Geometric approach to sampling and communication

IRWIN AND JOAN JACOBS CENTER FOR COMMUNICATION AND INFORMATION TECHNOLOGIES Geometric Approach to Sampling and Communication

Relationships that exists between the classical, Shannontype, and geometric-based approach to sampling are investigated. Some aspects of coding and communication through a Gaussian channel problem are considered. In particular, a constructive method to determine the quantizing dimension in Zador’s theorem is provided. A geometric version of Shannon’s Second Theorem is introduced. Applications t...

Irwin and Joan Jacobs Center for Communication and Information Technologies on the Classical – and Not so Classical – Shannon Sampling Theorem

We proceed with our recently-introduced geometric approach to sampling of manifolds and investigate the relationship that exists between the classical, i.e. Shannon type, and geometric sampling concepts and formalism. Some aspects of coding and the Gaussian channel problem are considered. A geometric version of Shannon’s Second Theorem is introduced. Applications to Pulse Code Modulation and Ve...

A representation for some groups, a geometric approach

‎In the present paper‎, ‎we are going to use geometric and topological concepts‎, ‎entities and properties of the‎ ‎integral curves of linear vector fields‎, ‎and the theory of differential equations‎, ‎to establish a representation for some groups on $R^{n} (ngeq 1)$‎. ‎Among other things‎, ‎we investigate the surjectivity and faithfulness of the representation‎. At the end‎, ‎we give some app...

Morphological Image Coding Based on a Geometric Sampling Theorem and a Modified Skeleton Representation

Geometric Sampling of Images, Vector Quantization and Zador’s Theorem

We present several consequences of the geometric approach to image sampling and reconstruction we have previously introduced. We single out the relevance of the geometric method to the vector quantization of images and, more important, we give a concrete and candidate for the optimal embedding dimension in Zador’s Thorem. An additional advantage of our approach is that that this provides a cons...