High-Resolution Functional Quantization

Suppose a function of N real source variables XN 1 = (X1, X2, . . . , XN ) is desired at a destination constrained to receive a limited number of bits. If the result of evaluating the function, Y = G(XN 1 ), can be itself encoded, this is the optimal strategy--the origin of Y becomes irrelevant to the communication problem. We consider two alternative scenarios: distributed quantization, in which each Xi must be separately encoded; and linear transform coding of XN 1 . Optimal fixed- and variable-rate scalar quantizers are derived under the conventional assumptions of high-resolution quantization theory, and we find optimal transforms for transform coding. For certain classes of functions, examples demonstrate large improvements over using quantizers designed to minimize distortion of the Xis.

• Type: Conference
• Year: 2008
• Where: DCC
• Authors: Vinith Misra, Vivek K. Goyal, Lav R. Varshney
• Keywords: Computer Graphics, DCC 2008, Optimal Strategy--the Origin, Optimal Transforms, Transform Coding