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, arid 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

I. Introduction

The chirp signal is a type of signal often encountered in ultrasound, radar, sonar, seismic signals, EEG and speech [1]–[13]. The chirp signal parameters represent valuable information pertaining to the shape, size and orientation of the reflectors in ultrasonic nondestructive evaluation, the location and velocity of the moving targets in radar-target detection, or the propagation path in seismic signal analysis. Recently, a modified, continuous wavelet transform (MCWT) based on the Gabor-Helstorm transformation has been introduced as a means to decompose ultrasonic echoes in terms of Gabor functions [14], [15]. The MCWT decomposition has not been found effective in representing ultrasonic echoes with chirp characteristics. Compared with the Gabor function [14], [15], the Gaussian chirplet model has one more parameter, the chirp rate, and thereby can better represent chirp-type signals. In this paper, we introduce a chirplet decomposition algorithm to represent chirp-type signals in terms of Gaussian chirplets, which are sparse and energy preserving. The sparseness property aims for a compact representation of the complex signal by decomposing it into a limited number of chirp components. The energy preservation property, by coherently distributing the signal energy into composing functions, enables the linear addition of the time-frequency (TF) distributions of composing functions to represent the TF of the signal. Hence, a high resolution TF representation can be achieved by decomposing the signal into a limited number of chirp functions with known TF distributions [16]–[18]. Furthermore, once the signal is decomposed by a family of chirplet echoes, these echoes, individually or collectively, can be used to describe the nonstationary behavior of the signal.