交替使用小波去噪和全变差正则化的盲图像恢复算法

盲图像恢复就是在点扩散函数未知情况下从降质观测图像恢复出原图像.该文提出了一种交替使用小波去噪和全变差正则化的盲图像恢复算法.观测模型首先被分解成两个相互关联的子模型,这种分解转化盲恢复问题成为图像去噪和图像恢复两个问题,可以交替采用图像去噪和图像恢复算法求解.模糊辨识阶段,使用全变差正则化算法估计点扩散函数;图像恢复阶段,使用小波去噪和全变差正则化相结合的算法恢复图像.实验结果和与其它方法的比较表明该文算法能够获得更好的恢复效果.     

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.     

基于全变分扩展方法的压缩感知磁共振成像算法研究

针对全变分算法在压缩感知磁共振成像(CS-MRI)重构过程中存在阶梯效应的问题,该文研究3种基于全变分扩展方法的CS-MRI成像算法,即高阶全变分、总广义变分和组合稀疏全变分,并将其与平移不变离散小波稀疏基相结合,建立稀疏模型,采用快速复合分裂算法求解CS-MRI重构的凸优化问题。同时,讨论了全变分及其扩展方法对两种不同磁共振图像数据和径向欠采样模式重构CS-MRI的精度。实验结果表明,基于全变分扩展的重构算法能有效解决全变分重建中存在阶梯效应的缺点;另外,相比高阶全变分和总广义变分重构算法,组合稀疏全变分方法具有更好的重建效果,获得更高重构信噪比。     

带总观测误差约束的模糊图像恢复

模糊图像恢复是数字图像处理领域的研究热点之一,总变差(Total Variation, TV)规整化可以很好的保持图像的细节,然而,传统的TV图像恢复模型需要考虑最优的正则化参数,由此,提出了一族包含不同规整化因子,带总观测误差约束的模糊图像恢复模型,并分为去模糊和去噪两步求解此模型。在去模糊过程中,利用共轭梯度法求出一个满足总观测误差约束的初始恢复图像;在去噪过程中,首先,以去模糊的结果作为初始估计;其次,针对 范数最小化问题,利用优化—最小化(Majoriziation-Minimization, MM)算法的思想,将原问题转化为一系列容易求解的优化子问题;最后,极小化优化子问题,得到最终的恢复图像。实验结果表明,该算法对模糊图像的恢复效果是显著地。      

An adaptive two phase blind image deconvolution algorithm for an iterative regularization model

This paper proposes a blind image deconvolution method which consists of two sequential phases, i.e., blur kernel estimation and image restoration. In the first phase, we adopt the L₀-norm of image gradients and total variation (TV) to regularize the latent image and blur kernel, respectively. Then we design an alternating optimization algorithm which jointly incorporates the estimation of intermediately restored image, blur kernel and regularization parameters into account. In the second phase, we propose to take the mixture of L₀-norm of image gradients and TV to regularize the latent image, and design an efficient non-blind deconvolution algorithm to achieve the restored image. Experimental results on both a benchmark image dataset and real-world blurred images show that the proposed method can effectively restore image details while suppress noise and ringing artifacts, the result is of high quality which is competitive with some state of the art methods.     

基于全变分模型的多分辨率光照处理算法

针对人脸识别中的光照问题,本文提出一种多分辨率分层的快速处理算法.该算法建立在扩展的全变分模型的理论基础之上,具有模型简单,优化参数少等优点,并能有效的减少光晕现象.算法从快速性入手,首先将光照劣化图像进行多分辨率分层,在每一层上利用模型进行估计,从而得出整体的光照成分,然后恢复出入脸的反射系数图像,并以此作为光照不变量来进行识别.实验证明,通过多分辨率分层的方法,不仅能使系统在不同光照条件下的识别率得到提高,而且还能解决单独用TV(Total Variation)模型进行估计时处理速度较慢的缺点.     

Bi-l0-l2-norm regularization for blind motion deblurring

In blind motion deblurring, leading methods today tend towards highly non-convex approximations of the l₀-norm, especially in the image regularization term. In this paper, we propose a simple, effective and fast approach for the estimation of the motion blur-kernel, through a bi-l₀-l₂-norm regularization imposed on both the intermediate sharp image and the blur-kernel. Compared with existing methods, the proposed regularization is shown to be more effective and robust, leading to a more accurate motion blur-kernel and a better final restored image. A fast numerical scheme is deployed for alternatingly computing the sharp image and the blur-kernel, by coupling the operator splitting and augmented Lagrangian methods. Experimental results on both a benchmark image dataset and real-world motion blurred images show that the proposed approach is highly competitive with state-of-the-art methods in both deblurring effectiveness and computational efficiency.     

Minmax-concave total variation denoising

Total variation (TV) denoising is a commonly used method for recovering 1-D signal or 2-D image from additive white Gaussian noise observation. In this paper, we define the Moreau enhanced function of \(L_1\) norm as \({\varPhi }_\alpha (x)\) and introduce the minmax-concave TV (MCTV) in the form of \({\varPhi }_\alpha (Dx)\), where D is the finite difference operator. We present that MCTV approaches \(\Vert Dx\Vert _0\) if the non-convexity parameter \(\alpha \) is chosen properly and apply it to denoising problem. MCTV can strongly induce the signal sparsity in gradient domain, and moreover, its form allows us to develop corresponding fast optimization algorithms. We also prove that although this regularization term is non-convex, the cost function can maintain convexity by specifying \(\alpha \) in a proper range. Experimental results demonstrate the effectiveness of MCTV for both 1-D signal and 2-D image denoising.     

Fast optimization for multichannel total variation minimization with non-quadratic fidelity

Total variation (TV) has been proved very successful in image processing, and it has been combined with various non-quadratic fidelities for non-Gaussian noise removal. However, these models are hard to solve because TV is non-differentiable and nonlinear, and non-quadratic fidelity term is also nonlinear and even non-differentiable for some special cases. This prevents their widespread use in practical applications. Very recently, it was found that the augmented Lagrangian method is extremely efficient for this kind of models. However, only the single-channel case (e.g., gray images) is considered. In this paper, we propose a general computational framework based on augmented Lagrangian method for multichannel TV minimization with non-quadratic fidelity, and then show how to apply it to two special cases: L¹ and Kullback-Leibler (KL) fidelities, two common and important data terms for blurry images corrupted by impulsive noise or Poisson noise, respectively. For these typical fidelities, we show that the sub-problems either can be fast solved by FFT or have closed form solutions. The experiments demonstrate that our algorithm can fast restore high quality images.     

基于结构组全变分模型的图像压缩感知重建

针对基于传统全变分(TV)模型的图像压缩感知(CS)重建算法不能有效地恢复图像的细节和纹理,从而导致图像过平滑的问题,该文提出一种基于结构组全变分(SGTV)模型的图像压缩感知重建算法。该算法利用图像的非局部自相似性和结构稀疏特性,将图像的重建问题转化为由非局部自相似图像块构建的结构组全变分最小化问题。算法以结构组全变分模型为正则化约束项构建优化模型,利用分裂Bregman迭代将算法分离成多个子问题,并对每个子问题高效地求解。所提算法很好地利用了图像自身的信息和结构稀疏特性,保护了图像细节和纹理。实验结果表明,该文所提出的算法优于现有基于全变分模型的压缩感知重建算法,在PSNR和视觉效果方面取得了显著提升。     

MR images reconstruction based on TVWL2–L1 model

Compressive sensing (CS) theory, which has been widely used in magnetic resonance (MR) image processing, indicates that a sparse signal can be reconstructed by the optimization programming process from non-adaptive linear projections. Since MR Images commonly possess a blocky structure and have sparse representations under certain wavelet bases, total variation (TV) and wavelet domain ?₁ norm regularization are enforced together (TV-wavelet L1 method) to improve the recovery accuracy. However, the components of wavelet coefficients are different: low-frequency components of an image, that carry the main energy of the MR image, perform a decisive impact for reconstruction quality. In this paper, we propose a TV and wavelet L2–L1 model (TVWL2–L1) to measure the low frequency wavelet coefficients with ?₂ norm and high frequency wavelet coefficients with ?₁ norm. We present two methods to approach this problem by operator splitting algorithm and proximal gradient algorithm. Experimental results demonstrate that our method can obviously improve the quality of MR image recovery comparing with the original TV-wavelet method.     

基于高斯平滑压缩感知分数阶全变分算法的图像重构

In view of the gradient effect caused by the gradient effect of the Total Variation (TV) algorithm and the environmental noise in the single pixel imaging system, an image reconstruction based on the Gaussian Smooth compressed sensing Fractional Order Total Variation algorithm (FOTVGS) is proposed. Fractional differential loss of low-frequency components of the image increases the high-frequency components of the image to achieve the purpose of enhancing image details. The Gaussian smoothing filter operator updates the Lagrangian gradient operator to filter out the additive white Gaussian noise caused by the differential operator. Simulation results show that, compared with other four similar algorithms, the algorithm can achieve the maximum Peak Signal-to-Noise Ratio (PSNR) and Structural SIMilarity(SSIM) at the same sampling rate and noise level. When the sampling rate is 0.2, compared with the Fractional Order Total Variation (FOTV) algorithm, the maximum PSNR and SSIM increase by 1.39 dB (0.035) and 3.91 dB (0.098) respectively. It can be proved that this algorithm can improve the reconstruction quality of the image in the absence of noise and noise, especially in the case of noise, the quality of image reconstruction is greatly improved. The proposed algorithm provides a feasible solution for image reconstruction of noise caused by environment in single-pixel imaging and other computing imaging system.     

一种应用于欠采样图像的自适应稀疏重建方法

针对图像稀疏重建中因使用固定参数的全变分(TV)正则项所带来的图像细节缺失和阶梯效应问题,提出了一种自适应二阶广义全变分(TGV)约束的图像稀疏重建算法.该算法采用二阶广义全变分模型权衡图像的一阶导数和二阶导数,且能够根据每次迭代得到的重构解及对应张量函数自适应地修正权重系数,实现图像的稀疏重建.与全变分正则模型和固定参数广义全变分正则模型相比,该算法能更好地保持图像轮廓和细节信息,提高重建图像的峰值信噪比(PSNR)和结构相似度(SSIM).     

Low-illumination image denoising method for wide-area search of nighttime sea surface

In order to suppress complex mixing noise in low-illumination images for wide-area search of nighttime sea surface, a model based on total variation (TV) and split Bregman is proposed in this paper. A fidelity term based on L1 norm and a fidelity term based on L2 norm are designed considering the difference between various noise types, and the regularization mixed first-order TV and second-order TV are designed to balance the influence of details information such as texture and edge for sea surface image. The final detection result is obtained by using the high-frequency component solved from L1 norm and the low-frequency component solved from L2 norm through wavelet transform. The experimental results show that the proposed denoising model has perfect denoising performance for artificially degraded and low-illumination images, and the result of image quality assessment index for the denoising image is superior to that of the contrastive models.     

Nonlocal discrete regularization on weighted graphs: a framework for image and manifold processing

We introduce a nonlocal discrete regularization framework on weighted graphs of the arbitrary topologies for image and manifold processing. The approach considers the problem as a variational one, which consists of minimizing a weighted sum of two energy terms: a regularization one that uses a discrete weighted p-Dirichlet energy and an approximation one. This is the discrete analogue of recent continuous Euclidean nonlocal regularization functionals. The proposed formulation leads to a family of simple and fast nonlinear processing methods based on the weighted p-Laplace operator, parameterized by the degree p of regularity, the graph structure and the graph weight function. These discrete processing methods provide a graph-based version of recently proposed semi-local or nonlocal processing methods used in image and mesh processing, such as the bilateral filter, the TV digital filter or the nonlocal means filter. It works with equal ease on regular 2-D and 3-D images, manifolds or any data. We illustrate the abilities of the approach by applying it to various types of images, meshes, manifolds, and data represented as graphs.     

基于全变分模型的图像噪声去除效果比较

基于偏微分方程的图像去噪方法由于将数学与工程结合得更加紧密,具有较强的自适应能力和灵活性.本文首先介绍了目前已经提出的变分模型的快速Split-Bregman算法,然后通过大量数值实验对不同模型的去噪效果进行了比较.所研究的模型包括L1范数、L2范数、LTV(1ayered total variation)规则项、MTV(multicharmel total variation)规则项和CTV(color total variation)规则项,从灰度图像和彩色多通道图像两方面进行分析.实验结果表明对于灰度图像基于L1范数的TV去噪模型效果较好,彩色图像中CTV模型对图像去噪边缘保持最好,其他依次是MTV模型、LTV模型.     

In Vivo Impedance Imaging With Total Variation Regularization

We show that electrical impedance tomography (EIT) image reconstruction algorithms with regularization based on the total variation (TV) functional are suitable for in vivo imaging of physiological data. This reconstruction approach helps to preserve discontinuities in reconstructed profiles, such as step changes in electrical properties at interorgan boundaries, which are typically smoothed by traditional reconstruction algorithms. The use of the TV functional for regularization leads to the minimization of a nondifferentiable objective function in the inverse formulation. This cannot be efficiently solved with traditional optimization techniques such as the Newton method. We explore two implementations methods for regularization with the TV functional: the lagged diffusivity method and the primal dual–interior point method (PD-IPM). First we clarify the implementation details of these algorithms for EIT reconstruction. Next, we analyze the performance of these algorithms on noisy simulated data. Finally, we show reconstructed EIT images of in vivo data for ventilation and gastric emptying studies. In comparison to traditional quadratic regularization, TV regulariza tion shows improved ability to reconstruct sharp contrasts.      

自适应非局部patch正则化图像恢复

 非局部均值利用图像自相似性,有效保持了图像的几何结构信息.提出了非局部patch正则和TV正则结合的图像恢复模型,利用改进的结构张量矩阵构造自适应非局部权函数,根据像素的局部结构计算图像中patch的相似性,提高了图像结构信息的保持性能.在数值解法上,采用分裂Bregman算法迭代求解模型,得到简单快速的迭代形式.数值实验证明所提出方法在提高恢复图像质量和算法效率上都有显著改进.     

基于结构保持的MR图像运动伪影快速抑制方法

目前核磁共振图像运动伪影的校正方法普遍是基于K空间数据的方法,本文提出一种直接对核磁共振图像进行伪影校正的后处理方法.基于非局部均值总变差去噪的思想设计构造了结构保持的运动伪影校正模型,该模型由非局部均值正则项和块相似保真项构成,正则项可以有效去除运动伪影和噪声的同时保持图像的结构;将各向异性结构张量作为块相似保真项中的权函数,实现在不同区域有不同的扩散方式,在去除图像运动伪影的同时保留图像的细节信息.模型的数值求解采用分裂Bregman方法实现.本文提出的方法充分考虑了图像的几何结构特性,实验结果表明,该方法能有效去除运动伪影并保留有价值的图像细节信息,同时提高了运算速度.