基于字典学习和TV的能谱CT重建算法

能谱CT可以将较宽的能谱数据划分为几个单独的窄谱数据,从而同时获得多个能量通道下的投影.但由于窄谱通道内接收到的光子数较少,投影通常包含较大的噪声.针对这一问题,基于压缩感知理论提出了一种基于字典学习和全变分TV(total-variation)的迭代重建算法用于能谱CT重建,应用交替最小化方法优化相关目标函数,并采用Split-Bregman算法求解.同时,采用有序子集方法加速迭代收敛过程,提高运算速率.为了验证和评估所提出的方法,使用简单模型和实际临床小鼠模型进行了仿真实验,实验结果表明,所提出的算法有较好的去噪及细节保存能力.     

能谱CT投影域降噪算法的比较研究

能谱CT的光子计数探测器可以将较宽的能谱按照选定的能量段进行计数,得到物体在不同能段的成像信息.由于能谱CT需要确定能量通道,且单个窄谱通道探测的光子数为总光子数的一部分,数目减少,导致窄谱投影数据的噪声增大.为降低低能噪声对成像结果的影响,将传统MAP降噪算法,基于各向异性模型的改进MAP算法及SB(Split Bregman)算法引入能谱CT投影域去噪中.首先通过选定一个能量来验证三种算法对能谱CT的适用性.然后分别对三个确定的能量通道添加高斯噪声,使用上述算法分别去噪,并对去噪后投影使用FBP,OS-SART算法重建,结果表明三种算法均可以有效去噪,且改进的MAP算法优于传统MAP算法,SB算法去噪效果最佳.     

广义全变差正则化图像去噪模型研究

本文研究了全变差正则化模型在图像去噪过程中易产生阶梯效应的问题,依据图像的局部结构特利用联合高斯滤波器和边缘检测算子的方法,构建了广义全变差正则化图像去噪模型,获得了在消除噪声的同时能够保留图像边缘细节和纹理信息的结果.实验结果表明,广义全变差正则化模型在平滑噪声的同时能够保留图像的边缘轮廓等细节信息,得到的复原图像在峰值信噪比、平均结构相似度和主观视觉效果方面均有所提高.     

图像域增强约束卷积稀疏编码的稀疏角度CT重建算法研究

稀疏角度CT重建因其可以降低辐射剂量引起广泛关注,然而减少角度会降低重建图像质量,影响诊断结果分析.为解决上述问题,提出了图像域增强约束卷积稀疏编码的稀疏角度CT重建算法,该算法继承了卷积稀疏编码的优点,通过直接处理整幅图像提取特征,克服了字典学习因图像分块聚合引起的伪影.继而引入全变分正则项来增强图像域的约束,可以有效地进一步抑制噪声.通过几组稀疏角度的重建实验与不同算法对比,实验结果表明,所提算法在噪声抑制、伪影减少和图像细节恢复方面性能优越.     

基于字典学习方法的CT不完全投影图像重建算法

对于不完全投影角度的重建研究是CT图像重建中一个重要的问题.将压缩感知中字典学习的方法与CT重建算法ART迭代算法相结合.字典学习方法中字典更新采用K-SVD(K-奇异值分解)算法,稀疏编码采用OMP(正交匹配追踪)算法.最后通过对标准Head头部模型进行仿真实验,验证了字典学习方法在CT图像重建中对于提高图像的重建质量和提高信噪比的可行性与有效性.另外还研究了字典学习中图像块大小和滑动距离对重建图像的影响     

非局部加权模糊C均值聚类图像分割

去除噪声与保持图像细节特征是含噪声图像分割中面临的一对矛盾。为此,提出一种改进的模糊C均值算法,通过引入非局部加权距离以抑制噪声影响。其中,权值通过局部图像块距离的指数形式计算,并利用半局部统计特性自适应调整其光滑参数。实验结果表明,新方法具有较强的抗噪声能力,同时能够保持较多地细节特征。     

一种管线CT成像模型

管线是维系很多设施的命脉,它们的腐蚀问题受到了广泛的重视.工业X射线CT成像技术可以实现对管线的非破坏检测,发现它们的腐蚀状况以及各种缺陷,从而掌握其质量情况和变化规律.本文主要研究了海水管线的CT成像方法,在每个角度都存在数据缺失的情况下,给出了它的CT扫描和重建模型,提出了基于TV约束和加权均值化处理的分组ART迭代算法的重建方法.模拟实验表明该方法可以获得管线横截面的高质量CT图像,为其内部腐蚀参数的计算和腐蚀程度的判断提供了重要依据.     

基于CT图像重建的多重集合分裂可行性问题应用分析

为了较好地应用CQ算法解决稀疏角度CT 图像重建的问题,提出了一种新的实时的分块逐次混合算法．首先将稀疏角度CT 图像重建的重建问题转化成分裂可行性问题．其次,通过分析非空闭凸集C和Q的不同的定义,在N维实空间中分别针对不同的CQ算法给出了7种不同的实现方案．通过试验,分别对不同算法及其方案的重建精度和收敛速度进行了对比分析,并对多重集合分裂可行性问题算法中约束权因子的选取及其对输出的影响进行了研究,从而给出了CQ算法在稀疏角度CT图像重建问题中应用的最佳凸集定义方案．以此为基础,给出了所提出算法的最佳实现方案．试验结果表明,该算法收敛速度快,重建精度高,为多重集合分裂可行性问题及其改进算法在该重建问题上的应用提供了参考．     

分层不动点和变分不等式公共解的迭代算法

目的是利用全渐近非扩张映象研究分层不动点和变分不等式公共不动点的迭代算法.在适当条件下,某些强收敛定理被证明.结果改进和推广了Yao Y H(2010)和ZHANG S S等人(2011)的最新结果.     

基于ADI格式的多尺度图像分解

针对文献[Xu R et al.,IEEE Trans.Biomed.Eng.,2014]的多尺度图像分解模型,该文提出了Alternating Direction Implicit (ADI)格式下的多尺度图像分解算法,并证明了在该模型下ADI格式的收敛性和稳定性,进一步,通过对不同图像的数值实验,验证了该文提出的算法具有更好的纹理提取效果.     

IMAGE RESTORATION UNDER CAUCHY NOISE WITH SPARSE REPRESENTATION PRIOR AND TOTAL GENERALIZED VARIATION

This article introduces a novel variational model for restoring images degraded by Cauchy noise and/or blurring.The model integrates a nonconvex data-fidelity term with two regularization terms,a sparse representation prior over dictionary learning and total generalized variation(TGV)regularization.The sparse representation prior exploiting patch information enables the preservation of fine features and textural patterns,while adequately denoising in homogeneous regions and contributing natural visual quality.TGV regularization further assists in effectively denoising in smooth regions while retaining edges.By adopting the penalty method and an alternating minimization approach,we present an efficient iterative algorithm to solve the proposed model.Numerical results establish the superiority of the proposed model over other existing models in regard to visual quality and certain image quality assessments.     

Total image constrained diffusion tensor for spectral computed tomography reconstruction

Photon counting detector (PCD)-based spectral computed tomography (CT) is a promising imaging technique that enables high energy resolution imaging with narrow energy bins. However, the image quality is degraded because the number of photons in each energy bin is less than the number of photons in the full spectrum. To reconstruct high quality spectral CT images with narrow energy bins, we developed a total image constrained diffusion tensor (TICDT) for statistical iterative reconstruction (SIR) based on a penalized weighted least-squares (PWLS) principle, which is called “PWLS-TICDT.” Specifically, TICDT uses supplementary information from a high-quality total image as a structural prior for SIR, so that the narrow energy bin image can be enhanced, while some primary features are preserved. We also developed an alternating minimization algorithm to solve the associated objective function. We conducted qualitative and quantitative studies to validate and evaluate the PWLS-TICDT method using digital phantoms and preclinical data. Results from both numerical simulation and real PCD data studies show that the proposed PWLS-TICDT method achieves noticeable gains over competing methods in terms of suppressing noise, detecting low contrast objects, and preserving resolution. More importantly, the multi-energy images reconstructed by PWLS-TICDT method can generate more accurate basis material decomposition results than the other methods.     

Image reconstruction model for limited-angle CT based on prior image induced relative total variation

Limited-angle computed tomography (CT) reconstruction has a great potential to reduce X-ray radiation dose or scanning time. Suppressing shading artifacts is challenging, but of great practical significance in limited-angle CT. Traditional methods based on total variation (TV) cannot effectively remove the shading artifacts, prior image constrained compressed sensing (PICCS) is a promising method, but is sensitive to the quality of the prior image. In micro-CT, a prior image reconstructed by filtered back-projection (FBP) may contain high-level noise. An image reconstructed by PICCS tends to inherit both structures and noise of the prior image. In this study, to suppress noise and shading artifacts, we propose a new limited-angle CT reconstruction model called prior image induced relative total variation (piiRTV), that uses the structure information of a prior image to guide limited-angle CT reconstruction. The proposed piiRTV is compared to TV and PICCS. Numerical simulations and experiments on real CT projections demonstrate the effectiveness of piiRTV in suppression of noise and shading artifacts. In addition, the proposed piiRTV is more robust to the prior image quality than PICCS.     

Segmentation of Pulmonary Nodule Images Using 1-Norm Minimization

Total variation minimization (in the 1-norm) has edge preserving and enhancing properties which make it suitable for image segmentation. We present Image Simplification, a new formulation and algorithm for image segmentation. We illustrate the edge enhancing properties of 1-norm total variation minimization in a discrete setting by giving exact solutions to the problem for piecewise constant functions in the presence of noise. In this case, edges can be exactly recovered if the noise is sufficiently small. After optimization, segmentation is completed using edge detection. We find that our image segmentation approach yields good results when applied to the segmentation of pulmonary nodules.     

修正的TV-Stokes模型的新快速算法

基于Tai等人的前期工作,本文研究修正的TV-Stokes图像去噪模型,提出一些新的求解该两步模型的快速算法.我们利用对偶形式和多重网格方法得到一个求解第1步的快速算法.给出另外一种新的求解光滑的切向量场的保不可压性质的算法.在第2步中,我们提出一类有效的全新算法:首先通过计算Poisson方程得到具有光滑法向量场的函数g,然后利用Jia和Zhao的方法得到恢复的图像.新算法的运算速度非常快,用于图像恢复的CPU时间少于0.1 s.数值结果显示新的快速算法是有效的和稳定的,恢复图像的质量也超过了一般去噪方法.     

A Nonlocal Total Variation Model for Image Decomposition: Illumination and Reflectance

In this paper, we study to use nonlocal bounded variation (NLBV) techniques to decompose an image intensity into the illumination and reflectance components. By considering spatial smoothness of the illumination component and nonlocal total variation (NLTV) of the reflectance component in the decomposition framework, an energy functional is constructed. We establish the theoretical results of the space of NLBV functions such as lower semicontinuity, approximation and compactness. These essential properties of NLBV functions are important tools to show the existence of solution of the proposed energy functional. Experimental results on both grey-level and color images are shown to illustrate the usefulness of the nonlocal total variation image decomposition model, and demonstrate the performance of the proposed method is better than the other testing methods.     

A variational approach for restoring images corrupted by noisy blur kernels and additive noise

In this paper, we study a deblurring algorithm for distorted images by random impulse response. We propose and develop a convex optimization model to recover the underlying image and the blurring function simultaneously. The objective function is composed of 3 terms: the data‐fitting term between the observed image and the product of the estimated blurring function and the estimated image, the squared difference between the estimated blurring function and its mean, and the total variation regularization term for the estimated image. We theoretically show that under some mild conditions, the resulting objective function can be convex in which the global minimum value is unique. The numerical results confirm that the peak‐to‐signal‐noise‐ratio and structural similarity of the restored images by the proposed algorithm are the best when the proposed objective function is convex. We also present a proximal alternating minimization scheme to solve the resulting minimization problem. Numerical examples are presented to demonstrate the effectiveness of the proposed model and the efficiency of the numerical scheme.     

Image process in imaging through a scattering medium using fs electronic holography

Aimed at imaging technology through scattering medium using fs electronic holography, a set of image process algorithm is put forward. This algorithm can be divided into three stages. First, every hologram is pre-processed, whose contrast is enhanced. Second, the first-order spatial spectrum is low-pass-filtered through a two-step process, so that high-frequency noise can be removed. Finally, many reconstructed images are ensemble-averaged. This stage can smooth random noise and is advantageous to restraining the speckle noise of image. The operation of this algorithm shows that all of processes in the three stages have obvious effects on improving image quality.     

A Compound Algorithm of Denoising Using Second-Order and Fourth-Order Partial Differential Equations

In this paper, we propose a compound algorithm for the image restoration. The algorithm is a convex combination of the ROF model and the LLT model with a parameter function 6. The numerical experiments demonstrate that our compound algorithm is efficient and preserves the main advantages of the two models. In particular, the errors of the compound algorithm in L2 norm between the exact images and corresponding restored images are the smallest among the three models. For images with strong noises, the restored images of the compound algorithm are the best in the corresponding restored images. The proposed algorithm combines the fixed point method, an improved AMG method and the Krylov acceleration. It is found that the combination of these methods is efficient and robust in the image restoration.