Image Enhancement via Extrapolation Techniques: A Two Dimensional Iterative Scheme a Direct Matrix Inversion Scheme

In [1] and [2], we have developed a model and three dimensional inversion algorithm for detecting flaw in structures. The model, based on rigorous electromagnetic theory, and the algorithm have as their main objective the high resolution imaging of the flaw. The algorithm is computationally intensive and, like other inversion techniques, involves the solution of some ill conditioned problems

Minimal symmetric Darlington synthesis

We consider the symmetric Darlington synthesis of a p x p rational symmetric Schur function S with the constraint that the extension is of size 2p x 2p. Under the assumption that S is strictly contractive in at least one point of the imaginary axis, we determine the minimal McMillan degree of the extension. In particular, we show that it is generically given by the number of zeros of odd multiplicity of I-SS*. A constructive characterization of all such extensions is provided in terms of a symmetric realization of S and of the outer spectral factor of I-SS*. The authors's motivation for the problem stems from Surface Acoustic Wave filters where physical constraints on the electro-acoustic scattering matrix naturally raise this mathematical issue

Realization Theory for Deterministic Boundary-Value Descriptor Systems

This paper examines the realization of acausal weighting patterns with two-point boundary-value descriptor systems (TPBVDSs). We restrict our attention to the subclass of TPBVDSs which are extendible, i.e., whose input-output weighting pattern can be extended outwards indefinitely, and stationary, so that their weighting pattern is shift-invariant. Then, given an infinite acausal shift-invariant weighting pattern, the realization problem consists in constructing a minimal TPBVDS over a fixed interval, whose extended weighting pattern matches the given pattern. The realization method which is proposed relies on a new transform, the (s,t) transform, which is used to determine the dimension of a minimal realization, and to construct a minimal realization by factoring two homogeneous rational matrices in the variables s and t. 1