Ipswich Data Research Articles

Image reconstruction from Ipswich data. III

Image reconstruction from Ipswich data. III

The third annual special session on image reconstruction using real data. 2. The application of back-propagation algorithms to the Ipswich data: preliminary results

For pt.1 see ibid., vol.41, no.1, p.34-51 (1999). The Ipswich data provide a unique opportunity for the validation of the approximate back-propagation (ABP) methods, which were originally developed to identify the shape of acoustic scatterers in the resonance region. These methods rely on a heuristic relationship, i.e., ABP, between the expansion coefficients that represent the scattered wave in the far zone and those on the obstacle boundary, /spl Gamma/. The unknown is the shape-parameter vector, /spl psi//spl I.oarr//spl isin//spl Psi//sub ad/, the admissible set. The objective function to be minimized is the L/sup 2/(/spl Gamma/)-norm of the boundary defect. In the vertical-polarization case, ABP consists of an affine map, which is easy to derive. Its ingredients are arrays of inner products in L/sup 2/(/spl Gamma/), where outgoing cylindrical wave functions are involved. The corresponding numerical results, based on the IPS001VV data, are satisfactory. The attraction domain of the expected solution, the reference obstacle (a disk), is numerically determined by varying the initial conditions in a wide subset of /spl Psi//sub ad/. Reconstruction seems to be unique, although no uniqueness condition is known for the obstacle. In the horizontal-polarization case, ABP relies on vector harmonic functions in a cylindrical geometry. The complexity of the algorithm is higher. Results based on the TPS001HH set are summarized. Although the numerical solution does not show any focal minimum other than the reference obstacle, the corresponding attraction domain is smaller than in the vertical-polarization case.

Image reconstruction from real scattering data using an iterative scheme 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.

A numerical method to solve the inverse medium problem: an application to the Ipswich data. II

For pt.I see ibid., vol.39, no.14-19 (1997). The following electromagnetic inverse scattering problem is considered: reconstruction of the refractive index of a cylindrically symmetric inhomogeneity from knowledge of the scattered electromagnetic fields, when the inhomogeneity is hit by known incident electromagnetic fields. Taking advantage of the cylindrical symmetry, the problem for the Maxwell equations is reduced to a boundary-value problem for the two-dimensional scalar Helmholtz equation. The inverse problem is formulated using the Born approximation for the far-field patterns of the scattered fields. The numerical algorithm proposed in Maponi et al. (1997) is used.

A numerical method to solve the inverse medium problem: an application to the Ipswich data

We consider the propagation of electromagnetic waves in an inhomogeneous medium. The inhomogeneity is contained in a vertical cylinder with a compact base. When an incident wave meets the inhomogeneity, a scattered wave is generated. We consider the problem of the reconstruction of the inhomogeneous refractive index from some knowledge of the scattered waves generated by the interaction of the inhomogeneity with several known incident waves. We give a mathematical formulation of the problem, a numerical method to solve it, and some numerical results obtained using the numerical method proposed on the Ipswich data. The Ipswich data are experimental data. The inverse-scattering problem considered above is of great theoretical and practical interest. It is an ill-posed problem.

Reconstructing objects from the Ipswich data set

Inverse scattering, or imaging, has many important technological applications. In this paper, we present experimental results of refractive-index reconstruction using a previously developed algorithm that is based on an enhanced diffraction tomography. In addition, we also present experimental results of a shape-reconstruction algorithm that utilizes the null-field method for solving the direct problem, and the Newton-Kantorovich technique for inversion. For testing of both algorithms, we make use of experimental scattering data contained in the Ipswich data set.

Imaging of strongly-scattering targets from real data

Measured bistatic scattered fields for five new targets were added to the Ipswich data set. Three of the targets remained a mystery until revealed at a special session on image reconstruction from real data, at the 1996 IEEE AP-S International Symposium and URSI Radio Science Meeting in Baltimore. We provided coherent scattered-field data for more complicated scattering structures, as well as many more transmit-illumination directions, or views, than we had previously. Reconstructions corresponding to the first. We show back-propagated images of all five targets, using aspect diversity in diffraction tomography at a 3 cm wavelength. As expected, those targets that possess multiple-scattering effects, and/or have high contrast, fail to image properly. Targets from the Ipswich data set may serve as a useful standard against which researchers, involved in inverse scattering, can compare the merits of their inversion algorithms.

Conjugate-gradient algorithm with edge-preserving regularization for image reconstruction from Ipswich data for mystery objects

This paper presents some evidence of the effectiveness of adding edge preserving (EP) regularization to the conjugate radient (CG) method, in reconstructing the shape and permittivity profile of dielectric objects. Without any a priori information, our CG algorithm is also still efficient, and succeeded in reconstructing two mystery targets. As the two targets are now known, we hope we can greatly enhance the reconstruction quality by choosing better values for the calibration factors, and by applying our EP regularization to these data.

Inversion of the 1996 Ipswich data using binary specialization of modified gradient methods

The paper considers the application of two different solution methods to the inversion of the Ipswich data available in June, 1996. The first one is derived from diffraction tomography in a cylindrical measurement geometry whereas the second one is based on the modified gradient method specialized to the case of binary targets.

Newton-Kantorovich and Modified Gradient - Inversion Algorithms Applied to Ipswich Data

The present paper considers the application of the Newton-Kantorovich and modified-gradient methods to the Ipswich data. The object is assumed to be an inhomogeneous lossy dielectric cylinder of arbitrary cross section. Both inverse-scattering methods are based on electric-field integral representations. The Newton-Kantorovich technique builds up the solution by solving successively the forward problem and a linear inverse problem. This method needs regularization, and we use either the identity operator or a gradient operator for regularization. The modified-gradient method is iterative, as is the Newton algorithm, but does not involve a linearization at each step of the nonlinear inverse problem. Results of inversions with both methods, on two known impenetrable targets, are discussed.

Image Reconstruction From Ipswich Data

For pt.II see ibid., vol.39, p.29-32 (1997). We describe results obtained in image reconstruction using the Ipswich data sets IPS009-IPS012. In van den Berg et al. (1995, 1997) and van den Berg and Kleinman (1996), we employed versions of the modified gradient method to reconstruct the shape, location, and index of refraction of known and unknown scatterers, both dielectric and perfectly conducting, from the measured scattered field data contained in IPS001-IPS008. In the present paper, we employ a new inversion method, the contrast source inversion (CSI) method, for the reconstructions. We include here a brief description of the method, given in greater detail in van den Berg and Kleinman. In the case of the new Ipswich experiments, we have 36 angles of incidence, equidistantly distributed around the object. The unknown scatterer is assumed to be located somewhere in a known, bounded, test domain D (taken to be square), and the scattered field is measured on a domain S (taken to be a circle) containing the test domain D in its interior. In the case of the Ipswich experiments, S was taken to be in the far zone of the scattered field, and measurements were made at 18 angles of observation, equidistantly distributed over a semicircle. For each experiment, this semicircle started with the forward-scattering angle.

Processing Ipswich Data with the Local Shape Function Method

Processing Ipswich Data with the Local Shape Function Method