Project A6: Fast Optimization Algorithms for Efficient Data Representation in Highly Redundant Dictionaries


We will study two different approaches.

On the one hand, we consider new frameworks for dictionary learning from given large training sets. In this context we connect data clustering methods and multi-scale approaches to construct new adaptive dictionaries, where each dictionary element may possess a pre-defined structure. These ideas will be connected with our computational techniques for optimal transport in Project A2. Applications arise for sparse representation, denoting and reconstruction problems in image processing, acoustics, machine learning, geophysics etc.

On the other hand, we consider signal and image feature separation using structured matrices and its low-rank approximations in close collaboration with Project B6.

Methods: multi-scale methods, structured low-rank approximation, non-convex optimization
Applications: sparse signal representation, image feature separation