An image reconstruction algorithm for three-dimensional electrical impedance tomography

Electrical impedance tomography (EIT) has been studied by many authors and in most of this work it has been considered to be a two-dimensional problem. Many groups are now turning their attention to the full three-dimensional case in which the computational demands become much greater. It is interesting to look for ways to reduce this demand and in this paper we describe an implementation of an algorithm that is able to achieve this by precomputing many of the quantities needed in the image reconstruction. The algorithm is based on a method called NOSER introduced some years ago by Cheney et al. [3]. In this paper we have significantly extended the method by introducing a more realistic electrode model into the analysis. We have given explicit formulae for the quantities involved so that the reader can reproduce our results.     

Generalized true three-dimensional reconstruction algorithm

A generalized true three-dimensional reconstruction (TTR) algorithm applicable to a sphere or cylindrical geometry is described. A new composite filter concept which is applicable to all forms of three-dimensional geometries, especially suitable for a truncated sphere is introduced and incorporated into image reconstruction of physically realizable detector array system such as the truncated spherical positron detector array.     

True three-dimensional cone-beam reconstruction (TTCR) algorithm

A true three-dimensional cone-beam reconstruction (TTCR) algorithm for direct volume image reconstruction from 2-D cone-beam projections is developed for the complete sphere geometry. The algorithm is derived from the parallel-beam true three-dimensional reconstruction (TTR) algorithm and is based on the modified filtered backprojection technique, which uses a set of 2-D space-invariant filters. The proposed algorithm proved to be superior in spatial resolution to the parallel-beam TTR algorithm and to offer better computational efficiency.     

An iterative algorithm for signal reconstruction from bispectrum

The author presents a procedure to reconstruct a (minimum or nonminimum phase) discrete-time signal from its bispectrum. The algorithm is iterative and based on using the method of projections onto convex sets (POCS) in an inner product space in which the vector space consists of real sequences, and vector addition, is defined in terms of the convolution operation. Prior information, such as an energy bound on the signal, can be incorporated into this algorithm. An algorithm that employs energy information was found to produce better results in simulation than one that ignores energy constraints     

An interior point iterative maximum-likelihood reconstruction algorithm incorporating upper and lower bounds with application to SPECT transmission imaging

The algorithm we consider here is a block-iterative (or ordered subset) version of the interior point algorithm for transmission reconstruction. Our algorithm is an interior point method because each vector of the iterative sequence [x(k)], k = 0, 1, 2, ... satisfies the constraints a(j) < x(j)k < b(j), j = 1, ..., J. Because it is a block-iterative algorithm that reconstructs the transmission attenuation map and places constraints above and below the pixel values of the reconstructed image, we call it the BITAB method. Computer simulations using the three-dimensional mathematical cardiac and torso phantom, reveal that the BITAB algorithm in conjunction with reasonably selected prior upper and lower bounds has the potential to improve the accuracy of the reconstructed attenuation coefficients from truncated fan beam transmission projections. By suitably selecting the bounds, it is possible to restrict the over estimation of coefficients outside the fully sampled region, that results from reconstructing truncated fan beam projections with iterative transmission algorithms such as the maximum-likelihood gradient type algorithm.     

一种有效的天线三维辐射方向图计算方法

提出了一种根据已知的天线E面和H面方向图计算天线的三维辐射方向图的近似算法.以全向和定向天线为例,仿真比较了此算法和两种已有算法计算得到的天线三维辐射方向图与理论结果之间的误差.结果表明,该算法误差较小,可以有效地计算天线的三维辐射方向图.根据生成的三维辐射方向图,计算了天线的方向性系数,所得结果与理论值吻合良好.     

An algorithm for dual-channel noiseless signal reconstruction andits performance analysis

We present an algorithm for estimating a two-input two-output system and recovering its inputs from noise-free observations of its outputs. The algorithm involves minimization of a set of cross-correlations between the reconstructed signals and a nonlinear function of these signals. A performance analysis of the algorithm is presented. It is shown that for the optimal choice of the nonlinear function, the performance of the algorithm is close to the Cramer-Rao lower bound (CRLB). Other choices of the function provide insights into the performance of moment/cumulant-based deconvolution techniques     

An efficient algorithm for MR image reconstruction without low spatial frequencies

It is demonstrated that if the image to be reconstructed is known to have some zero-valued pixels, the dynamic ranges can be better used by disregarding the largest signals and using signal restoration methods. Low-frequency and high-frequency signals are related, using the knowledge that some pixels are zero, by a set of linear equations in which the number of equations is equal to the number of zero pixels, and the number of unknowns is equal to the number of low-frequency signal samples rejected. An improved Fourier transform (FT), magnetic resonance (MR) imaging method based on a least-square-error (LSE) technique, and an efficient algorithm for signal restoration when the low-frequency components are discarded are presented. In this method, the regions of support in both the image domain and the frequency domain can have arbitrary shapes, and all zero pixels in the image domain can be taken into account. The algorithm has been tested on simulated and experimental data with acceptable results     

An alternating direction algorithm for total variation reconstruction of distributed parameters

Augmented Lagrangian variational formulations and alternating optimization have been adopted to solve distributed parameter estimation problems. The alternating direction method of multipliers (ADMM) is one of such formulations/optimization methods. Very recently, the number of applications of the ADMM, or variants of it, to solve inverse problems in image and signal processing has increased at an exponential rate. The reason for this interest is that ADMM decomposes a difficult optimization problem into a sequence of much simpler problems. In this paper, we use the ADMM to reconstruct piecewise-smooth distributed parameters of elliptical partial differential equations from noisy and linear (blurred) observations of the underlying field. The distributed parameters are estimated by solving an inverse problem with total variation (TV) regularization. The proposed instance of the ADMM solves, in each iteration, an l(2) and a decoupled l(2) - l(1) optimization problems. An operator splitting is used to simplify the treatment of the TV regularizer, avoiding its smooth approximation and yielding a simple yet effective ADMM reconstruction method compared with previously proposed approaches. The competitiveness of the proposed method, with respect to the state-of-the-art, is illustrated in simulated 1-D and 2-D elliptical equation problems, which are representative of many real applications.     

One-dimensional dense disparity estimation for three-dimensional reconstruction

We present a method for fully automatic three-dimensional (3D) reconstruction from a pair of weakly calibrated images in order to deal with the modeling of complex rigid scenes. A two-dimensional (2D) triangular mesh model of the scene is calculated using a two-step algorithm mixing sparse matching and dense motion estimation approaches. The 2D mesh is iteratively refined to fit any arbitrary 3D surface. At convergence, each triangular patch corresponds to the projection of a 3D plane. The proposed algorithm relies first on a dense disparity field. The dense field estimation modelized within a robust framework is constrained by the epipolar geometry. The resulting field is then segmented according to homographic models using iterative Delaunay triangulation. In association with a weak calibration and camera motion estimation algorithm, this 2D planar model is used to obtain a VRML-compatible 3D model of the scene.     

Direct three-dimensional image reconstruction

The problem of radar target-shape estimation for perfectly conducting complex objects is formulated as an image-reconstruction problem. A convolve-and-backproject algorithm is derived when the measurements are taken by radars located in three-dimensional space around the object region. The algorithm can be used directly in that there are no restrictions on the sensor placement; the sensors are not required to lie in a plane, for example, as is often assumed in many applications. Two possible convolving functions with desirable implementation characteristics are described. The algorithm is applicable to the general problem of reconstructing the density function of three-dimensional objects and applies to the radar shape-estimation problem as a special case.     

An improved reconstruction algorithm for 3-D diffraction tomography using spherical-wave sources

Diffraction tomography (DT) is an inversion technique that reconstructs the refractive index distribution of a weakly scattering object. In this paper, a novel reconstruction algorithm for three-dimensional diffraction tomography employing spherical-wave sources is mathematically developed and numerically implemented. Our algorithm is numerically robust and is much more computationally efficient than the conventional filtered backpropagation algorithm. Our previously developed algorithm for DT using plane-wave sources is contained as a special case.     

Public-key encryption algorithm incorporating error detection

Owing to their mathematical properties, quadratic residues have been used successfully in designing a number of cryptographic applications, such as oblivious transfer protocol and coin flipping protocol. The authors propose an encryption scheme based on quadratic residue theory. In particular, they incorporate the encrypting procedure and error-detecting code into a complete communication system.<>     

一种改进的压缩感知重构算法研究

主要研究重构算法的贪婪算法中的正交匹配追踪算法,并提出了基于正交匹配追踪算法的改进算法,对图像进行列变换后,再对原图像进行行变换,然后综合两幅图像的优点,重构出原图像.仿真结果表明这种改进的算法能够有效地提高重构效果.     

三维医疗影像数据自动分割算法研究

对传统的边缘提取及区域分割方法进行了一定的改进,将其扩张到了三维体数据中,并针对hessian矩阵边缘效应特别强的特点,提取其最大特征值进行图像分割,取得了一定的效果。     

A super-resolution reconstruction algorithm for hyperspectral images

The spatial resolution of a hyperspectral image is often coarse because of the limitations of the imaging hardware. Super-resolution reconstruction (SRR) is a promising signal post-processing technique for hyperspectral image resolution enhancement. This paper proposes a maximum a posteriori (MAP) based multi-frame super-resolution algorithm for hyperspectral images. Principal component analysis (PCA) is utilized in both parts of the proposed algorithm: motion estimation and image reconstruction. A simultaneous motion estimation method with the first few principal components, which contain most of the information of a hyperspectral image, is proposed to reduce computational load and improve motion field accuracy. In the image reconstruction part, different image resolution enhancement techniques are applied to different groups of components, to reduce computational load and simultaneously remove noise. The proposed algorithm is tested on both synthetic images and real image sequences. The experimental results and comparative analyses verify the effectiveness of this algorithm.     

An efficient algorithm for the three-dimensional analysis ofpassive microstrip components and discontinuities for microwave andmillimeter-wave integrated circuits

A numerical technique for the full-wave analysis of shielded, passive microstrip components on a two-layer substrate is presented. The distinct feature of the technique is an efficient formulation for establishing the system matrix in the moment method procedure which allows the derivation of the elements of any large matrix by a linear combination of elements in a precomputed index table. The table is obtained from a two-dimensional discrete fast Fourier transform. In the moment method procedure, the two-dimensional surface current is represented by locally defined rooftop functions. The effect of the resonant modes associated with the metallic enclosure on the numerical procedure is examined. In order to demonstrate the features and the accuracy of the technique, numerical results for a microstrip open end and for a right-angle bend with and without the compensated corner are computed by using the resonant technique and are compared with other published computational and experimental data     

一种基于压缩传感和SART的图像重建迭代算法

滤波反投影算法已被广泛应用到CT图像重建领域,但由于算法需要大量的投影数据,会延长扫描时间和累积高剂量的辐射。为了降低辐射的剂量,文中提出一种基于压缩传感和联合代数重建方法 (SART)的迭代算法,将图像的梯度稀疏性与SART图像重建相结合,减小梯度图像的l1范数直至算法迭代结束。实验结果表明,文中算法能利用少量的投影数据准确地重建出图像,减少了由于投影数据不充分而造成的条状伪影。     

A direct reconstruction algorithm for electrical impedance tomography

A direct (noniterative) reconstruction algorithm for electrical impedance tomography in the two-dimensional (2-D), cross-sectional geometry is reviewed. New results of a reconstruction of a numerically simulated phantom chest are presented. The algorithm is based on the mathematical uniqueness proof by A. I. Nachman [1996] for the 2-D inverse conductivity problem. In this geometry, several of the clinical applications include monitoring heart and lung function, diagnosis of pulmonary embolus, diagnosis of pulmonary edema, monitoring for internal bleeding, and the early detection of breast cancer.