Efficient Total Variation Minimization Methods for Color Image Restoration

In this paper, we consider and study a total variation minimization model for color image restoration. In the proposed model, we use the color total variation minimization scheme to denoise the deblurred color image. An alternating minimization algorithm is employed to solve the proposed total variation minimization problem. We show the convergence of the alternating minimization algorithm and demonstrate that the algorithm is very efficient. Our experimental results show that the quality of restored color images by the proposed method are competitive with the other tested methods.     

Image-pair-based deblurring with spatially varying norms and noisy image updating

This paper presents a deblurring method that effectively restores fine textures and details, such as a tree’s leaves or regular patterns, and suppresses noises in flat regions using consecutively captured blurry and noisy images. To accomplish this, we used a method that combines noisy image updating with one iteration and fast deconvolution with spatially varying norms in a modified alternating minimization scheme. The captured noisy image is first denoised with a nonlocal means (NL-means) denoising method, and then fused with a deconvolved version of the captured blurred image on the frequency domain, to provide an initially restored image with less noise. Through a feedback loop, the captured noisy image is directly substituted with the initially restored image for one more NL-means denoising, which results in an upgraded noisy image with clearer outlines and less noise. Next, an alpha map that stores spatially varying norm values, which indicate local gradient priors in a maximum-a-posterior (MAP) estimation, is created based on texture likelihoods found by applying a texture detector to the initially restored image. The alpha map is used in a modified alternating minimization scheme with the pair of upgraded noisy images and a corresponding point spread function (PSF) to improve texture representation and suppress noises and ringing artifacts. Our results show that the proposed method effectively restores details and textures and alleviates noises in flat regions.     

基于Hessian核范数正则化的快速图像复原算法

利用Hessian核范数进行图像复原是目前较好的高阶正则化方法,但是由于Hessian核范数正则项的高度非线性和不可微性,图像去模糊和去噪过程耦合度高,求解算法的复杂度高.本文利用变量分裂设计了一种具有闭解形式的交替迭代最小化快速图像复原算法,将图像去模糊、去噪分步进行,并给出算法的收敛性证明.实验结果表明,本文方法不仅在峰值信噪比方面优于原有的基于Hessian核范数图像复原的主优化(Majorization-Minimization,MM)方法,而且大大降低了算法的迭代次数和运行时间.     

A regularization approach to joint blur identification and imagerestoration

The primary difficulty with blind image restoration, or joint blur identification and image restoration, is insufficient information. This calls for proper incorporation of a priori knowledge about the image and the point-spread function (PSF). A well-known space-adaptive regularization method for image restoration is extended to address this problem. This new method effectively utilizes, among others, the piecewise smoothness of both the image and the PSF. It attempts to minimize a cost function consisting of a restoration error measure and two regularization terms (one for the image and the other for the blur) subject to other hard constraints. A scale problem inherent to the cost function is identified, which, if not properly treated, may hinder the minimization/blind restoration process. Alternating minimization is proposed to solve this problem so that algorithmic efficiency as well as simplicity is significantly increased. Two implementations of alternating minimization based on steepest descent and conjugate gradient methods are presented. Good performance is observed with numerically and photographically blurred images, even though no stringent assumptions about the structure of the underlying blur operator is made.     

激光雷达主动偏振图像散斑抑制算法研究

针对激光主动偏振图像的散斑去除问题,提出了一种新的非局部正则化方法:根据激光主动偏振图像的噪声特点,在全变差模型的基础上,提出了非局部全变差正则化模型.该算法充分利用了图像的全局信息复原图像,在很好地抑制散斑的同时,保持了图像的细节信息.新模型使用轮流最小化方法进行求解,则原始图像和点扩散函数都可以在最小化框架中求解,...     

Inexact alternating direction method based on Newton descent algorithm with application to Poisson image deblurring

The recovery of images from the observations that are degraded by a linear operator and further corrupted by Poisson noise is an important task in modern imaging applications such as astronomical and biomedical ones. Gradient-based regularizers involving the popular total variation semi-norm have become standard techniques for Poisson image restoration due to its edge-preserving ability. Various efficient algorithms have been developed for solving the corresponding minimization problem with non-smooth regularization terms. In this paper, motivated by the idea of the alternating direction minimization algorithm and the Newton’s method with upper convergent rate, we further propose inexact alternating direction methods utilizing the proximal Hessian matrix information of the objective function, in a way reminiscent of Newton descent methods. Besides, we also investigate the global convergence of the proposed algorithms under certain conditions. Finally, we illustrate that the proposed algorithms outperform the current state-of-the-art algorithms through numerical experiments on Poisson image deblurring.     

Alternating minimization algorithms for transmission tomography

A family of alternating minimization algorithms for finding maximum-likelihood estimates of attenuation functions in transmission X-ray tomography is described. The model from which the algorithms are derived includes polyenergetic photon spectra, background events, and nonideal point spread functions. The maximum-likelihood image reconstruction problem is reformulated as a double minimization of the I-divergence. A novel application of the convex decomposition lemma results in an alternating minimization algorithm that monotonically decreases the objective function. Each step of the minimization is in closed form. The family of algorithms includes variations that use ordered subset techniques for increasing the speed of convergence. Simulations demonstrate the ability to correct the cupping artifact due to beam hardening and the ability to reduce streaking artifacts that arise from beam hardening and background events.     

Blind restoration of turbulence degraded images based on two-channel alternating minimization algorithm

Due to the atmospheric turbulence and the system noise, images are blurred in the astronomical or space object detection. Wavefront aberrations and system noise make the capability of detecting objects decrease greatly. A two-channel image restoration method based on alternating minimization is proposed to restore the turbulence degraded images. The images at different times are regarded as separate channels, then the object and the point spread function (PSF) are reconstructed in an alternative way. There are two optimization parameters in the algorithm:the object and the PSF. Each optimization step is transformed into a constraint problem by variable splitting and processed by the augmented Lagrangian method. The results of simulation and actual experiment verify that the two-channel image restoration method can always converge rapidly within five iterations, and values of normalized root mean square error (NRMSE) remain below 3% after five iterations. Standard deviation data show that optimized alternating minimization (OAM) has strong stability and adaptability to different turbulent levels and noise levels. Restored images are approximate to the ideal imaging by visual assessment, even though atmospheric turbulence and systemnoise have a strong impact on imaging. Additionally, the method can remove noise effectively during the process of image restoration.     

Total variation blind deconvolution

We present a blind deconvolution algorithm based on the total variational (TV) minimization method proposed by Acar and Vogel (1994). The motivation for regularizing with the TV norm is that it is extremely effective for recovering edges of images as well as some blurring functions, e.g., motion blur and out-of-focus blur. An alternating minimization (AM) implicit iterative scheme is devised to recover the image and simultaneously identify the point spread function (PSF). Numerical results indicate that the iterative scheme is quite robust, converges very fast (especially for discontinuous blur), and both the image and the PSF can be recovered under the presence of high noise level. Finally, we remark that PSFs without sharp edges, e.g., Gaussian blur, can also be identified through the TV approach.     

基于光谱加权低秩矩阵分解的高光谱影像去噪方法

高光谱遥感影像在获取和传输过程中会受到各种类型噪声的污染,不仅降低影像质量,也限制了其后续应用的精度。高光谱影像噪声类型复杂多样,且噪声在不同波段上的强度也并不相同。通过引入光谱域上的权重矩阵,文中提出了一种基于光谱加权低秩矩阵分解的高光谱遥感影像混合噪声去除方法,利用光谱权重矩阵均衡不同波段的噪声强度差异性。为进一步将噪声与纯净影像分离,利用加权核范数最小化来约束纯净高光谱影像的局部低秩结构,并利用交替方向乘子法对所提出的模型进行优化求解。通过对模拟与真实高光谱遥感数据的实验,验证了所提方法的有效性与优越性。     

Unsupervised multi class segmentation of 3D images with intensity inhomogeneities

Intensity inhomogeneities in images cause problems in gray-value based image segmentation since the varying intensity often dominates over gray-value differences of the image structures. In this paper we propose a novel biconvex variational model that includes the intensity inhomogeneities to tackle this task. We combine a total variation approach for multi class segmentation with a multiplicative model to handle the inhomogeneities. In our model we assume that the image intensity is the product of a smoothly varying part and a component which resembles important image structures such as edges. Therefore, we penalize in addition to the total variation of the label assignment matrix a quadratic difference term to cope with the smoothly varying factor. A critical point of the resulting biconvex functional is computed by a modified proximal alternating linearized minimization method (PALM). We show that the assumptions for the convergence of the algorithm are fulfilled. Various numerical examples demonstrate the very good performance of our method. Particular attention is paid to the segmentation of 3D FIB tomographical images serving as a motivation for our work.     

基于偏微分方程的图像盲恢复模型

提出了一种新的基于偏微分方程的图像盲恢复模型.改进了Chan和Wong的交替最小化思想.扩散系数不是直接来源于图像的梯度幅值而是在图像梯度模的基础上恢复出图像的边缘信息,消除了梯度模在分母中对实验产生的误差,给出了模型粘性解的存在性,唯一性和稳定性的定理.并给出实验结果,通过比较表明该模型有很好的性能.     

张量低秩约束下的多帧图像去模糊

矩阵低秩估计模型在图像处理任务中有着广泛地运用。针对图像去模糊,利用矩阵低秩先验能保留图像的重要边缘信息从而实现去模糊。而对于多帧图像去模糊,基于矩阵的低秩模型并未充分考虑多帧图像间的时序和空间关系。针对该问题,我们提出基于三维张量低秩先验的多帧视频图像盲去模糊模型。在模型中,首先将多帧连续图像按时序维堆叠成张量,显式地考虑多帧图像间的时空关系,同时利用张量低秩先验约束保留图像重要纹理结构信息。利用交替迭代的方法求解模型,实现去模糊。通过在不同的数据集上实验结果表明,该方法能达到较好的去模糊结果。      

Ultrasound kidney segmentation with a global prior shape

In this paper, we focus on segmentation of ultrasound kidney images. Unlike previous work by using trained prior shapes, we employ a parametric super-ellipse as a global prior shape for a human kidney. The Fisher–Tippett distribution is employed to describe the grey level statistics. Combining the grey level statistics with a global character of a kidney shape, we propose a new active contour model to segment ultrasound kidney images. The proposed model involves two subproblems. One subproblem is to optimize the parameters of a super-ellipse. Another subproblem is to segment an ultrasound kidney image. An alternating minimization scheme is used to optimize the parameters of a super-ellipse and segment an image simultaneously. To segment an image fast, a convex relaxation method is introduced and the split Bregman method is incorporated to propose a fast segmentation algorithm. The efficiency of the proposed method is illustrated by numerical experiments on both simulated images and real ultrasound kidney images.     

L1范数的图像超分辨率重建改进算法

介绍了超分辨率图像重建的数学模型和基于L1范数的超分辨率重建算法。针对在所观察到的低分辨率图像不足情况下的超分辨率重建,在L1范数重建算法框架下,提出了一种新的代价方程,在其中增加了关于丢失的低分辨率观察信息的保真度项和正则化项。该方法同时对高分辨率图像和丢失的观察信息进行迭代估计,并利用交替最小方法求解。实验结果表明,在获取低分辨率图像较少的情况下,提出的算法能够有效地改进重建的结果。     

Variational level set method for image segmentation with simplex constraint of landmarks

Landmarks are prior image features for a variety of computer vision tasks. In the image processing domain, research on image segmentation methods has always been a significant topic. Due to the image characteristics of heterogeneous nature, lack of clear boundaries, noise and so on, accurate segmentation of the image is still a challenge. In this paper, utilizing a level set framework and the simplex constraint, preferred image point landmarks are combined into a variational segmentation model to enforce the contour evolve with prior points. Then the alternating minimization algorithm of the proposed model is designed, meanwhile the landmarks constraints are doubled ensured with simplex projection. Finally, experiments on many synthetic and real-world images were implemented. Comparing with other state-of-the-art segmentation variational models, the most striking result to emerge from the data is that the proposed method has higher segmentation performance. Benefiting from appropriate point landmarks, the proposed segmentation method can tackle noisy, weak edges and corrupted area images effectively and robustly.     

基于快速稀疏低秩和鲁棒主成分分析的图像处理算法

实际的稀疏低秩处理图像过程中，在视觉显示效果没有很大的差异的情况下，CPU的处理时间是唯一一个的评价指标。我们发现快速交替极小化(FAST PCP)和鲁棒主成分分析(RPCA)的结合是最快速、最有效的利用CPU的高效稀疏低秩处理图像的方法，并且在无法保证计算机配置的情况下，其运算速度也是最快的。在课题中，将Steffensen迭代法用于改进FAST PCP，由此得到的结果较普通版本的FAST PCP和RPCA更加好。      

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.     

The magic of split augmented Lagrangians applied to K-frame-based l 0–l 2 minimization image restoration

We propose a simple, yet efficient image deconvolution approach, which is formulated as a complementary K-frame-based l ₀–l ₂ minimization problem, aiming at benefiting from the advantages of each frame. The problem is solved by borrowing the idea of alternating split augmented Lagrangians. The experimental results demonstrate that our approach has achieved competitive performance among state-of-the-art methods.     

Weighted truncated nuclear norm regularization for low-rank quaternion matrix completion

In recent years, quaternion matrix completion (QMC) based on low-rank regularization has been gradually used in image processing. Unlike low-rank matrix completion (LRMC) which handles RGB images by recovering each color channel separately, QMC models retain the connection of three channels and process them as a whole. Most of the existing quaternion-based methods formulate low-rank QMC (LRQMC) as a quaternion nuclear norm (a convex relaxation of the rank) minimization problem. The main limitation of these approaches is that they minimize the singular values simultaneously such that cannot approximate low-rank attributes efficiently. To achieve a more accurate low-rank approximation, we introduce a quaternion truncated nuclear norm (QTNN) for LRQMC and utilize the alternating direction method of multipliers (ADMM) to get the optimization in this paper. Further, we propose weights to the residual error quaternion matrix during the update process for accelerating the convergence of the QTNN method with admissible performance. The weighted method utilizes a concise gradient descent strategy which has a theoretical guarantee in optimization. The effectiveness of our method is illustrated by experiments on real visual data sets.