Before revision:  In this work, a Bayesian approach is taken to addressing the problem of rank-(L_r,L_r,1) BTD model selection and computation, based on the idea of imposing column sparsityjointly on the factors and in a hierarchical manner and estimating the ranks as the numbers of factor columns  of  non-negligible energy.
After revision:  In this work, a Bayesian approach is taken to addressing the problem of rank-(L_r,L_r,1) BTD model selection and computation, based on the idea of imposing column sparsityjointly we build on ideas of sparse Bayesian learning (SBL) and put forward a fully automated Bayesian approach. Through a suitably crafted multi-level hierarchical manner and estimating the ranks as the numbers of factor columns of non-negligible energy.