A fast refinement for adaptive Gaussian chirplet decomposition

The chirp function is one of the most fundamental functions in nature. Many natural events, for example, most signals encountered in seismology and the signals in radar systems, can be modeled as the superposition of short-lived chirp functions. Hence, the chirp-based signal representation, such as the Gaussian chirplet decomposition, has been an active research area in the field of signal processing. A main challenge of the Gaussian chirplet decomposition is that Gaussian chirplets do not form an orthogonal basis. A promising solution is to employ adaptive type signal decomposition schemes, such as the matching pursuit. The general underlying theory of the matching pursuit method has been well accepted, but the numerical implementation, in terms of computational speed and accuracy, of the adaptive Gaussian chirplet decomposition remains an open research topic. We present a fast refinement algorithm to search for optimal Gaussian chirplets. With a coarse dictionary, the resulting adaptive Gaussian chirplet decomposition is not only fast but is also more accurate than other known adaptive schemes. The effectiveness of the algorithm introduced is demonstrated by numerical simulations.