Publications

Delaurentis, John M.; Bickel, Douglas L.

We present new methods for resolving IFSAR ambiguities and SAR layover. The analytic properties of these techniques make them well suited for reliable, efficient computation.

Proposed for publication in IEEE Transactions on Evolutionary Computation.

Hart, William E.; Hart, William E.; Delaurentis, John M.

We consider the convergence properties of a non-elitist self-adaptive evolutionary strategy (ES) on multi-dimensional problems. In particular, we apply our recent convergence theory for a discretized (1,{lambda})-ES to design a related (1,{lambda})-ES that converges on a class of seperable, unimodal multi-dimensional problems. The distinguishing feature of self-adaptive evolutionary algorithms (EAs) is that the control parameters (like mutation step lengths) are evolved by the evolutionary algorithm. Thus the control parameters are adapted in an implicit manner that relies on the evolutionary dynamics to ensure that more effective control parameters are propagated during the search. Self-adaptation is a central feature of EAs like evolutionary stategies (ES) and evolutionary programming (EP), which are applied to continuous design spaces. Rudolph summarizes theoretical results concerning self-adaptive EAs and notes that the theoretical underpinnings for these methods are essentially unexplored. In particular, convergence theories that ensure convergence to a limit point on continuous spaces have only been developed by Rudolph, Hart, DeLaurentis and Ferguson, and Auger et al. In this paper, we illustrate how our analysis of a (1,{lambda})-ES for one-dimensional unimodal functions can be used to ensure convergence of a related ES on multidimensional functions. This (1,{lambda})-ES randomly selects a search dimension in each iteration, along which points generated. For a general class of separable functions, our analysis shows that the ES searches along each dimension independently, and thus this ES converges to the (global) minimum.

Leung, Vitus J.; Delaurentis, John M.

Abstract not provided.

Delaurentis, John M.; Dickey, Fred M.; Dickey, Fred M.

Superresolution concepts offer the potential of resolution beyond the classical limit. This great promise has not generally been realized. In this study we investigate the potential application of superresolution concepts to synthetic aperture radar. The analytical basis for superresolution theory is discussed. In a previous report the application of the concept to synthetic aperture radar was investigated as an operator inversion problem. Generally, the operator inversion problem is ill posed. This work treats the problem from the standpoint of regularization. Both the operator inversion approach and the regularization approach show that the ability to superresolve SAR imagery is severely limited by system noise.

Delaurentis, John M.

We investigate the rate of convergence of stochastic basis elements to the solution of a stochastic operator equation. As in deterministic finite elements, the solution may be approximately represented as the linear combination of basis elements. In the stochastic case, however, the solution belongs to a Hilbert space of functions defined on a cross product domain endowed with the product of a deterministic and probabilistic measure. We show that if the dimension of the stochastic space is n, and the desired accuracy is of order {var_epsilon}, the number of stochastic elements required to achieve this level of precision, in the Galerkin method, is on the order of | ln {var_epsilon} |{sup n}.

Delaurentis, John M.; Doerry, Armin; Doerry, Armin

A Synthetic Aperture Radar (SAR) image is a two-dimensional projection of the radar reflectivity from a 3-dimensional object or scene. Stereoscopic SAR employs two SAR images from distinct flight paths that can be processed together to extract information of the third collapsed dimension (typically height) with some degree of accuracy. However, more than two SAR images of the same scene can similarly be processed to further improve height accuracy, and hence 3-dimensional position accuracy. This report shows how.