Stochastic Filtering Solutions for Ill-Posed Linear Problems and Their Extension to Measurable Transformations.
Abstract
An ill-posed linear problem Ax=y in Hilbert space is considered as a filtering problem AX+Z=Y for Hilbert space valued random elements. Depending on the models for the signal X and the noise Z, the solutions of this problem are discussed in the context of cylinder measures on hilbert spaces and their radification by the Abstract Wiener space concept. Extensions of the solutions to measurable transformations are given explicity. The filtering solution is related to the solution of the problem Ax=y obtained by Tichonov's regularization method.
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 01, 1987
- Accession Number
- ADA186016
Entities
People
- R. Brigola
Organizations
- University of North Carolina at Chapel Hill