## Sparse Representations with Chirplets via Maximum Likelihood Estimation

Citations: | 2 - 0 self |

### BibTeX

@MISC{O'neill_sparserepresentations,

author = {Jeffrey C. O'neill and Patrick Flandrin and William C. Karl},

title = {Sparse Representations with Chirplets via Maximum Likelihood Estimation},

year = {}

}

### OpenURL

### Abstract

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 refined 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. I. Introduction Chirplets are a class of signals that consists of Gaussians that are translated in time and frequency, scaled, and chirped. They are defined as s t;!;c;d = s(n; t; !; c; d) = ( p 2d) \Gamma 1 2 exp n \Gamma \Gamma n\Gammat 2d \Delta 2 + j c 2 (n \Gamma t) 2 + j!(n \Gamma t) o : where t, !, and c...