Consensus Equilibrium: A Framework for Model Integration

Abstract

We introduce a framework for integrating heterogeneous models based on a modular framework which we call consensus equilibrium (CE). In the CE framework, each source of information, such as for example a sensor or machine learning algorithm, is represented by a functional map or agent. The estimate of the desired unknown is than computed as the solution to a set of force-balance equations. We show that the CE framework is a generalization of the previous plug & play (P&P) approach because it allows for the integration of multiple models each of which can be implemented as either the solution to an optimization problem (i.e., a proximal map) or a machine learning technique (e.g., a DNN). We present results illustrating the use of the CE method in a variety of applications ranging from restoration of images with unknown blurring models, to tomographic reconstruction of additively manufactured parts, to holographic imaging through deep turbulence.