Mutational signature analysis is a powerful tool to unveil the mutagenic processes associated with cancer. Traditionally, mutational signatures are inferred by applying non-negative matrix factorization (NMF) algorithms to the matrix of counts of 96 strand-agnostic single-nucleotide-substitution mutations detected along the genome across several tumor samples. However, increasing evidence shows that certain processes act preferentially on the transcription strand relative to the untranscribed one, potentially leading to transcriptional stand biases in the signatures. In this case, one has to account for strand dependence across mutational channels to obtain a deeper characterization of the processes molding the tumor of interest. In this paper, we apply the recently introduced compressive Bayesian NMF model, which allows for the automatic selection of the factorization rank, to detect mutational signatures with potential strand asymmetries. We illustrate the method in an application to pediatric brain tumors.