Image reconstruction from real scattering data using an iterativescheme with incorporated a priori information

The two-dimensional inverse electromagnetic-scattering problem of reconstructing the material properties of inhomogeneous lossy dielectric cylindrical objects is considered. The material properties are reconstructed from measured far-field scattering data, provided by the USAF Rome Laboratory Electromagnetic Measurement Facility in Ipswich. The targets in the Ipswich data set include perfectly electrically conducting (PEC) targets, penetrable (PEN) targets, and hybrid targets. A new method, which incorporates a priori information about the material properties, is proposed to solve the nonlinear inverse-scattering problem     

Image reconstruction from the 1997 Ipswich data using aconjugate-gradient algorithm

The conjugate gradient algorithm is shown to be effective in reconstructing targets from experimental radar measurements. Enhancement, using the reciprocity relation to complete the scattered data, is also shown. The small number of iterations needed to obtain a satisfying solution (less than 50 iterations), combined with the increasing computation power of new processors (an SGI R10000 needs 30 sec to compute one iteration), make it possible for this algorithm to be used for practical applications     

Image reconstruction from frequency-offset Fourier data

Motivated by the ability of synthetic-aperture radar and related imaging systems to produce images of surprisingly high quality, we consider the problem of reconstructing the magnitude of a complex signal f from samples of the Fourier transform of f located in a small region offset from the origin. It is shown that high-quality speckle reconstructions are possible so long as the phase of f is highly random. In this case, the quality of the reconstruction is insensitive to the location of the known Fourier data, and edges at all orientations are reproduced equally well. A large number of computer examples are presented demonstrating these attributes. Methods for improving image quality are also briefly discussed.     

Image reconstruction from Ipswich data. II

In this paper, we describe the results obtained by using variants of the modified gradient method. These are applied to the new Ipswich data sets to reconstruct the shape, location, and/or index of refraction of unknown two-dimensional scatterers (infinite cylinders in three dimensions)     

Analysis of TE scattering from dielectric cylinders using amultifilament magnetic current model

A moment solution is presented for the problem of transverse electric (TE) scattering from homogeneous dielectric cylinders. The moment solution uses fictitious filamentary magnetic currents to simulate both the field scattered by the cylinder and the field inside the cylinder and in turn point-matches the continuity conditions for the tangential components of the electric and magnetic fields across the cylinder surface. The procedure is simple to execute and is general in that cylinders of arbitrary shape and complex permittivity can be handled effectively. Metallic cylinders are treated as reduced cases of the general procedure. Results are given and compared with available analytic solutions, which demonstrate the very good performance of the procedure     

Image reconstruction from multiple frames of sparse data

High-resolution image reconstruction from sparse data is an important problem in sensor array imaging (SAI). The reconstructed images from such a data are poorly resolved. However, there may exist possibilities of making multiple measurements, for example, collecting many frames of data in a dynamic scene situation where there is relative motion between the object and the receiver. We discuss here a method of reconstructing good-quality images from multiple frames of sparse data obtained from a simulated dynamic scene situation. This method, based on projection onto convex sets (POCS), not only restricts the solution set by satisfying the constraints in the multiple measurements but also reconstructs a high-resolution image.     

Image reconstruction from acoustical holograms using microprocessors

An acoustic imaging system using holographic techniques is described. Insonification of the object is achieved using a phased array scanner. Image reconstruction uses Fourier Transformations to produce a 128 × 128 pixel TV display. The system has the ability to focus in the ‘near field’ of its transducer arrays and has a frame rate of approximately 0.3 Hz.     

Image reconstruction from incomplete projection data: iterative reconstruction-reprojection techniques

This paper addresses the task of image reconstruction from an incomplete set of projection data. Several methods which first estimate the missing data and then utilize standard reconstruction algorithms to obtain an image are investigated. Results from simulations are presented which illustrate the difficulty in comparing algorithms objectively, particularly when a simple test phantom is chosen. The incorporation of a priori information into the algorithm, an approach which has previously been discussed in the literature, is shown to produce faster convergence.     

Variable pitch reconstruction using John's equation

We present an algorithm to reconstruct helical cone beam computed tomography (CT) data acquired at variable pitch. The algorithm extracts a halfscan segment of projections using an extended version of the advanced single slice rebinning (ASSR) algorithm. ASSR rebins constant pitch cone beam data to fan beam projections that approximately lie on a plane that is tilted to optimally fit the source helix. For variable pitch, the error between the tilted plane chosen by ASSR and the source helix increases, resulting in increased image artifacts. To reduce the artifacts, we choose a reconstruction plane, which is tilted and shifted relative to the source trajectory. We then correct rebinned fan beam data using John's equation to virtually move the source into the tilted and shifted reconstruction plane. Results obtained from simulated phantom images and scanner images demonstrate the applicability of the proposed algorithm.      

Microwave imaging-Location and shape reconstruction frommultifrequency scattering data

The problem of determining the shape and location of an object embedded in a homogeneous dissipative medium from measurements of the field scattered by the object is considered in this paper. The object is assumed to be an infinite cylinder of known cross section illuminated by a TM plane wave and the scattered field is measured on a line segment perpendicular to the direction of incidence. Measurement data are carried out at three different frequencies for a homogeneous cylinder of known dielectric constant. The location and contour shape are determined using two different reconstruction algorithms, a Newton-Kantorovich (NK) method and the modified gradient (MG) method whose effectiveness and robustness are compared. Both methods are based on domain integral representations of the field in the body. They involve an iterative minimization of the defect between an integral representation of the field measured on the line and the actual measured data. The NK method involves a linearization of the nonlinear relation between the field and the contrast, as well as the solution of a direct scattering problem at each iteration. The MG method seeks the simultaneous reconstruction of the field and the characteristic function of the support of the scatterer without solving a direct problem at each step. Both methods employed the same initial guess and the a priori information that the characteristic function is nonnegative     

Radar scattering from bodies of revolution using an efficientpartial differential equation algorithm

A technique is presented for solving the problem of scattering by a three-dimensional body of revolution using a partial differential equation (PDE) technique in conjunction with a radiation boundary condition applied in the Fresnel region of the scatterer. The radiation boundary condition, which is used to truncate the PDE mesh, is based on an asymptotic expansion derived by Wilcox (1956). Numerical results illustrating the procedure and verifying the accuracy of the results are included     

Image upconversion using coherent anti-stokes Raman scattering

We report an experimental and theoretical study of real-time image upconversion with coherent anti-Stokes Raman scattering. Experimental results for image upconversion in hydrogen are presented. Various parameters affecting the efficiency of the upconverted signal and image resolution are discussed     

Oblique scattering from inhomogeneous cylinders using a coupledintegral equation formulation with triangular cells

A novel method of moments formulation for scattering from penetrable two-dimensional cylinders illuminated by an obliquely incident excitation is presented. The permittivity and permeability profiles may have arbitrary piecewise-constant dependence on the transverse variables. Regardless of the polarization of the incident field, the response of the scatterer is a combination of transverse electric (TE) and transverse magnetic (TM) waves. Coupled integral equations for the longitudinal electric and magnetic fields are used in conjunction with a triangular-cell discretization, a piecewise linear representation for E_z and H_z, and point-matching. Numerical results for the internal fields and scattering cross-section are presented to illustrate the accuracy of the approach     

Analysis of transient electromagnetic scattering from closedsurfaces using a combined field integral equation

In the past, both the time-domain electric and magnetic field integral equations have been applied to the analysis of transient scattering from closed structures. Unfortunately, the solutions to both these equations are often corrupted by the presence of spurious interior cavity modes. In this article, a time-domain combined field integral equation is derived and shown to offer solutions devoid of any resonant components. It is anticipated that stable marching-on-in-time schemes for solving this combined field integral equation supplemented by fast transient evaluation schemes such as the plane wave time-domain algorithm will enable the analysis of scattering from electrically large closed bodies capable of supporting resonant modes     

Image recovery using the anisotropic diffusion equation

A new approach for image recovery using the anisotropic diffusion equation is developed which is based on the first derivative of the signal in time embedded in family of images with different scales. The diffusion coefficient is determined as a function of the gradient of the signal convolved with a symmetric exponential filter. A new discrete realization is developed for the simultaneous removal of noise and preservation of edges.     

Image reconstruction from localized phase

The authors present a novel approach to image representation using partial information defined by the localized phase. The scheme is implemented using the short-time (short-distance) Fourier transform. This is a generalization of the Gabor scheme which is well-established with regard to biological representation of visual information at the level of the visual cortex. Similar to processing in vision, the DC component is first extracted from the signal and treated separately. Computational results and theoretical analysis indicate that image reconstruction from the localized phase representation requires fewer computer operations and yields an improved rate of convergence compared to reconstruction from the global phase representation. It is also implementable with fast algorithms using highly parallel architecture     

TE scattering from a slit in a thick conducting screen: revisited

TE plane-wave scattering from a slit in a thick conducting screen is reexamined. The boundary conditions are enforced to obtain simultaneous equations for the transmitted field inside the thick conducting screen. The simultaneous equations are solved to represent the transmitted and scattered fields in series forms. An approximate series solution for transmission is obtained in closed form which is valid for the high-frequency scattering regime     

A fast high-order solver for EM scattering from complex penetrablebodies: TE case

We present a new high-order integral algorithm for the solution of scattering problems by heterogeneous bodies under TE radiation. Here, a scatterer is represented by a (continuously or discontinuously) varying refractive index n(x) within a two-dimensional (2-D) bounded region. Solutions of the associated Helmholtz equation under given incident fields are then obtained by high-order inversion of the Lippmann-Schwinger integral equation. The algorithm runs in O(N log(N)) operations, where N is the number of discretization points. Our method provides highly accurate solutions in short computing times, even for problems in which the scattering bodies contain complex geometric singularities     

Image data compression using subband coding

A general reversive subband coding system with 2-D infinite impulse response filters is proposed. The system considered guarantees perfect image reconstruction (free of phase distortions). Application of wave digital filters is considered. A new technique of high-frequency source encoding is proposed. The experiments with real images prove high efficiency of the technique proposed.