Time Frequency Brown Bag Seminar

Wednesday, April 1, 1998

12:00 noon

EQuad E415

Speaker: Xin Li

Title: On Implementing Transforms from Integers to Integers

Abstract:

In this talk we study how to implement the transforms from integers to integers. They are called reversible transforms in lossless coding because they build up a one-to-one correspondence between the input and the output. But they also have a lot of application in more general coding and quantization theory, e.g. multiple description coding.

In the first part, we shall introduce other people’s work in this area, mainly characterized by the factorization into elementary matrices. We observe that although they achieve the reversibility, some other issues such as quantization error have been totally ignored. So we shall present our new idea for solving this problem and compare it with the former one with experiment results. We also generalize our solution into higher dimension and into modulation domain.

Note that this is a fascinating geometry problem itself and we shall present it as a game of moving boxes although we can only see the boxes in low dimension.