Reconstruction of Multidimensional Signals from Multiple Level Threshold Crossings.
Abstract
The first approach extended new theoretical results in multivariate polynomial interpolation theory, in order to define a variety of semi-implicit 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 multiple-level crossings. Although these semi-implicit 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 multi-level 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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1988
- Accession Number
- ADA195561
Entities
People
- Avideh Zakhor
Organizations
- Massachusetts Institute of Technology