
Accession Number : ADA195561
Title : Reconstruction of Multidimensional Signals from Multiple Level Threshold Crossings.
Descriptive Note : Doctoral thesis,
Corporate Author : MASSACHUSETTS INST OF TECH CAMBRIDGE RESEARCH LAB OF ELECTRONICS
Personal Author(s) : Zakhor, Avideh
PDF Url : ADA195561
Report Date : Jan 1988
Pagination or Media Count : 187
Abstract : The first approach extended new theoretical results in multivariate polynomial interpolation theory, in order to define a variety of semiimplicit sampling strategies. These strategies, which provide sufficient conditions for recovery of multidimensional signals from nonuniform samples on lines of rational slope, are ultimately applied to the problem of reconstruction from multiplelevel crossings. Although these semiimplicit results are general enough to be used for recovery from signal crossings with arbitrary functions, they do not provide conditions for reconstruction of signals from an arbitrarily small number of thresholds. To circumvent this difficulty, a second approach which is implicit, uses algebraic geometric concepts to find conditions under which a signal is almost always reconstructable from its multilevel threshold crossings. A problem distinct from that of uniquely specifying signals with level crossings is that of developing specific algorithms for recovering them from level crossing information, once it is known that the signals satisfy the appropriate constraints. A variety of reconstruction algorithms are proposed for each of our two approaches, and results for several images demonstrated. Keywords: Transformations, Mathematics, Theses. (JHD)
Descriptors : *MULTIVARIATE ANALYSIS, *TRANSFORMATIONS(MATHEMATICS), ALGEBRA, ALGORITHMS, CROSSINGS, GEOMETRY, INTERPOLATION, NONUNIFORM, POLYNOMIALS, RECOVERY, SAMPLING, SIGNALS, SLOPE, THEORY, THESES, THRESHOLD EFFECTS
Subject Categories : Numerical Mathematics
Electricity and Magnetism
Distribution Statement : APPROVED FOR PUBLIC RELEASE