A convolutional factor-analysis model is developed, with the number of filters (factors) inferred via the beta process (BP) and hierarchical BP, for single-task and multi-task learning, respectively. The computation of the model parameters is implemented within a Bayesian setting, employing Gibbs sampling; we explicitly exploit the convolutional nature of the expansion to accelerate computations. The model is used in a multi-level ("deep") analysis of general data, with specific results presented for image-processing data sets, e.g., classification. Copyright 2011 by the author(s)/owner(s).