Rational systems exhibit moderate risk aversion with respect to “gambles” on variable-resolution compression

Abstract

In an embedded wavelet scheme for progressive transmission, a tree structure naturally defines the spatial relationship on the hierarchical pyramid. Transform coefficients over each tree correspond to a unique local spatial region of the original image, and they can be coded bit-plane by bit-plane through successive-approximation quantization. After receiving the approximate value of some coefficients, the decoder can obtain a reconstructed image. We show a rational system for progressive transmission that, in absence of a priori knowledge about regions of interest, chooses at any truncation time among alternative trees for further transmission in such a way as to avoid certain forms of behavioral inconsistency. We prove that some rational transmission systems might exhibit aversion to risk involving gambles on tree-dependent quality of encoding while others favor taking such risks. Based on an acceptable predictor for visual distinctness from digital imagery, we demonstrate that, without any outside knowledge, risk-prone systems as well as those with strong risk aversion appear in capable of attaining the quality of reconstructions that can be achieved with moderate risk-averse behavior.