On entropy of pyramid structures

An information-theoretic analysis of multiresolution pyramid structures is presented. The analysis is carried out using the concept of spectral entropy which, for Gaussian sources, is linearly related to the differential entropy. The spectral entropy is used to define the spectral roughness measure that, in turn, is an indicator of the amount of memory in a source. The more the memory in a source, the greater is the value of its spectral roughness measure. The spectral roughness measure also plays an important role in lower bounding the rate-distortion function. The main result is that the spectral roughness measure of a pyramid structure is less than that of the original fullband process. This means that substantial reduction in bits can be obtained by merely representing a source as a pyramid. Simulations using one-dimensional and two-dimensional sources verifying these claims are presented