Langev(in)ference Dynamics for Heterogeneous Tissue Imaging in MRE

We propose a novel second-order dynamical Bayesian inference method for tissue imaging using magnetic resonance elastography data. 

In vivo tissue material property imaging is difficult - the space of heterogenous models has a huge dimensionality.

Current methods are constrained to techniques involving first order gradient descent of the posterior information content, requiring a multitude of regularizers to converge.

Unfortunately, even the simplest models have highly non-linear likelihoods plagued with degeneracies and multiple minima - as we show in several lower-dimensional toy models.

By expanding belief updating to second order and incorporating the idea of epistemic resources, we show a direct analogy with Langevin dynamics. 

Tuning these resources is done dynamically, unlike similar methods such as simulated annealing, in a way that lends itself for paralleization, thereby naturally incorporating the well known technique of zoning into the framework. 

The resulting stochastic dynamics of inference have a fascinating interpretation within the context of analytical epistemology, as well as the practical feature of breaking degeneracies and tunneling out of local minima.