Title :
Dark Energy in Sparse Atomic Estimations
Author :
Sturm, Bob L. ; Shynk, John J. ; Daudet, Laurent ; Roads, Curtis
Author_Institution :
Univ. of California, Santa Barbara
fDate :
3/1/2008 12:00:00 AM
Abstract :
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 ldquodisappearrdquo in the reconstruction, we refer to the destructive and constructive interference between the atoms of a sparse atomic estimation as ldquodark energy.rdquo 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.
Keywords :
iterative methods; signal processing; time-frequency analysis; atomic estimation; decomposition process; destructive-constructive interference; matching pursuit; sparse atomic estimations; sparse overcomplete methods; Matching pursuit; signal estimation; sparse overcomplete methods;
Journal_Title :
Audio, Speech, and Language Processing, IEEE Transactions on
DOI :
10.1109/TASL.2007.914975