Bayesian Spectrum Analysis of Non-Linear Ultrasound Contrast Microbubble Signals

The localization of individual contrast microbubbles (MBs)is key to the emerging field of super-resolution ultrasound. The Fourier Transform (FT)is typically used for the frequency domain analysis of MB signals in ultrasound contrast imaging. Bayesian spectrum analysis offers a viable solution to overcome the limited frequency resolution achieved by the FT for MB scatterers. A typical MB signal sampled at 20 MHz and consisting of approximately 80 samples was investigated. The conventional frequency resolution for Fourier-based methods in this instance was 241 kHz. The Bayesian spectral estimation resulted in 12 distinct frequency components many of which were separated by less than 241 kHz. The smallest separation was 52 kHz. The resulting frequency and amplitude estimates matched relatively well with the Fast Fourier Transform (FFT)spectral peaks. Using these estimates the MB signal was reconstructed, and a correlation coefficient of approximately 0.99 was achieved between original and reconstructed signals. The result was reproduced in the analysis of a synthetic MB signal, similar to the original one, and all 12 frequencies were always resolved. Overall, the method promises high spectral resolution without sacrificing the temporal one, and provides information that may be used to differentiate the MB non-linear signal from that of linear scatterers.