Optimization of the autocorrelation weighting function for the time-domain calculation of spectral centroids

Spectral centroid from the backscattered ultrasound provides important information about the attenuation properties of soft tissues and Doppler effects of blood flows. Because the spectral centroid is originally determined from the power spectrum of backscattered ultrasound signals in the frequency domain, it is natural to calculate it after converting time-domain signals into spectral domain signals, using the fast Fourier transform (FFT). Recent research, however, derived the time-domain equations for calculating the spectral centroid using a Parseval´s theorem, to avoid the calculation of the Fourier transform. The work only presented the final result, which showed that the computational time of the proposed time-domain method was 4.4 times faster than that of the original FFT-based method, whereas the average estimation error was negligible. In this paper, we present the optimal design of the autocorrelation weighting function, which is used for the time-domain spectral centroid estimation process, to reduce the computational time significantly. We also carry out a comprehensive analysis of the computational complexities of the FFT-based and time-domain methods with respect to the length of ultrasound signal segments. The simulation results using numerical phantoms show that, with the optimized autocorrelation weighting function, we only need approximately 3% of the full set of data points. In addition to that, because the proposed optimization technique requires a fixed number of data points to calculate the spectral centroid, the execution time is constant as the length of the data segment increases, whereas the execution time of the conventional FFT-based method is increased. Analysis of the computational complexities between the proposed method and the conventional FFT-based method presents O(N) and O(Nlog₂N), respectively.