Sparse Representations with Chirplets viaMaximum Likelihood

| We formulate the problem of approximating a signal with a sum of chirped Gaussians, the so-called chirplets, under the framework of maximum likelihood estimation. For a signal model of one chirplet in noise, we formulate the maximum likelihood estimator (MLE) and compute the Cram er-Rao lower bound. An approximate MLE is developed, based on time-frequency methods, and is applied sequentially to obtain a decomposition of multiple chirplets. The decomposition is reened after each iteration with the expectation-maximization algorithm. A version of the algorithm , which is O(N) for each chirplet of the decomposition, is applied to a data set of whale whistles.

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