Innovation modelling is a framework for constructing stochastic representations of phenomena, where it is assumed that at a fundamental level, the phenomenon under investigation is composed of independent atoms of randomness or `innovations' that go through a process of `mixing'. In certain cases, the assumption of independence in such models may be derived from physical considerations, but most often, it is based on the level of complexity one is willing or able to incorporate in the model while meeting computational and/or analytical limitations. In any case, this modelling principle can be employed in order to interpret, guide, and inform the design of schemes and algorithms for treating data obtained from observation, with applications in many areas of science and engineering including biomedical imagine and reconstruction. Motivated by the intellectual appeal and wide-spread success of multi-scale and wavelet-based methods in signal and image processing, in this project we aim to interpret these methods in the context of temporal/spatial innovation models with first-order temporal and/or spatial coupling. The objective is to develop a rigorous statistical theory and to explore its connections with information theoretical principles and statistical physics. It is hoped that this statistical theory can then direct us to improved schemes and algorithms for signal and image processing using multi-scale and wavelet analysis.