A successive parameter estimation algorithm for chirplet signal decomposition

In ultrasonic imaging systems, the patterns of detected echoes correspond to the shape, size, and orientation of the reflectors and the physical properties of the propagation path. However, these echoes often are overlapped due to closely spaced reflectors and/or microstructure scattering. The decomposition of these echoes is a major and challenging problem. Therefore, signal modeling and parameter estimation of the nonstationary ultrasonic echoes is critical for image analysis, target detection, and object recognition. In this paper, a successive parameter estimation algorithm based on the chirplet transform is presented. The chirplet transform is used not only as a means for time-frequency representation, but also to estimate the echo parameters, including the amplitude, time-of-arrival, center frequency, bandwidth, phase, and chirp rate. Furthermore, noise performance analysis using the Cramer Rao lower bounds demonstrates that the parameter estimator based on the chirplet transform is a minimum variance and unbiased estimator for signal-to-noise ratio (SNR) as low as 2.5 dB. To demonstrate the superior time-frequency and parameter estimation performance of the chirplet decomposition, ultrasonic flaw echoes embedded in grain scattering, and multiple interfering chirplets emitted by a large, brown bat have been analyzed. It has been shown that the chirplet signal decomposition algorithm performs robustly, yields accurate echo estimation, and results in SNR enhancements. Numerical and analytical results show that the algorithm is efficient and successful in high-fidelity signal representation.