New relative multifractal dimension measures

This paper introduces a new class of fractal dimension measures which we call relative multifractal measures. The relative multifractal measures developed are formed through a melding of the Renyi dimension spectrum, which is based on the Renyi generalized entropy, and relative entropy as given with the Kullback-Leibler distance. This new class of multifractal measures is then used to find the relative multifractal complexity differences between two signals, an image and its lossy approximation. It is proposed that relative multifractal measures can be used as the basis for a new form of signal and image quality measure based on signal complexity.