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 to Pulse Code Modulation and Vector Quantization of Images are provided. In addition, we sketch the geometerization of wavelets for Image Processing purposes. We also discuss the implications of the Uncertainty Principle on sampling and reconstruction of images. An extension of our sampling scheme to a certain class of infinite dimensional manifolds is considered. 1. General background 1.