The Rate-Distortion Function on Classes of Sources Determined by Spectral Capacities.
Abstract
The case in which the class a is specified in terms of spectral information is treated for general class of spectral measures whose upper measures are capacities (in the sense of Choquet) alternating of order two. This type of class includes many common models for spectral uncertainty such as mixture models, spectral band models, and neighborhoods generated by Kolmogorov (total-variation) and Prohorov metrics. It is shown that each such class contains a worst-case source whose rate-distortion function achieves the supremum over the class for each value of distortion. This source is characterized as having a spectral density that is a derivative (in the sense of Huber and Strassen) of the upper spectral measure. Moreover it is shown that the spectral measure of the worst-case source is closest, in a sense defined by directed divergence, to Lebesgue measure (which corresponds to a memoryless source). Numerical results are presented for the particular case in which the source spectral measure is a mixture of a Gauss-Markov spectrum and an unknown contaminating component.
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 01, 1981
- Accession Number
- ADA124529
Entities
People
- Vincent Poor
Organizations
- University of Illinois Urbana–Champaign