Synthesis models for N-dimensional discrete-space self-similar signals

New formulations and models are proposed for describing statistical self-similarity in general N-dimensional settings. By using a matrix scaling operator for defining statistical self-similarity, a wide class of continuous-space N-D processes can be characterized as self-similar with respect to specific matrix classes. Further, discrete-space versions of N-D statistical self-similarity are treated through a discrete-domain scaling operation. The mathematical basis for the approaches is provided along with 2-D synthesis examples.