Sparse Approximation and the Pursuit of Meaningful Signal Models With Interference Adaptation

In the pursuit of a sparse signal model, mismatches between the signal and the dictionary, as well as atoms poorly selected by the decomposition process, can diminish the efficiency and meaningfulness of the resulting representation. These problems increase the number of atoms needed to model a signal for a given error, and they obscure the relationships between signal content and the elements of the model. To increase the efficiency and meaningfulness of a signal model built by an iterative descent pursuit, such as matching pursuit (MP), we propose integrating into its atom selection criterion a measure of
interference
between an atom and the model. We define interference and illustrate how it describes the contribution of an atom to modeling a signal. We show that for any nontrivial signal, the convergent model created by MP must have as much destructive as constructive interference, i.e., MP cannot avoid correction in the signal model. This is not necessarily a shortcoming of orthogonal variants of MP, such as orthogonal MP (OMP). We derive interference-adaptive iterative descent pursuits and show how these can build signal models that better fit the signal locally, and reduce the corrections made in a signal model. Compared with MP and its orthogonal variants, our experimental results not only show an increase in model efficiency, but also a clearer correspondence between the signal and the atoms of a representation.