Generalized Combinatorial Approach Using Single Filter Basis for Convolutional Sparse Modeling

Learning separable filters, by either approximating from nonseparable ones or estimating in native fashion, have demonstrated to be a powerful strategy in Convolutional Neural Network (CNN) and Convolutional Sparse Representation (CSR). Particularly, in the latter field, a combinatorial separable filter based approach has been proposed in order to improve both runtime and memory requirements. It exploits the redundancy in the filter banks by efficiently modeling 2D dictionaries from all possible combinations of vertical and horizontal separable filters instead of the standard form based on pairwise sets. In this paper, we explore a generalized case of the combinatorial approach which models 2D dictionaries from a single set of 1D basis filters that can be used to represent natural images akin to the vertical and horizontal filters based approach. We show that our proposed method reduces the number of filter combinations involved in the image reconstruction by a half, while preserving quality performance for denoising and inpainting tasks. Furthermore, it also provides an increase of speedup by a factor of 10% during the learning process.