超声层析成像的迭代重建

利用变形Born迭代方法,建立了超声衍射重建算法。在迭代过程中,为了解决超声逆散射问题中的非线性性,需要反复地求解前向散射方程和逆散射方程,以达到全场和未知函数的近似,较好地重建物体内部的断层图象。由于逆散射方程是一个不适定性的方程组,要用正则化方法处理方程的不适定性问题,使迭代方法收敛于问题的真实解,才能成功地应用于较高对比度物体的图象重建问题。用Picard准则对不适定问题进行了分析,给出了通过简单图形．确定模型受噪声污染情况以及正则化方法适用范围的方法。在重建实验中。对建立的图像重建算法进行了实验仿真。达到了较好的效果。     

An eigenfunction method for reconstruction of large-scale and high-contrast objects

A multiple-frequency inverse scattering method that uses eigenfunctions of a scattering operator is extended to image large-scale and high-contrast objects. The extension uses an estimate of the scattering object to form the difference between the scattering by the object and the scattering by the estimate of the object. The scattering potential defined by this difference is expanded in a basis of products of acoustic fields. These fields are defined by eigenfunctions of the scattering operator associated with the estimate. In the case of scattering objects for which the estimate is radial, symmetries in the expressions used to reconstruct the scattering potential greatly reduce the amount of computation. The range of parameters over which the reconstruction method works well is illustrated using calculated scattering by different objects. The method is applied to experimental data from a 48-mm diameter scattering object with tissue-like properties. The image reconstructed from measurements has, relative to a conventional B-scan formed using a low f-number at the same center frequency, significantly higher resolution and less speckle, implying that small, high-contrast structures can be demonstrated clearly using the extended method.     

An adaptive level set method based on two‐level uniform meshes and its application to dislocation dynamics

In this paper, we present an adaptive level set method for motion of high codimensional objects (e.g., curves in three dimensions). This method uses only two (or a few fixed) levels of meshes. A uniform coarse mesh is defined over the whole computational domain. Any coarse mesh cell that contains the moving object is further divided into a uniform fine mesh. The coarse‐to‐fine ratios in the mesh refinement can be adjusted to achieve optimal efficiency. Refinement and coarsening (removing the fine mesh within a coarse grid cell) are performed dynamically during the evolution. In this adaptive method, the computation is localized mostly near the moving objects; thus, the computational cost is significantly reduced compared with the uniform mesh over the whole domain with the same resolution. In this method, the level set equations can be solved on these uniform meshes of different levels directly using standard high‐order numerical methods. This method is examined by numerical examples of moving curves and applications to dislocation dynamics simulations. This two‐level adaptive method also provides a basis for using locally varying time stepping to further reduce the computational cost. Copyright © 2013 John Wiley & Sons, Ltd.     

Multilevel, hybrid regularization method for reconstruction of fluorescent molecular tomography

In this paper, a multilevel, hybrid regularization method is presented for fluorescent molecular tomography (FMT) based on the hp-finite element method (hp-FEM) with a continuous wave. The hybrid regularization method combines sparsity regularization and Landweber iterative regularization to improve the stability of the solution of the ill-posed inverse problem. In the first coarse mesh level, considering the fact that the fluorescent probes are sparsely distributed in the entire reconstruction region in most FMT applications, the sparse regularization method is employed to take full advantage of this sparsity. In the subsequent refined mesh levels, since the reconstruction region is reduced and the initial value of the unknown parameters is provided from the previous mesh, these mesh levels seem to be different from the first level. As a result, the Landweber iterative regularization method is applied for reconstruction. Simulation experiments on a 3D digital mouse atlas and physical experiments on a phantom are conducted to evaluate the performance of our method. The reconstructed results show the potential and feasibility of the proposed approach.     

Solution of convergence problem in ultrasound inverse scattering tomography

When the product of contrast and size of an object, which is to be reconstructed by using the ultrasound inverse scattering tomography algorithm, is large, it is well known that those algorithms fail to converge to a unique global minimum. In order to solve this well known and difficult convergence problem, in this paper we present a new method, which converges to the true solution, for obtaining the scattering potential without using the Born or Rytov approximation. This method converts the nonlinear nature of the problem into a linear one. Through computer simulations we will show the validity of the new approach for high contrast two-dimensional scattering objects which are insonified by an incident ultrasound plane wave. Numerical results show that the reconstruction error is very small for circularly symmetric two-dimensional cylindrical objects whose refractive indices range from small to even sufficiently large values for which the previous inverse scattering algorithms fail to converge.     

Non-interferometric methods of phase estimation for application in optical tomography

Abstract

We describe here two non-interferometric methods for the estimation of the phase of transmitted wavefronts through refracting objects. The phase of the wavefronts obtained is used to reconstruct either the refractive index distribution of the objects or their contours. Refraction corrected reconstructions are obtained by the application of an iterative loop incorporating digital ray tracing for forward propagation and a modified filtered back projection (FBP) for reconstruction. The FBP is modified to take into account non-straight path propagation of light through the object. When the iteration stagnates, the difference between the projection data and an estimate of it obtained by ray tracing through the final reconstruction is reconstructed using a diffraction tomography algorithm. The reconstruction so obtained, viewed as a correction term, is added to the estimate of the object from the loop to obtain an improved final refractive index reconstruction.     

Enhanced reconstruction of three-dimensional shape and texture from integral photography images

A method for the reconstruction of 3D shape and texture from integral photography (IP) images is presented. Sharing the same principles with stereoscopic-based object reconstruction, it offers increased robustness to noise and occlusions due to the unique characteristics of IP images. A coarse-to-fine approach is used, employing what we believe to be a novel grid refinement step in order to increase the quality of the reconstructed objects. The proposed method's properties include configurable depth accuracy and direct and seamless triangulation. We evaluate our method using synthetic data from a computer-simulated IP setup as well as real data from a simple yet effective digital IP setup. Experiments show reconstructed objects of high-quality indicating that IP can be a competitive modality for 3D object reconstruction.     

An iterative solution of the two-dimensional electromagnetic inverse scattering problem

A new method, based on an iterative procedure, for solving the two-dimensional inverse scattering problem is presented. This method employs an equivalent Neumann series solution in each iteration step. The purpose of the algorithm is to provide a general method to solve the two-dimensional imaging problem when the Born and the Rytov approximations break down. Numerical simulations were calculated for several cases where the conditions for the first order Born approximation were not satisfied. The results show that in both high and low frequency cases, good reconstructed profiles and smoothed versions of the original profiles can be obtained for smoothly varying permittivity profiles (lossless) and discontinuous profiles (lossless), respectively. A limited number of measurements around the object at a single frequency with four to eight plane incident waves from different directions are used. The method proposed in this article could easily be applied to the three-dimensional inverse scattering problem, if computational resources are available.     

Comparison of the born iterative method and tarantola's method for an electromagnetic time-domain inverse problem

Two methods of solving the nonlinear two-dimensional electromagnetic inverse scattering problem in the time domain are considered. These are the Born iterative method and the method originally proposed by Tarantola for the seismic reflection inverse problems. The former is based on Born-type iterations on an integral equation, whereby at each iteration the problem is linearized, and its solution is found via a regularized optimization. The latter also uses an iterative method to solve the nonlinear system of equations. Although it linearizes the problem at each stage as well, no optimization is carried out at each iteration; rather the problem as a whole is posed as a (regularized) optimization. Each method is described briefly and its computational complexity is analyzed. Tarantola's method is shown to have a lower numerical complexity compared to the Born iterative method for each iteration, but in the examples considered, required more iterations to converge. Both methods perform well when inverting a smooth profile; however, the Born iterative method gave better results in resolving localized point scatterers.     

Remote metrology by comparative digital holography

A method for the remote comparison of objects with regard to their shape or response to a load is presented. The method allows interferometric sensitivity for comparing objects with different microstructure. In contrast to the well-known incoherent techniques based on inverse fringe projection this new approach uses the coherent optical wave field of the master object as a mask for the illumination of the sample object. The coherent mask is created by digital holography to allow instant access to the complete optical information of the master object at any place desired. The mask is reconstructed by a spatial light modulator (SLM). The optical reconstruction of digital holograms with SLM technology allows modification of reconstructed wavefronts with respect to improvement of image quality, the skilled introduction of additional information about the object (augmented reality), and the alignment of the master and test object.     

An optimization method for quantitative impedance tomography

A near-field ultrasonic tomography method providing high resolution imaging for soft tissue in the reflection mode is reported. When the Born approximation is valid, the main limitation of this method is that it requires an incident pulse with infinite bandwidth, whereas the incident pulses used in practice have a limited bandwidth, which makes quantitative reconstruction impossible. The reconstructed image is qualitative in the sense that it is a band-pass filtered reconstruction of the impedance distribution. An optimization method based on the use of the geometrical information provided by the tomographic reconstruction is developed to obtain the quantitative information required. The object was approximated locally by an equivalent canonical body, on the basis of the previous global estimation. The inversion procedure is then carried out using the minimization of a cost function, which is the average over frequency of the difference between the measured field scattered by the object and the estimated field scattered by the equivalent canonical body. Assuming the object to be homogeneous by regions, the last step consists of assigning the estimated local impedance value to the region of interest. When the geometry of the real body is almost canonical, the optimization method yields accurate impedance assessments.     

Helmholtz-Type Regularization Method for Permittivity Reconstruction Using Experimental Phantom Data of Electrical Capacitance Tomography

Electrical capacitance tomography (ECT) attempts to image the permittivity distribution of an object by measuring the electrical capacitance between sets of electrodes placed around its periphery. Image reconstruction in ECT is a nonlinear ill-posed inverse problem, and regularization methods are needed to stabilize this inverse problem. The reconstruction of complex shapes (sharp edges) and absolute permittivity values is a more difficult task in ECT, and the commonly used regularization methods in Tikhonov minimization are unable to solve these problems. In the standard Tikhonov regularization method, the regularization matrix has a Laplacian-type structure, which encourages smoothing reconstruction. A Helmholtz-type regularization scheme has been implemented to solve the inverse problem with complicated-shape objects and the absolute permittivity values. The Helmholtz-type regularization has a wavelike property and encourages variations of permittivity. The results from experimental data demonstrate the advantage of the Helmholtz-type regularization for recovering sharp edges over the popular Laplacian-type regularization in the framework of Tikhonov minimization. Furthermore, this paper presents examples of the reconstructed absolute value permittivity map in ECT using experimental phantom data.      

Reconstruction of Cracks with Multiple Eddy Current Coils Using a Database Approach

This paper presents some recent studies dealing with flaw reconstruction using eddy current testing. The locations of parallel planar cracks in an Inconel 600 plate specimen are determined and the shapes of them are reconstructed at the same time using the signals from a multi-pancake coil probe. The reconstruction strategy, consisting of a data base used fast forward solver and a first order optimization algorithm, relies on the minimization of the nonlinear least square residual function. Validity of the inverse analysis method is investigated with respect to the influence of the arrangement of scanning paths. The efficiency of the computation is also discussed.     

Deterministic versus stochastic level-set regularization in nonlinear phase contrast tomography

A new nonlinear level-set regularization method to reconstruct the complex refractive index distribution with in-line phase contrast tomography measurements is presented under the assumption that the index is piecewise constant. The nonlinear iterative approach is based on the Fréchet derivative of the intensity recorded at a single propagation distance and for several projection angles. The algorithm is successfully applied to a multi-material object for several noise levels. Better reconstruction results are achieved with a stochastic perturbation of the level-set function. This evolution corresponds to a stochastic evolution of the shape of the reconstructed regions. The reconstruction errors can be further decreased with topological derivatives. The different algorithms are tested on various multi-material objects.     

Microwave imaging: Reconstructions from experimental data using conjugate gradient and enhancement by edge-preserving regularization

A method for reconstructing the complex permittivity profile of lossy dielectric objects from measured scattered far-field data is presented. An iterative reconstruction algorithm based on a conjugate gradient method is derived from an integral representation of the electric field and applying a moment method solution. Results obtained from experimental data are shown for both known and unknown targets. Then, a new regularization procedure is developed to enhance the quality of the reconstruction. This method, based on a Markov random fields approach, models the object to be reconstructed by homogeneous areas separated by borderlike discontinuities. Finally, the enhancement is shown by the reconstruction of a polystyrene square cylinder. © 1997 John Wiley & Sons, Inc. Int J Imaging Syst Technol, 8, 337–342, 1997     

Iterative algorithm of phase determination in digital holography for real-time recording of real objects

We propose a numerical method to obtain complex amplitude distribution of a three-dimensional (3D) object from a digital hologram. The method consists of two processes. The first process is to measure simultaneously a hologram of the 3D object and an object intensity distribution by two image sensors. These intensity distributions give us the amplitude and absolute value of phase of the 3D object at the image sensor plane. The second process is the determination of phase distribution by a proposed iterative process based on the criterion that the reconstructed 3D object is in focus and its conjugate reconstruction is out of focus. Numerical and experimental results show the effectiveness of the proposed method.     

Wave field reconstruction from multiple plane intensity-only data: augmented lagrangian algorithm

A complex-valued wave field is reconstructed from intensity-only measurements given at multiple observation planes parallel to the object plane. The phase-retrieval algorithm is obtained from the constrained maximum likelihood approach provided that the additive noise is gaussian. The forward propagation from the object plane to the measurement plane is treated as a constraint in the proposed variational setting of reconstruction. The developed iterative algorithm is based on an augmented lagrangian technique. An advanced performance of the algorithm is demonstrated by numerical simulations.     

Ultrasonic inverse scattering of multidimensional objects buried in multilayered elastic background structures

The authors focus on the multidimensional inverse scattering of objects buried in an inhomogeneous elastic background structure. The medium is probed by an ultrasonic force and the scattered field is observed along a receiver array. The goal is to retrieve both the geometry (imaging problem) and the constitutive parameters (inverse problem) of the object through an appropriate multiparameter direct linear inversion. The problem is cast in terms of a vector integral equation elastic scattering framework. The multidimensional inverse scattering problem, being nonlinear and ill-posed, is linearized within the Born approximation for inhomogeneous background, and a minimum-norm least-square solution to the discretized version of the vector integral formulation is sought. The solution is based on a singular value decomposition of the forward operator matrix. The method is illustrated on a 2-D problem where constrained least-square inversion of the object is performed from synthetic data. A Tikhonov regularization scheme is examined and compared to the minimum-norm least-square estimate.     

一种电容层析成像图像重建优化算法

提出一种电学层析成像(ECT)图像重建优化算法。通过将传统正则化算法转化为最小二乘问题进行求解,结合lp范数逼近正则化最小化问题,利用重新加权的方法进行迭代计算。以油-气两相流模型进行仿真及静态实验,将所提出的优化算法与常用的LBP、Landweber迭代及Tikhonov正则化算法进行对比。结果表明,与常用算法相比,采用该优化算法对管道中心物体及多物体分布流型进行图像重建,其图像相对误差均为最低,且重建图像的形状保真度明显提高。     

Imaging strongly scattering media using a multiple frequency distorted Born iterative method

The distorted Born iterative (DBI) method is a powerful approach for solving the inverse scattering problem for ultrasound tomographic imaging. This method alternates between solving the inverse scattering problem for the scattering function and the forward scattering problem for the total field and the inhomogeneous Green's function. The algorithm is initialized using the basic Born inverse solution. One fundamental problem is the algorithm diverges for strongly scattering media. This is caused by the limitation of the Born assumption in estimating the initial step of the algorithm. We present a multiple frequency DBI approach to alleviate this problem, thus extending the applicability of the DBI method to the level of dealing with biological tissue. In this multiple frequency approach, a low frequency DBI-based solution, is used to initialize the algorithm at higher frequencies. The low frequency allows convergence of the algorithm to a contrast level that is close to the true level, however, with a poor spatial resolution. The high frequency improves the spatial resolution while preserving convergence because the difference between the true contrast and the initial contrast is relatively small. We present numerical simulations that demonstrate the ability of this method to reconstruct strongly scattering regions.