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Partial Measurement and reconstruction in electrical impedance tomography; Polarisation in electromagnetic inverse problems; Inverse thermoelastic Rayleight scattering by a rigid ellipsoid; An inverse moving boundary problem for Laplace's equation; The scattering of velocity fields by an airfoil in compressible flow; Boundary problems in electrical impedance tomography.

Partial Measurement and reconstruction in electrical impedance tomography; Polarisation in electromagnetic inverse problems; Inverse thermoelastic Rayleight scattering by a rigid ellipsoid; An inverse moving boundary problem for Laplace's equation; The scattering of velocity fields by an airfoil in compressible flow; Boundary problems in electrical impedance tomography.

The objective of this basic research project is to describe an imaging protocol which will allow optical imaging to resolve nanoscale features (Near Field Tomography), both a the surface and below, of various components. The AF anticipates exploiting ever smaller devices and the manufacturing/inspection of these will benefit from the basic research done here. The PI will continue his seminal research into near field EM. In this not-well understood area the classical rules of thumb regarding wave-length limited resolution do not apply since recourse is now made to the evanescent waves always present in the near field. The PI proposes a mathematical approach involving principles from Inverse Scattering theory requiring the inversion of a suitable Laplace transformation.

The objectives of this project were to conduct rigorous mathematical and computational research on inverse problems in optical imaging of direct interest to the Army and also the intelligence agencies. Research problems included research on integrated optical systems design, array imaging, and related technologies. Our technique of combining optical/electronic hardware with digital processing is associated with our work on Pupil-Phase Engineering (PPE), for which we have a patent pending. The ARO project was primarily funded over the last three years by supplements from the Biometrics Division at the NSA, the Intelligence Technology Innovation Center at the CIA, and the Disruptive Technology Office. Technology transfer included the transition of our work to the ARL, to the Army Night Vision Lab, and to biometrics groups at the NSA and CIA. Industrial technology transfer took place with Iridian Technologies Co., CDM-Optics Inc., and Sarnoff Corp.

In this paper, first a great number of inverse problems which arise in instrumentation, in computer imaging systems and in computer vision are presented. Then a common general forward modeling for them is given and the corresponding inversion problem is presented. Then, after showing the inadequacy of the classical analytical and least square methods for these ill posed inverse problems, a Bayesian estimation framework is presented which can handle, in a coherent way, all these problems. One of the main steps, in Bayesian inversion framework is the prior modeling of the unknowns. For this reason, a great number of such models and in particular the compound hidden Markov models are presented. Then, the main computational tools of the Bayesian estimation are briefly presented. Finally, some particular cases are studied in detail and new results are presented.

The main focus of this work is the reconstruction of the signals $f$ and $g_{i}$, $i=1,...,N$, from the knowledge of their sums $h_{i}=f+g_{i}$, under the assumption that $f$ and the $g_{i}$'s can be sparsely represented with respect to two different dictionaries $A_{f}$ and $A_{g}$. This generalizes the well-known "morphological component analysis" to a multi-measurement setting. The main result of the paper states that $f$ and the $g_{i}$'s can be uniquely and stably reconstructed by finding sparse representations of $h_{i}$ for every $i$ with respect to the concatenated dictionary $[A_{f},A_{g}]$, provided that enough incoherent measurements $g_{i}$ are available. The incoherence is measured in terms of their mutual disjoint sparsity. This method finds applications in the reconstruction procedures of several hybrid imaging inverse problems, where internal data are measured. These measurements usually consist of the main unknown multiplied by other unknown quantities, and so the disjoint sparsity approach can be directly applied. As an example, we show how to apply the method to the reconstruction in quantitative photoacoustic tomography, also in the case when the Gr\"uneisen parameter, the optical absorption and the diffusion coefficient are all unknown.

This document contains the final report on the research activities supported by the AFOSR Grant No. F49620-00-1-0155 (to be called the grant hereafter) in the area of post processing and inverse problems in ground based imaging over the two-year duration of the grant. The principal objective of the grant was to establish an active research program in astronomical imaging and image processing at the Maui High Performance Computing Center (MHPCC). A number of vehicles were proposed to accomplish this objective over the grant period, specifically (1) two workshops a year at MHPCC; (ii) active participation of several distinguished imaging scientists from around the country in those workshops and by collaborative visits to MHPCC and the Univ. of New Mexico (UNM); and (iii) a series of seminars and courses to stimulate. foster, and organize existing resources and research personnel working with Air Force imaging assets particularly on Maui but also at the Starfire Optical Range (SOR), Kirtland AFB.