复原算法

从贝叶斯估计出发,构造了一种新的变分模型,用于复原被泊松噪声污染的模糊图像.首先讨论了模型正则化项中具有边缘保持能力的函数选取以及模型求解的相关问题,然后将变分模型的求解转化为可快速求解的非线性扩散方程,给出了正则化参数选取的初步空间自适应方法,可以区分平滑区域和图像边缘自适应的调节参数.实验结果表明,本文方法的复原效果整体上优于传统的迭代正则化方法,复原图像的边缘得到了有效的保护,泊松噪声的抑制效果明显,复原图像提高的改进信噪比(ISNR)要比迭代正则化方法平均提高1 dB以上.     

Parameter estimation in TV image restoration using variational distribution approximation.

In this paper, we propose novel algorithms for total variation (TV) based image restoration and parameter estimation utilizing variational distribution approximations. Within the hierarchical Bayesian formulation, the reconstructed image and the unknown hyper parameters for the image prior and the noise are simultaneously estimated. The proposed algorithms provide approximations to the posterior distributions of the latent variables using variational methods. We show that some of the current approaches to TV-based image restoration are special cases of our framework. Experimental results show that the proposed approaches provide competitive performance without any assumptions about unknown hyper parameters and clearly outperform existing methods when additional information is included.     

Unsupervised learning of multi-task deep variational model

We propose a general deep variational model (reduced version, full version as well as the extension) via a comprehensive fusion approach in this paper. It is able to realize various image tasks in a completely unsupervised way without learning from samples. Technically, it can properly incorporate the CNN based deep image prior (DIP) architecture into the classic variational image processing models. The minimization problem solving strategy is transformed from iteratively minimizing the sub-problem for each variable to automatically minimizing the loss function by learning the generator network parameters. The proposed deep variational (DV) model contributes to the high order image edition and applications such as image restoration, inpainting, decomposition and texture segmentation. Experiments conducted have demonstrated significant advantages of the proposed deep variational model in comparison with several powerful techniques including variational methods and deep learning approaches.     

A noise-suppressing and edge-preserving multiframe super-resolution image reconstruction method

Super-resolution technology is an approach that helps to restore high quality images and videos from degraded ones. The method stems from an ill-posed minimization problem, which is usually solved using the L² norm and some regularization techniques. Most of the classical regularizing functionals are based on the Total Variation and the Perona–Malik frameworks, which suffer from undesirable artifacts (blocking and staircasing). To address these problems, we have developed a super-resolution framework that integrates an adaptive diffusion-based regularizer. The model is feature-dependent: linear isotropic in flat regions, a condition that regularizes an image uniformly and removes noise more effectively; and nonlinear anisotropic near boundaries, which helps to preserve important image features, such as edges and contours. Additionally, the new regularizing kernel incorporates a shape-defining parameter that can be automatically updated to ensure convexity and stability of the corresponding energy functional. Comparisons with other methods show that our method is superior and, more importantly, can achieve higher reconstruction factors.     

面向多尺度分割的疑似违章建筑提取算法

针对城市中疑似违章建筑物信息提取的问题,提出了一种基于多尺度分割方法提取疑似违章建筑信息的新算法.该算法首先通过设置多尺度分割参数对遥感影像进行分割,然后通过正射校正、辐射定标、大气校正对遥感影像进行预处理,最后通过多尺度分割实验分析各参数对尺度分割效果的影响.研究结果表明分割尺度为150、形状比例系数为0.7、紧致度...     

A novel image restoration scheme based on structured side information and its application to image watermarking

This paper presents a new image restoration method based on a linear optimization model which restores part of the image from structured side information (SSI). The SSI can be transmitted to the receiver or embedded into the image itself by a digital watermarking technique. In this paper we focus on a special type of SSI for digital watermarking where the SSI is composed of mean values of 4×4 image blocks which can be used to restore manipulated blocks. Different from existing image restoration methods for similar types of SSI, the proposed method minimizes image discontinuity according to a relaxed definition of smoothness based on a 3×3 averaging filter of four adjacent pixel value differences, and the objective function of the optimization model has a second regularization term corresponding to a second-order smoothness criterion. Our experiments on 100 test images showed that given complete information of the SSI, the proposed image restoration technique can outperform the state-of-the-art model based on a simple linear optimization model by around 2 dB in terms of an average Peak Signal-to-Noise Ratio (PSNR) value and around 0.04 in terms of a Structural Similarity Index (SSIM) value. We also tested the robustness of the image restoration method when it is applied to a self-restoration watermarking scheme and the experimental results showed that it is moderately robust to errors in SSI (which is embedded as a watermark) caused by JPEG compression (the average PSNR value remains above 16.5 dB even when the JPEG QF is 50), additive Gaussian white noises (the average PSNR value is approximately 18.4 dB when the noise variance σ² is 10) and image rescaling assuming the original image size is known at the receiver side (e.g. the average PSNR value is approximately 19.6 dB when the scaling ratio is 1.4).     

Oriented total variation l1/2 regularization

Total Variation (TV) is a widely used image restoration/decomposition model. It is observed that the classical TV l1 and TV l2 regularization, on the one hand, do not favor higher-gradient structures over lower-gradient details as expected for structure preserving image processing, and on the other hand, tend to reduce the horizontal and vertical gradients, and thus inevitably blur the oblique edges in images. In this paper, we address these two problems by defining Oriented Total Variation l1/2 (OTV l1/2). It is theoretically and experimentally demonstrated that applying l1/2 regularization to the directional derivatives of images leads to superior structure preservation. OTV l1/2 regularization can be applied to image denoising and video compression, and the experimental results verify that OTV l1/2 outperforms other similar models.     

Variational Bayesian Blind Deconvolution Using a Total Variation Prior

In this paper, we present novel algorithms for total variation (TV) based blind deconvolution and parameter estimation utilizing a variational framework. Using a hierarchical Bayesian model, the unknown image, blur, and hyperparameters for the image, blur, and noise priors are estimated simultaneously. A variational inference approach is utilized so that approximations of the posterior distributions of the unknowns are obtained, thus providing a measure of the uncertainty of the estimates. Experimental results demonstrate that the proposed approaches provide higher restoration performance than non-TV-based methods without any assumptions about the unknown hyperparameters.      

非合作水雷目标图像非均匀强噪声去除方法

水雷目标探测会受到水下非均匀强噪声（有机质、悬浮颗粒等）的干扰,为了解决这一问题,提出了一种新的去噪方法。首先优化局部保边缘滤波算法,提出了基于边缘感知约束的局部保边缘滤波,在模型中引入了一个空间自适应的边缘感知约束正则化项,用来更好地表征图像的边缘及细节,使得算法的保边缘平滑特性更好。其次针对强噪声的非均匀特性,采用多尺度策略,迭代地将优化后的模型运用到每个尺度的去噪结果上生成多尺度分解,并在多尺度分解的过程中,逐步增加去噪尺度,将不同尺度的噪声逐步从上一尺度的去噪结果中分离出来。实验结果表明,相较于其他经典去噪方法,提出的算法能够在更好地去除水下非均匀强噪声的同时保留水雷目标信息,对实时水雷作业有着一定的指导意义。     

Minimizing the total variation under a general convex constraint for image restoration

We present a general framework for image restoration; despite its simplicity, certain variational and certain wavelet approaches can be formulated within this framework. This permits the construction of a natural model, with only one parameter, which has the advantages of both approaches. We give a mathematical analysis of this model, describe our algorithm and illustrate this by some experiments.     

Presentation attack detection based on two-stream vision transformers with self-attention fusion

Aiming at the performance degradation of the existing presentation attack detection methods due to the illumination variation, a two-stream vision transformers framework (TSViT) based on transfer learning in two complementary spaces is proposed in this paper. The face images of RGB color space and multi-scale retinex with color restoration (MSRCR) space are fed to TSViT to learn the distinguishing features of presentation attack detection. To effectively fuse features from two sources (RGB color space images and MSRCR images), a feature fusion method based on self-attention is built, which can effectively capture the complementarity of two features. Experiments and analysis on Oulu-NPU, CASIA-MFSD, and Replay-Attack databases show that it outperforms most existing methods in intra-database testing and achieves good generalization performance in cross-database testing.     

基于小波空间的图像分解变分模型

本文从不同的角度考虑OSV模型,提出一种基于全变差和H^-1范数的图像分解变分模型.通过分析OSV模型的性质,给出该模型基于小波空间的非线性偏微分方程和迭代算法.同时,从理论上分析了该模型的极小值存在性.实验表明该方法具有可行性.     

Fast algorithm for multiplicative noise removal

In this work, we consider a variational restoration model for multiplicative noise removal problem. By using a maximum a posteriori estimator, we propose a strictly convex objective functional whose minimizer corresponds to the denoised image we want to recover. We incorporate the anisotropic total variation regularization in the objective functional in order to preserve the edges well. A fast alternating minimization algorithm is established to find the minimizer of the objective functional efficiently. We also give the convergence of this minimization algorithm. A broad range of numerical results are given to prove the effectiveness of our proposed model.     

ML parameter estimation for Markov random fields with applicationsto Bayesian tomography

Markov random fields (MRFs) have been widely used to model images in Bayesian frameworks for image reconstruction and restoration. Typically, these MRF models have parameters that allow the prior model to be adjusted for best performance. However, optimal estimation of these parameters (sometimes referred to as hyperparameters) is difficult in practice for two reasons: (i) direct parameter estimation for MRFs is known to be mathematically and numerically challenging; (ii) parameters can not be directly estimated because the true image cross section is unavailable. We propose a computationally efficient scheme to address both these difficulties for a general class of MRF models, and we derive specific methods of parameter estimation for the MRF model known as generalized Gaussian MRF (GGMRF). We derive methods of direct estimation of scale and shape parameters for a general continuously valued MRF. For the GGMRF case, we show that the ML estimate of the scale parameter, sigma, has a simple closed-form solution, and we present an efficient scheme for computing the ML estimate of the shape parameter, p, by an off-line numerical computation of the dependence of the partition function on p. We present a fast algorithm for computing ML parameter estimates when the true image is unavailable. To do this, we use the expectation maximization (EM) algorithm. We develop a fast simulation method to replace the E-step, and a method to improve the parameter estimates when the simulations are terminated prior to convergence. Experimental results indicate that our fast algorithms substantially reduce the computation and result in good scale estimates for real tomographic data sets.