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 on the factors and in a hierarchical probabilistic model, which gives rise to heavy-tailed prior distributions for the BTD factors, structured sparsity is of non-negligible energy.