Revisiting the Wiener postfilter for ultrasound image quality improvement

The Wiener postfilter [1] was introduced to ultrasound by Nilsen and Holm as a weighting mask designed to minimize the mean squared error (MSE) between the weighted noisy beamformed signal and the true noiseless signal [2]. Its application requires estimation of the expected signal power, or the expected noise power and the assumption that signal and noise are uncorrelated. In this paper we review the Wiener postfilter theory, examine the case of minimizing MSE in linear or log domain, and the cases where only expected signal power or only expected noise power can be accurately estimated. Upper bounds of performance of each approach are illustrated with an experimental setup where signal and noise powers are available. If expected signal power is known, the Wiener formulation is effective at restoring image quality if MSE is minimized in log domain instead of linear domain. Linear domain MSE minimization results in overly attenuated noise areas and artificially increased contrast beyond ground truth. If expected noise power is known, subtracting it from the measured noisy signal power yields expected signal power if signal and noise are uncorrelated. Leveraging this, signal power estimators are proposed and used in conjunction with linear and log domain MSE minimization. This approach can be advantageous if we are able to leverage noise characteristics or a noise model, however it suffers from artefacts in the case where signal and noise are correlated.