有限角CT少数投影重建图像技术

叙述了有限角CT少数投影重建图像技术研究所取得的进展：正交全息光路、干涉条纹处理系统、修改的联合代数重建技术、频谱分析图像重建技术和神经网络重建技术。     

Digital reconstruction of images from their projections in polar coordinates

In a wide variety of applications, it is necessary to infer the structure of a three-dimensional object from its projections. Usually, the problem is reduced to the reconstruction of a series of two-dimensional (planar) sections from a set of one-dimensional (linear) projections. In this paper, starting from a polar representation of the density function, we present some closed form formulas, which can be successfully used in the reconstruction of images. The results of some numerical tests are also presented.     

A note on exact image reconstruction from a limited number of projections

In a recent paper in this journal by Kesidis and Papamarkos “A new method for the exact reconstruction of any gray-scale image from its projections is proposed.” In this note we point out that this method is a special case of a well-known approach (peeling) and that it can produce exact reconstructions only under assumptions that are not realistic for practical methods of data collection. Further, we point out that some statements made in the paper regarding disadvantages of the algebraic reconstruction techniques (ART) as compared to the method of the paper are false.     

Tomographic image reconstruction using the theory of convex projections

The method of convex projections is applied to reconstruct an image in computer tomography. This appears to the first time that the method has been used to obtain geometry-free reconstruction from ray-sum data. It is shown that a special set of convex projections duplicates the result of the algebraic reconstruction technique (ART). The similarities and differences of these two methods are discussed. It is pointed out that use of a priori information enhances the quality of the results, especially when partial data have been used, in which case ART fails. Simulations and reconstruction of a CT image are also furnished to demonstrate the feasibility of this method.     

Model-based reconstruction of multiple circular and ellipticalobjects from a limited number of projections

We consider tomographic image reconstruction from a limited number of noisy projections. An efficient algorithm based on maximum likelihood estimation (MLE) is developed to reconstruct images of multiple discs with unknown locations and radii. The algorithm is successfully applied to images with signal-to-noise ratio (SNR) as low as 0 dB, using as few as 16 projections, and containing as many as twelve discs with widely varying radii. Experimental results show that our approach significantly outperforms conventional convolution back projection. The algorithm is successfully extended to the multiple ellipse case.     

利用灰度图减小Fourier变换轮廓术的频谱混叠

本文利用常常被人们忽略的灰度图中包含的频谱信息来减小零频分量对基频分量的影响。先记录一帧被测物体灰度图,然后投影正弦条纹到被测物体表面,记录变形条纹图。在对变形条纹图进行处理以前,先从变形条纹图中通过灰度图消除非均匀反射率对变形条纹的影响,得到均匀的变形条纹分布。文中给出的理论分析和实验结果可以证明：该方法可以限制零频分量的扩展,提高了FTP测量范围和精度,且测量系统简单,无相移装置。     

基于有限角图像重建的两种迭代算法研究

针对有限角度投影数据的CT图像重建问题,本文介绍了两种迭代算法,其中主要介绍了基于最小化图像总变差的优化准则的迭代重建算法--TV算法,以及简单介绍了改进后的ART算法,该算法的基本思想是运用已知角度的投影数据来补全未知角度的投影数据,再用ART算法进行图像重建.最后用模拟的有限角度投影数据分别对这两种迭代算法进行了图...     

Tomographic image reconstruction from incomplete view data by convex projections and direct fourier inversion

We consider the problem of reconstructing CAT imagery by the direct Fourier method (DFM) when not all view data are available. To restore the missing information we use the method of projections onto convex sets (POCS). POCS is a recursive image restoration technique that finds a solution consistent with the measured data and a priori known constraints in both the space and Fourier domain. Because DFM reconstruction is a frequency-domain technique it is ideally matched to POCS restoration when, for one reason or another, we are forced to generate an image from a less than complete set of view data. We design and apply an algorithm (PRDF) which interpolates/extrapolates the missing Fourier domain information by POCS and reconstructs an image by DFM. A simulated human thorax cross section is restored and reconstructed. The restorations using POCS are compared with the Gerchberg-Papoulis extrapolation method and shown to be superior. Applications of PRDF to other types of medical imaging modalities are discussed.     

实时图像盲复原技术

在有效的视频传输过程中图像的降质是不可避免的，可以通过图像盲复原重建降质的图像。因为不需要已知点扩展函数（PSF），所以得到广泛的应用。视频图像变化明显，传输的数据量大，因此需要一种计算复杂度小的方法来实现图像的盲复原。从此点出发包括两个主要的步骤：模糊图像到拉冬变换域的映射和在这个城内的盲模糊识别。这一映射使系统从2维到1维简化了计算的复杂度，更加符合实时的要求。     

圆锥扫描机制下的红外图像帧重建仿真研究

重点研究了圆锥扫描机制下,红外图像帧重建的仿真实现.在简要介绍圆锥扫描机制下基于变行频采样机理和红外图像完整重建技术的基础上,进行了大量的重建图像仿真研究.作为示例,文中列出第1、3、5、7、9场的扫描数据图像及其相应的场重建图像.从图像仿真结果可以看出这种技术能够完成红外图像的重建,重建的红外图像具有较高的分辨率,能够充分利用红外器件获得的扫描数据和相应的空间信息.     

REW软件——高分辨电子显微镜的像模拟与出射波函数重构的应用软件

通过像处理技术分析高分辨电子显微像有助于确定样品结构,提高显微镜的分辨率。本文开发的REW软件同时具有HRTEM像模拟与波函数重构的功能。用户可通过像模拟法来确定已知晶体的结构,另一方面,用户可利用系列离焦的HRTEM像重构样品的出射波函数,从而得到重要的相位信息并提高样品的分辨率。本文将简单介绍REW软件所运用的理论知识,并列举典型例子来描述REW软件的重要功能。     

基于小波变换的图像重构算法研究

小波变换是当前图像处理、应用数学和工程学科中一个迅速发展的领域,它具有多分辨率分析的特性,同时又在变换域有表征信号局部特征的能力,能有效地从信号中提取信息。本课题以MATLAB作为平台,研究小波变换的mallet算法,对一维离散采样信号进行滤波和重采样,并扩展到多维信号中。根据算法结果,对图像进行小波分解,重构其近似信...     

加强边缘保护的Curvelet图像去噪方法

提出了一种基于Curvelet变换的图像去噪方法。我们改进了Starck等所提出的Curvelet变换，去除了“环绕”现象，并将硬阈值去噪法与基于子带相关的图像去噪法相结合，在去除噪声的同时对图像的边缘特征予以保护。实验结果表明，用该方法去噪后的图像PSNR值更高，视觉效果也更好。     

带通信号的直接采样理论

用基本的数学方法和信号处理理论研究了带通信号的直接采样问题,得到了一般性的结论,进一步丰富和深化了信号的直接采样理论。     

Recursive total least squares algorithm for image reconstruction from noisy,undersampled frames

It is shown how the efficient recursive total least squares algorithm recently developed by C.E. Davila [3] for real data can be applied to image reconstruction from noisy, undersampled multiframes when the displacement of each frame relative to a reference frame is not accurately known. To do this, the complex-valued image data in the wavenumber domain is transformed into an equivalent real data problem to which Davila's algorithm is successfully applied. Two detailed illustrative examples are provided in support of the procedure. Similar reconstruction in the presence of blur as well as noise is currently under investigation.     

Extrapolation of signals using the method of alternating projections in fractional Fourier domains

The need for extrapolation of signals in time domain or frequency domain often arises in many applications in the area of signal and image processing. One of the approaches used for the extrapolation of the signals is the method of alternating projections (MAP) in conventional Fourier domains (CFD). Here we propose an extension of this approach using the fractional Fourier transform (FRFT) called here as the method of alternating projections in the FRFT domains (MAPFD). It is shown through the simulation results that the mean square error (MSE) between the true signal and the extrapolated signal obtained from the given signal is a function of the angle parameter of the FRFT, and the MAPFD gives lower MSE than the MAP in the CFD for the class of signals bandlimited in the FRFT domains, e.g., chirp signals. Moreover, the performance of the extrapolation using the MAPFD is shown to be shift-variant along the time axis.     

利用基追踪算法实现图像压缩感知重建研究

压缩感知理论突破了奈奎斯特采样频率的限制,利用该理论研究和实现了二维图像的压缩采样和重建。该方案利用小波变换实现图像稀疏化,利用标准伪随机数均匀分布和二维中心傅里叶变换生成随机测量矩阵,并对小波变换后的高频子带进行加权采样,用改进的基追踪算法实现二维图像压缩感知重建。仿真实验结果表明,该方案重建图像的客观评价PSNR效果较好。     

激光视觉焊缝跟踪图像处理与坡口识别

针对激光引导焊缝跟踪过程中坡口图像特点,首先对图像进行Radon变换,检测出激光条纹所在位置;然后对变换后图像进行处理,消除噪声对应的信息,保留激光条纹所对应的信息,再进行Radon逆变换复原图像,可较好地消除噪声;最后,采用OTSU法对图像进行分割,并识别出坡口区域。该方法效果较好,抗干扰性较强,耗时较少,适合于激光视觉焊缝跟踪过程。     

基于小波的图像超分辨率重建算法研究

在遥感图像、医学图像等领域，最初获得的图像分辨率往往达不到期望的水平。图像的超分辨率重建就是在低分辨率图像基础上重建出高分辨率图像的技术。针对已有重建算法中的不足，给出一种将高频能量适当降低的SHR重建算法；并进而针对高频细节不能高质量重建的问题，利用小波反变换对高频信息进行重建，提出了一种基于小波高频重建的图像超分辨率重建算法——SHW算法。实验证明，这两种算法的性能比已有图像超分辨率重建算法均有不同程度提高。     

Optimal Reconstruction of Natural Images by Small Sets of Gabor Filters

Images can be reconstructed after being filtered by a Gaussian and a few Gabor filters. Several search methods for the filter parameters for a (near) optimal reconstruction are examined. At first, the search is performed on a 1-D signal which satisfies the radial spectrum of the average of natural images. Later, these results are extended and applied to a 2-D example. It is shown that the resulting parameters are better than those of some existing models.