ISSN:0899-9457    

DOI:10.1002/ima.1850020202

出版商:John Wiley&Sons, Inc.    

年代:1990

数据来源: WILEY

摘要:

AbstractThe inverse conductivity problem is the mathematical problem that must be solved in order for electrical impedance tomography systems to be able to make images. Here we show how this inverse conductivity problem is related to a number of other inverse problem. We then explain the workings of an algorithm that we have used to make images from electrical impedance data measured on the boundary of a circle in two dimensions. This algorithm is based on the method of least squares. It takes one step of a Newton's method, using a constant conductivity as an initial guess. Most of the calculations can therefore be done analytically. The resulting code is named NOSER, for Newton's One‐Step Error Reconstructor. It provides a reconstruction with 496 degrees of freedom. The code does not reproduce the conductivity accurately (unless it differs very little from a constant), but it yields useful images. This is illustrated by images reconstructed from numerical and experimental data, including data from a human ches

ISSN:0899-9457    

DOI:10.1002/ima.1850020203

出版商:John Wiley&Sons, Inc.    

年代:1990

数据来源: WILEY

摘要:

AbstractThe purpose of this paper is to reappraise the linearizing methods frequently used to solve inverse scattering problems. We describe inversion algorithms based on the Born and the Rytov approximations and the nature of the distortions obtained in the reconstructions when using them. We present extensions of these methods, namely, the distorted‐wave Born and the distorted‐wave Rytov approximations, which incorporate prior knowledge about part of the scattering structure. A method for inverting scattered field data using these distorted‐wave approximations is described, which retains the computational simplicity of the Born and the Rytov techniques. Some examples of their use with simulated and real data are given. A further extension of our distorted‐wave formalism, which leads to improvements of the reconstructed image, is suggested. This entails a spectral estimation procedure also based on the incorporation of prior knowledge about the scatterer. This spectral estimation procedure can be useful for interpolation of scattered field data as well as resolution enha

ISSN:0899-9457    

DOI:10.1002/ima.1850020204

出版商:John Wiley&Sons, Inc.    

年代:1990

数据来源: WILEY

摘要:

AbstractThe effect of the limited‐angle measurements on the nonlinear inverse scattering problem is investigated. Because of incomplete information obtained in the limited‐angle inverse problem, the linearized system matrix in the inversion procedure becomes more ill‐conditioned compared to that of the conventional inverse scattering problem where the receivers are placed in a circle that completely surrounds the object. Consequently, the quality of the reconstruction is considerably reduced, and sometimes it is almost impossible to reconstruct the profile because of the sparsity of the measurement data. To overcome the above difficulty, a boosting procedure, which will help us to obtain the maximum amount of information for an arbitrary predefined experimental setup, has been proposed based on a physical viewpoint. The results of the computer simulations for well‐to‐well tomography demonstrate that by applying the boosting procedure the quality of the reconstruction and the speed of the convergence are improved significantly. Furthermore, for subsurface detection where both the transmitters and receivers are confined to the ground, the reconstruction becomes possible after applying the boosting

ISSN:0899-9457    

DOI:10.1002/ima.1850020205

出版商:John Wiley&Sons, Inc.    

年代:1990

数据来源: WILEY

摘要:

AbstractInverse scattering methods for reconstructing sound‐wave‐speed structure in the dimensions have been shown to be equivalent to inverting line integrals when the scattered field is of sufficiently high frequency and the scattering is sufficiently weak. Seismic traveltime tomography uses first arrival traveltime data to invert for wave‐speed structure. Of course, the traveltime is itself a line integral along a refracting ray path through the medium being probed. The similarity between these two inversion problems is discussed. One type of neural network‐the Hopfield net‐may be used to improve the traveltime inversion. We find that, by taking advantage of the general relationship between least‐squares solution and generalized inverses, the neural networks approach eliminates the need for inverting singular or poorly conditioned matrices and therefore also eliminates the need for the damping term often used to regularize such inversions. This procedure produces reconstructions with fewer artifacts and faster convergence than those attained previously using damped least‐sq

ISSN:0899-9457    

DOI:10.1002/ima.1850020206

出版商:John Wiley&Sons, Inc.    

年代:1990

数据来源: WILEY

摘要:

AbstractA method for reconstructing the index of refraction of a bounded inhomogeneous object of known geometric configuration from measured far‐field scattering data is presented. This work is an extension of recent results on the direct scattering problem wherein the governing domain integral equation was solved iteratively by a successive relaxation technique. The relaxation parameters were chosen to minimize the residual error at each step. Convergence of this process was established for indices of refraction much larger than required for convergence of the Born approximation. For the inverse problem, the same technique is applied, except is this case both the index of refraction and the field are unknown. Iterative solutions for both unknowns are postulated with two relaxation parameters at each step. They are determined by simultaneously minimizing the residual errors in satisfying the domain integral equation and matching the measured data. This procedure retains the nonlinear relation between the two unknowns. Numerical results are presented for the dielectric slab. The algorithm is shown to be effective in cases where the iterative solution of the direct problem is rapidly convergent and outperforms the Born‐based approac

ISSN:0899-9457    

DOI:10.1002/ima.1850020207

出版商:John Wiley&Sons, Inc.    

年代:1990

数据来源: WILEY

摘要:

AbstractWe address the problem of reconstructing the directional derivative and/or the Laplacian of an object functionfcharacterizing a weakly inhomogeneous scatterer directly from data collected in a set of scattering experiments. We employ the Rytov approximation to model the complex phase of the scattered wavefields and show that a minimum‐norm least‐squares solution can be obtained from the well known filtered backpropagation algorithm of diffraction tomography with appropriate modification of the tomographic filters employed in the filtering step of the algorithm. The procedure is illustrated by a computer simulation st

ISSN:0899-9457    

DOI:10.1002/ima.1850020208

出版商:John Wiley&Sons, Inc.    

年代:1990

数据来源: WILEY

摘要:

AbstractThe problem of determining the velocity and depth structure of a layered earth model from surface seismic data is of considerable interest in exploration seismology, and many variations on ways to pose the problem and solve it have been proposed. One popular approach is based on layer stripping, in which it is assumed that all layers above a given layer whose parameters are to be determined have been inverted. This information is then used, together with seismic reflection data, to invert for the parameters of the given layer. This procedure is repeated until the entire section of interest has been inverted. The problem may be posed as a one‐, two‐, or three‐dimensional problem. The one‐dimensional case has received considerable treatment in the literature. The purpose of this paper is to extend a theoretical result and the corresponding analysis from the 1‐D to the 2‐D case. Specifically, it is shown that for a dipping plane layer 2‐D stratified earth, the depth/dip/velocity structure of the section can be determined by a direct layer‐stripping algorithm in which a system of nonlinear equations is solved for the unknown layer parameters using only traveltime data from three offset locations. This is the minimal information required to solve the problem. In practice, the solution is extremely sensitive to data errors and so a minimum norm implementation would usually be employed, utilizing the redundancy of data available from more than three offsets. It is the theoretical development which is of interest here. Its actual implementation may

ISSN:0899-9457    

DOI:10.1002/ima.1850020209

出版商:John Wiley&Sons, Inc.    

年代:1990

数据来源: WILEY

摘要:

AbstractThis paper deals with numerical processing techniques and practical applications of active microwave imaging. Different wavefront processing are presented, from an immediate use of measured projections to more complex procedures. Both spectral approaches to diffraction tomography and spatial iterative methods for generalized imaging are considered using multi‐incidence of multifrequency techniques for 3D and/or 2D objects. The technology of the so‐called microwave camera is presented for the fast recording of the scattered field with arrays of probes involving one‐ or two‐dimensional sensors at a single frequency or in a broad‐frequency band. Three different systems are depicted: a single‐frequency linear sensor devoted to industrial applications (on‐line transverse control of conveyed products), a single‐frequency planar microwave camera for biomedical applications and research, and a broad‐frequency linear microwave camera for civil engineering applications (detection of the rebars in reinforced concrete strctures). Microwave images obtained experimentally with the three systems are presented on configurations of practical interest for each fie

ISSN:0899-9457    

DOI:10.1002/ima.1850020210

出版商:John Wiley&Sons, Inc.    

年代:1990

数据来源: WILEY

ISSN:0899-9457    

DOI:10.1002/ima.1850020201

出版商:John Wiley&Sons, Inc.    

年代:1990

数据来源: WILEY