Doppler spectral estimation using time-frequency distributions

The time-frequency distribution (TFD) of Doppler blood flow signals is usually obtained using the spectrogram, which requires signal stationarity and is known to produce large estimation variance. This paper examines four alternative, nonstationary spectral estimators: a smoothed pseudo-Wigner distribution (SPWD), the Choi-Williams distribution (CWD), the Bessel distribution (BD), and the novel, adaptive constant-Q distribution (AQD) for their applicability to Doppler ultrasound. A synthetic Doppler signal, simulating the nonaxial and pulsatile flow of the common carotid artery, was used for quantitative comparisons at different signal-to-noise-ratios (SNR) of 0, 10, 20, and 30 dB as well as noise free. The cross-correlation (rho) and the root-mean-square-error (RMSE) were calculated after log-compression for each technique and SNR relative to the theoretical distribution. The AQD consistently had the lowest RMSE (< or =53.7%) and the highest rho (> or =0.889) of all the TFDs, irrespective of the SNR. The SPWD performed better than the spectrogram, which performed better than the BD and the CWD. Qualitative comparisons were carried out using in vivo data acquired with a 10 MHz ultrasound cuff transducer positioned around the distal aorta of a rabbit. In vivo, the AQD was considered best with respect to background noise and internal gray scale features; it was rated second (after the spectrogram) in depicting the spectral envelope. The AQD performed better as a Doppler spectral estimator than the traditional spectrogram and the other TFDs under the conditions studied here.