(Theoretical project) Sparse-Dictionary Learning in the Continuum
In recent years, a popular trend in inverse problems is sparse-dictionary learning, or sparse coding. The idea is to recover a signal that is sparse in a certain dictionary basis, which is unknown \textit{a priori}. The dictionary is inferred from some training data. This is conceptually a very natural approach since a tailored dictionary can only be better suited than a predefined one - putting computational difficulties aside. This project will consist in the implementation of a sparse-dictionary-learning algorithm for continuous-domain signals, where the learned dictionary atoms are Green’s functions of differential operators. The dictionary-learning problem is formulated as an optimization problem in a function space, which aims at the selection of atoms that can best represent the training data in a sparse way. The project will be implemented in Matlab.
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