The Impact of Boundary Condition Alignment on Integrating Convolutional Sparse Representation with CNN Initialization

Convolutional sparse representation (CSR) can extract local spatial features modeled through convolutional operations only from given images and has become a reliable technique with its biological and theoretical interpretability. A recent study has integrated CSR with initializing convolutional neural networks (CNNs) to compensate for their black-box nature, showing potential performance benefits. However, the proposed method does not account for the gap in boundary conditions: CNNs adopt the usual zero padding while CSR convolves periodically extended images. The present paper shows the importance of aligning boundary conditions and the latent benefits of the initialization scheme through performance improvements achieved by replacing conventional zero padding with periodic padding.