  When working with PDEs the reconstruction of a previous state often proves
difficult. Good prior knowledge and fast computational methods are crucial to
build a working reconstruction. We want to identify the heat sources on a three
dimensional domain from later measurements under the assumption of small,
distinct sources, such as hot chippings from a milling tool. This leads us to
the need for a Prior reflecting this a priori information. Sparsity-inducing
hyperpriors have proven useful for similar problems with sparse signal or image
reconstruction. We combine the method of using a hierarchical Bayesian model
with gamma hyperpriors to promote sparsity with low-rank computations for PDE
systems in tensor train format.

Numerical Analysis;Numerical Analysis;Optimization and Control