Accession Number : ADA283140


Title :   Convolution Algebra for Fluid Modes with Finite Energy


Descriptive Note : Technical rept.


Corporate Author : BOSTON UNIV MA CENTER FOR SPACE PHYSICS


Personal Author(s) : Sandri, G H ; Konstantopoulos, C


Full Text : https://apps.dtic.mil/dtic/tr/fulltext/u2/a283140.pdf


Report Date : Apr 1992


Pagination or Media Count : 91


Abstract : A new set of parametric wavelets called Hermite-Rodriguez wavelets, and a new family of highly singular functions called hyperdistributions are introduced. Their introduction is motivated by the search for a consistent solution to the inverse problem in signals and systems analysis: the evaluation of the initial condition -or input- to a system given its final condition -or output- and its impulse response. We construct a novel mathematical framework for the search for a solution to the inverse problem, and apply it to a practical case: the inverse problem for blurring systems. Blurring systems are very common: they include telescopes and other optical systems, as well as satellite telecommunications, where the waveforms that transmit the relevant information have to travel long distances, and are partly scattered by molecules and ions in their path from the source to the observer. As a result, the waveforms that reach the observer are blurred. The goal is to recover the original waveforms. The mathematical equivalent for the solution to the inverse problem for blurring systems -in the case of gaussian blurring- is given. It consists in solving the antidiffusion equation, which is equivalent to solving the diffusion equation backwards in time, to determine the initial condition of the diffusive process, given the final condition. We apply this solution of the inverse problem to two practical cases: the reconstruction of blurred signals, and of blurred simulated astronomical images. We then extend these results to the more general case of non-gaussian blur.


Descriptors :   *ATMOSPHERIC PHYSICS , FOURIER TRANSFORMATION , OUTPUT , IONS , MOLECULES , WAVEFORMS , ALGEBRA , SIGNALS , IMAGES , POLYNOMIALS , CONVOLUTION , ARTIFICIAL SATELLITES , TELECOMMUNICATIONS , DIFFUSION , FLUID DYNAMICS , ATMOSPHERE MODELS , FOURIER ANALYSIS , TELESCOPES


Subject Categories : Atmospheric Physics
      Theoretical Mathematics


Distribution Statement : APPROVED FOR PUBLIC RELEASE