Interference-driven adaptation in sparse approximation

Sparse approximation attempts to find an efficient signal representation by adaptively building a signal vector space from elements of a usually redundant and over-complete dictionary of atoms. Often, however, representations produced by iterative descent methods, such as orthogonal matching pursuit (OMP), will contain atoms that are poorly chosen and might later be confused as features of the signal. Poorly selected atoms bring about the selection other atoms that serve to correct for previous choices using destructive interference. This behavior diminishes the efficiency of a representation. In this paper, we propose and study a modification of the atom selection in OMP that takes into account the aforementioned effects. We find that a pursuit adapting to the interference between atoms can create a more efficient representation than that created by OMP, and one that is more representative of the signal and its features and less a reflection of the decomposition process.