Deliverable 3.2: Report on Discovering Structure within Dictionary Learning

In this work package (WP), we investigate the possibility of discovering structure within dictionary learning. This could range from exploring groups of atoms that appear in clusters - a form of molecule learning - to learning graphical dependencies across the dictionary elements. In modeling a signal as a sparse combination of atoms, ties between atoms can be enforced. For example harmonic models Gabor dictionaries can be seen as this type of model. Here we aim to explore the "molecule-learning" problem - learning clusters of tied atoms - by generalizing existing dictionary learning methods. Our aim is to show that with this added feature, models tend to be more reliable towards the signals represented.