A Comparison of Classical and Deep Learning-based Techniques for Compressing Signals in a Union of Subspaces

Many natural signals lie in a union of subspaces, which we can exploit when compressing these signals to maintain a high level of fidelity while significantly reducing the storage size. Standard compression techniques for natural signals such as images follow a general pipeline which uses predetermined transformations to encode and decode data. Recent advances in deep learning-based techniques for compressing image data have shown results which compete with existing compression standards. Inspired by the success of these deep learning methods, we evaluate various classical and deep learning-based methods for encoding and decoding signals which follow a union-of-subspaces structure. On the classical side, we evaluate compressed sensing with a learned dictionary, whereas for deep learning-based techniques, we consider an autoencoder and a deep generative model-based variant of compressed sensing. Our results suggest that while classical compressed sensing-based methods work well, deep learning-based techniques perform better as the union-of-subspaces signal structure becomes more complex.