Dark energy in sparse atomic estimations

Sparse overcomplete methods, such as matching pursuit, attempt to find an efficient estimation of a signal using terms (atoms) selected from an overcomplete dictionary. In some cases, atoms can be selected that have energy in regions of the signal that have no energy. Other atoms are then used to destructively interfere with these terms in order to preserve the original waveform. Because some terms may even "disappear" in the reconstruction, we refer to the destructive and constructive interference between the atoms of a sparse atomic estimation as "dark energy." In this paper, we formally define dark energy for matching pursuit, explore its properties, and present empirical results for decompositions of audio signals. This paper demonstrates that dark energy is a useful measure of the interference between the terms of a sparse atomic estimation and might provide information for the decomposition process.