Measuring interference in overcomplete signal representations

Currently, there is no quantitative way to ascertain how an overcomplete signal representation describes a signal and its features using terms drawn from a dictionary. Though sparsity offers a measure of optimality with respect to the number of terms used, it does not describe how a signal is represented, or how well-suited a particular dictionary is for describing the signal. Building upon work that investigates the interactions between nonorthogonal terms of overcomplete signal representations, we define and examine interference in such representations built by an overcomplete method, such as matching pursuit. This interference comes from a lack of fit between a dictionary and the signal, as well as properties of the decomposition algorithm itself. Such behavior in a representation can be detrimental to its efficiency and the "meaningfulness" of its terms. In this paper, we consider interference as a possible way to gauge such properties of overcomplete signal representations.