无对应点匹配的三维重建

本文首先纠正了基于二次曲线匹配视觉算法中所存在的推导错误，并对于重建曲线解的存在性进行了讨论，给出了一种能保证解存在的修改算法，其次，为了保证解的唯一性，我们给出了采用三眼视觉的唯一性匹配定理，最后采用机械零件进行了实验，证明所提出的方法可以快速、准确、完整地重建空间曲线。     

The Theory of Three-Dimensional Image Reconstruction for PET

A review is made of selected recent publications on three-dimensional image reconstruction for PET. A new algorithm is proposed which is designed to fully utilize all emitted gamma rays which can be detected in a truncated spherical detector. By such full utilization of emitted rays the new algorithm should produce images of better statistical accuracy than could be produced by previously known algorithms.     

基于Mumford-Shah正则项与L1数据拟合的PET图像重建方法

在正电子发射断层重建(PET)算法中,正则项常被用来抑制噪声。本文将Mumford-Shah(MS)正则项与最新的L1数据保真项相结合,构造出一种新的变分结构用以进行PET图像重建。为了简化计算,本文采用了Ambrosio和Tortorelli提出的Г-收敛逼近方法,将MS函式对边界积分转化为一类合适的辅助光滑函数的区域积分。在仿真测试中,将算法与传统滤波反投影(FBP)算法,最大似然法(EM),最小交叉熵法(MXE)作比较。通过实验结果的研究,对算法的效率和可行性进行了分析。     

Microwave Imaging in Layered Media: 3-D Image Reconstruction From Experimental Data

A prototype microwave imaging system for imaging 3-D targets in layered media is developed to validate the capability of microwave imaging with experimental data and with 3-D nonlinear inverse scattering algorithms. In this experimental prototype, the transmitting and receiving antennas are placed in a rectangular tub containing a fluid. Two plastic slabs are placed in parallel in the fluid to form a five-layer medium. The microwave scattering data are acquired by mechanically scanning a single transmitting antenna and a single receiving antenna, thus avoiding the mutual coupling that occurs when an array is used. The collected 3-D experimental data in the fluid are processed by full 3-D nonlinear inverse scattering algorithms to unravel the complicated multiple scattering effects and produce 3-D digital images of the dielectric constant and conductivity of the imaging domain. The image reconstruction is focused on the position and dimensions of the unknown scatterers. Different dielectric and metallic objects have been imaged effectively at 1.64 GHz.      

一种有效的压缩感知图像重建算法

多数现有的压缩感知重建算法基于单观测向量,处理图像信号时将其表示成一维信号,算法效率低,重建图像的效果也有待提高.本文提出了一种基于多观测向量和稀疏贝叶斯学习的重建算法,通过同时处理观测矩阵的每一列直接求得加权系数矩阵,从而快速重建图像.在相同的采样率条件下,该算法的重建图像效果更好,算法效率明显提高.采用标准测试图像...     

Interior-point methodology for 3-D PET reconstruction

Interior-point methods have been successfully applied to a wide variety of linear and nonlinear programming applications. This paper presents a class of algorithms, based on path-following interior-point methodology, for performing regularized maximum-likelihood (ML) reconstructions on three-dimensional (3-D) emission tomography data. The algorithms solve a sequence of subproblems that converge to the regularized maximum likelihood solution from the interior of the feasible region (the nonnegative orthant). We propose two methods, a primal method which updates only the primal image variables and a primal-dual method which simultaneously updates the primal variables and the Lagrange multipliers. A parallel implementation permits the interior-point methods to scale to very large reconstruction problems. Termination is based on well-defined convergence measures, namely, the Karush-Kuhn-Tucker first-order necessary conditions for optimality. We demonstrate the rapid convergence of the path-following interior-point methods using both data from a small animal scanner and Monte Carlo simulated data. The proposed methods can readily be applied to solve the regularized, weighted least squares reconstruction problem.     

Least-Square NUFFT Methods Applied to 2-D and 3-D Radially Encoded MR Image Reconstruction

Radially encoded MRI has gained increasing attention due to its motion insensitivity and reduced artifacts. However, because its samples are collected nonuniformly in the $k$-space, multidimensional (especially 3-D) radially sampled MRI image reconstruction is challenging. The objective of this paper is to develop a reconstruction technique in high dimensions with on-the-fly kernel calculation. It implements general multidimensional nonuniform fast Fourier transform (NUFFT) algorithms and incorporates them into a $k$-space image reconstruction framework. The method is then applied to reconstruct from the radially encoded $k$-space data, although the method is applicable to any non-Cartesian patterns. Performance comparisons are made against the conventional Kaiser–Bessel (KB) gridding method for 2-D and 3-D radially encoded computer-simulated phantoms and physically scanned phantoms. The results show that the NUFFT reconstruction method has better accuracy–efficiency tradeoff than the KB gridding method when the kernel weights are calculated on the fly. It is found that for a particular conventional kernel function, using its corresponding deapodization function as a scaling factor in the NUFFT framework has the potential to improve accuracy. In particular, when a cosine scaling factor is used, the NUFFT method is faster than KB gridding method since a closed-form solution is available and is less computationally expensive than the KB kernel (KB griding requires computation of Bessel functions). The NUFFT method has been successfully applied to 2-D and 3-D in vivo studies on small animals.      

一种基于地形驻点分割的多通道SAR三维重建方法

多通道SAR具有高度向分辨能力,能够实现叠掩场景的3维重建,但是由于其基线长度有限,利用现有方法进行重建所得高程定位精度往往较差,而且由于叠掩区域散射系数起伏较大,重建结果中存在较多的漏检。针对以上问题,该文提出一种基于地形驻点分割的多通道SAR 3维重建方法,首先通过层析获得场景3维分布的草图,之后通过地形驻点定位及以地形驻点为门限的分割得到不叠掩的数据,最后利用干涉信号处理实现场景的3维重建。该方法结合了多通道SAR的高度向分辨能力和干涉信号处理的高精度,能够更加稳定、精确地实现叠掩场景的3维重建,基于实际场景缩比模型的仿真实验结果验证了该文算法的有效性。     

Analysis of Penalized Likelihood Image Reconstruction for Dynamic PET Quantification

Quantification of tracer kinetics using dynamic positron emission tomography (PET) provides important information for understanding the physiological and biochemical processes in humans and animals. A common procedure is to reconstruct a sequence of dynamic images first, and then apply kinetic analysis to the time activity curve of a region of interest derived from the reconstructed images. Obviously, the choice of image reconstruction method and its parameters affect the accuracy of the time activity curve and hence the estimated kinetic parameters. This paper analyzes the effects of penalized likelihood image reconstruction on tracer kinetic parameter estimation. Approximate theoretical expressions are derived to study the bias, variance, and ensemble mean squared error of the estimated kinetic parameters. Computer simulations show that these formulae predict correctly the changes of these statistics as functions of the regularization parameter. It is found that the choice of the regularization parameter has a significant impact on kinetic parameter estimation, indicating proper selection of image reconstruction parameters is important for dynamic PET. A practical method has been developed to use the theoretical formulae to guide the selection of the regularization parameter in dynamic PET image reconstruction.      

Multifocus Holographic 3-D Image Fusion Using Independent Component Analysis

We present multifocus holographic 3-D image fusion based on independent component analysis (ICA). In this paper, the ICA technique is used to fuse multiple reconstructed holographic images at different distances from the image sensor. A hologram of two dice located at distances of 315 and 345 mm, respectively, from the sensor is recorded using phase-shifting digital holography and used in our experiments. The resulting reconstructed fused holographic image shows both dice objects clearly in focus. This is compared with a single reconstructed holographic image in which only one of the die objects is in focus at a particular reconstruction distance.     

一种新的3－D小波变换图像编码方法

基于图像序列三维小波变换的视频编码技术是一种很有潜力的编码方法．本文针对目前实际中采用的三维小波变换只是一种准三维变换，不能提供对变换结果的统一描述等不足，推导了信号真正的三维小波变换的有关理论及其实现方法．在此基础上，我们将这种三维小波变换方法用于视频图像的编码，模拟结果表明这种编码结构具有良好性能，值得进一步的深入研究．     

Efficient Algorithm for the Unconditionally Stable 3-D ADI–FDTD Method

This letter presents a new efficient algorithm for the unconditionally stable three-dimensional alternating direction implicit finite-difference time-domain (3-D ADI-FDTD) method. The algorithm involves updating equations whose right-hand sides are much simpler and more concise than those in the conventional implementation. This leads to substantial reduction in the number of arithmetic operations required for their computations. To take full advantage of the efficiency gain, efforts are made as well to maintain or reduce other computation costs in for-looping and solving tridiagonal systems. Certain field array reuse is also exploited which reduces the memory space and the memory indexing overhead     

Investigation of time-of-flight benefit for fully 3-D PET

The purpose of this paper is to determine the benefit that can be achieved in image quality for a time-of-flight (TOF) fully three-dimensional (3-D) whole-body positron emission tomography (PET) scanner. We simulate a 3-D whole-body time-of-flight PET scanner with a complete modeling of spatial and energy resolutions. The scanner is based on LaBr3 Anger-logic detectors with which 300ps timing resolution has been achieved. Multiple simulations were performed for 70-cm long uniform cylinders with 27-cm and 35-cm diameters, containing hot spheres (22, 17, 13, and 10-mm diameter) in a central slice and 10-mm diameter hot spheres in a slice at 1/4 axial FOV. Image reconstruction was performed with a list-mode iterative TOF algorithm and data were analyzed after attenuation and scatter corrections for timing resolutions of 300, 600, 1000 ps and non-TOF for varying count levels. The results show that contrast recovery improves slightly with TOF (NEMA NU2-2001 analysis), and improved timing resolution leads to a faster convergence to the maximum contrast value. Detectability for 10-mm diameter hot spheres estimated using a nonprewhitening matched filter (NPW SNR) also improves nonlinearly with TOF. The gain in image quality using contrast and noise measures is proportional to the object diameter and inversely proportional to the timing resolution of the scanner. The gains in NPW SNR are smaller, but they also increase with increasing object diameter and improved timing resolution. The results show that scan times can be reduced in a TOF scanner to achieve images similar to those from a non-TOF scanner, or improved image quality achieved for same scan times.     

Fourier-based reconstruction for fully 3-D PET: optimization of interpolation parameters

Fourier-based approaches for three-dimensional (3-D) reconstruction are based on the relationship between the 3-D Fourier transform (FT) of the volume and the two-dimensional (2-D) FT of a parallel-ray projection of the volume. The critical step in the Fourier-based methods is the estimation of the samples of the 3-D transform of the image from the samples of the 2-D transforms of the projections on the planes through the origin of Fourier space, and vice versa for forward-projection (reprojection). The Fourier-based approaches have the potential for very fast reconstruction, but their straightforward implementation might lead to unsatisfactory results if careful attention is not paid to interpolation and weighting functions. In our previous work, we have investigated optimal interpolation parameters for the Fourier-based forward and back-projectors for iterative image reconstruction. The optimized interpolation kernels were shown to provide excellent quality comparable to the ideal sinc interpolator. This work presents an optimization of interpolation parameters of the 3-D direct Fourier method with Fourier reprojection (3D-FRP) for fully 3-D positron emission tomography (PET) data with incomplete oblique projections. The reprojection step is needed for the estimation (from an initial image) of the missing portions of the oblique data. In the 3D-FRP implementation, we use the gridding interpolation strategy, combined with proper weighting approaches in the transform and image domains. We have found that while the 3-D reprojection step requires similar optimal interpolation parameters as found in our previous studies on Fourier-based iterative approaches, the optimal interpolation parameters for the main 3D-FRP reconstruction stage are quite different. Our experimental results confirm that for the optimal interpolation parameters a very good image accuracy can be achieved even without any extra spectral oversampling, which is a common practice to decrease errors caused by interpolation in Fourier reconstruction.     

Rapid Execution of Fan Beam Image Reconstruction Algorithms Using Efficient Computational Techniques and Special-Purpose Processors

Rapid advances during the past ten years of several forms of computer-assisted tomography (CT) have resulted in the development of numerous algorithms to convert raw projection data into cross-sectional images. These reconstruction algorithms are either "iterative," in which a large matrix algebraic equation is solved by successive approximation techniques; or "closed form." Continuing evolution of the closed form algorithms has allowed the newest versions to produce excellent reconstructed images in most applications. This paper will review several computer software and special-purpose digital hardware implementations of closed form algorithms, either proposed during the past several years by a number of workers or actually implemented in commercial or research CT scanners. The discussion will also cover a number of recently investigated algorithmic modifications which reduce the amount of computation required to execute the reconstruction process, as well as several new special-purpose digital hardware implementations under development in our laboratories at the Mayo Clinic.     

超分辨率图像重构边缘振荡的高效去除算法

针对POCS超分辨率图像重构算法在放大倍数加大时存在边缘振荡效应加剧和计算复杂性上升的问题，提出了一个能同时解决这两个问题的新算法，它将放大过程分步进行，并在每步引入边界自适应约束。实验结果表明，该算法在有效消除边缘振荡效应的同时，极大地提高了超分辨率图像重构的速度。     

遗传算法和Powell法结合的多分辨率三维图像配准

基于互信息的配准方法具有精度高、鲁棒性强的特点,成为近年图像配准研究的热点,但基于互信息的目标函数存在许多局部极值,为配准的优化过程带来了很大的困难。本文以互信息作为相似性测度,采用基于小波变换的多分辨率策略,将遗传算法和Powell法结合起来对三维CT、MR图像进行了配准。实验结果表明,这种方法能够有效地克服信息函数的局部极值,配准精度达到亚像素级。     

A Hybrid Reconstruction Algorithm for 3-D Ionospheric Tomography

In this paper, a hybrid reconstruction algorithm (HRA) is presented to solve the ill-posed inverse problem associated with 3-D ionospheric stochastic tomography. In this new method, the ionospheric electron density (IED) can be inverted by using two steps. First, a truncated singular value decomposition (TSVD) method, whose value is independent on any initial estimation, is used to resolve the ill-posed problem of the tomography system. Second, taking into account the "approximation" of its solution, an iterative improvement process of the solution is then implemented by utilizing the conventional algebraic reconstruction algorithm (ART). The HRA, therefore, offers a more reasonable approach to choose an initial approximate for the ART and to improve the quality of the final reconstructed image. A simulated experiment demonstrates that the HRA method is superior to the TSVD or the ART alone for the tomographic inversion of IED. Finally, the HRA is used to perform GPS-based tomographic reconstruction of the IED at mid- and low-latitude regions.     

位相物体的三维非对称温度场的计算机模拟

应用计算机模拟实现了三维非对称温度场的重建，为莫尔偏折术测量三维非对称温度场提供了一种实时自动的和高精度的处理方法。