Fast Matching Pursuit with a multiscale dictionary of Gaussian Chirps

Abstract : We introduce a modified matching pursuit algorithm, called fast ridge pursuit, to approximate N-dimensional signals with M Gaussian chirps at a computational cost O(MN) instead of the expected O(MN^2 log N). At each iteration of the pursuit, the best Gabor atom is first selected, and then, its scale and chirp rate are locally optimized so as to get a “good” chirp atom, i.e., one for which the correlation with the residual is locally maximized. A ridge theorem of the Gaussian chirp dictionary is proved, from which an estimate of the locally optimal scale and chirp is built. The procedure is restricted to a sub-dictionary of local maxima of the Gaussian Gabor dictionary to accelerate the pursuit further. The efficiency and speed of the method is demonstrated on a sound signal.
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IEEE Transactions on Signal Processing, Institute of Electrical and Electronics Engineers, 2001, 49 (5), pp.994-1001. 〈10.1109/78.917803〉
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Rémi Gribonval. Fast Matching Pursuit with a multiscale dictionary of Gaussian Chirps. IEEE Transactions on Signal Processing, Institute of Electrical and Electronics Engineers, 2001, 49 (5), pp.994-1001. 〈10.1109/78.917803〉. 〈inria-00576201〉

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