Multi-Layer Convolutional Sparse Modeling: Pursuit and Dictionary Learning

Understand

The recently proposed Multi-Layer Convolutional Sparse Coding (ML-CSC) model, consisting of a cascade of convolutional sparse layers, provides a new interpretation of Convolutional Neural Networks (CNNs).

• Under this framework, the computation of the forward pass in a CNN is equivalent to a pursuit algorithm aiming to estimate the nested sparse representation vectors -- or feature maps -- from a given input signal.
• Despite having served as a pivotal connection between CNNs and sparse modeling, a deeper understanding of the ML-CSC is still lacking: there are no pursuit algorithms that can serve this model exactly, nor are there conditions to guarantee a non-empty model.
• While one can easily obtain signals that approximately satisfy the ML-CSC constraints, it remains unclear how to simply sample from the model and, more importantly, how one can train the convolutional filters from real data.