Bayesian inversion for electromyography using low-rank tensor formats

Abstract The reconstruction of the structure biological tissue using electromyographic (EMG) data is a non-invasive imaging method with diverse medical applications. Mathematically, this process an inverse problem. Furthermore, EMG are highly sensitive to changes in electrical conductivity that describes tissue. Modeling inevitable measurement error as stochastic quantity leads Bayesian approach. Solving discretized problem means drawing samples from posterior distribution parameters, e.g., conductivity, given data. Using, Metropolis–Hastings algorithm for purpose involves solving forward different parameter combinations which requires high computational effort. Low-rank tensor formats can reduce effort by providing data-sparse representation all occurring linear systems equations simultaneously and allow their efficient solution. application Bayes’ theorem proves well-posedness derivation proof low-rank precomputation solutions under certain assumptions, resulting theory-based sampling algorithm. Numerical experiments support theoretical results, but also indicate number needed obtain reliable estimates parameters. algorithm, precomputed solution format, draws therefore enables problems infeasible classical methods.