Open AccessEffects of envelope and dictionary structure on the performance of matching pursuit
Author(s) -
Różański Piotr T.
Publication year - 2020
Publication title -
iet signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.384
H-Index - 42
ISSN - 1751-9683
DOI - 10.1049/iet-spr.2019.0246
Subject(s) - matching pursuit , envelope (radar) , spectral envelope , computer science , decomposition , algorithm , gaussian , matching (statistics) , speech recognition , function (biology) , range (aeronautics) , pattern recognition (psychology) , set (abstract data type) , k svd , sparse approximation , artificial intelligence , mathematics , statistics , compressed sensing , telecommunications , ecology , radar , physics , materials science , quantum mechanics , evolutionary biology , composite material , biology , programming language
Matching pursuit is a greedy algorithm for computing a decomposition of the given signal as a linear combination of elements from an over‐complete set (a ‘dictionary’). This study generalises the construction of an optimal dictionary to non‐Gaussian envelope functions, and demonstrates that optimising the dictionary with regard to the envelope function has a significant effect on the decomposition accuracy. The dictionary construction is then evaluated and compared for a range of possible envelope functions. Based on the results, a novel ‘meta‐exponential’ envelope function is proposed and it is shown that for any given decomposition accuracy, it allows one to reduce the dictionary size (hence the computational time) by ∼10% compared to the most common case of decomposition with Gabor dictionaries. More importantly, the results of a decomposition study on high‐quality audio files are presented, confirming that both the choice of the envelope and adjusting the dictionary to a given envelope have a significant effect on the overall performance of matching pursuit.