Theoretical foundations of deep learning via sparse representations: A multilayer sparse model and its connection to convolutional neural networks

Modeling data is the way we-scientists-believe that information should be explained and handled. Indeed, models play a central role in practically every task in signal and image processing and machine learning. Sparse representation theory (we shall refer to it as Sparseland) puts forward an emerging, highly effective, and universal model. Its core idea is the description of data as a linear combination of few atoms taken from a dictionary of such fundamental elements.