Optimal beamforming in ultrasound using the ideal observer

Beamforming of received pulse-echo data generally involves the compression of signals from multiple channels within an aperture. This compression is irreversible, and therefore allows the possibility that information relevant for performing a diagnostic task is irretrievably lost. The purpose of this study was to evaluate information transfer in beamforming using a previously developed ideal observer model to quantify diagnostic information relevant to performing a task. We describe an elaborated statistical model of image formation for fixed-focus transmission and single-channel reception within a moving aperture, and we use this model on a panel of tasks related to breast sonography to evaluate receive-beamforming approaches that optimize the transfer of information. Under the assumption that acquisition noise is well described as an additive wide-band Gaussian white-noise process, we show that signal compression across receive-aperture channels after a 2-D matched-filtering operation results in no loss of diagnostic information. Across tasks, the matched-filter beamformer results in more information than standard delay-and-sum beamforming in the subsequent radio-frequency signal by a factor of two. We also show that for this matched filter, 68% of the information gain can be attributed to the phase of the matched-filter and 21% can be attributed to the amplitude. A 1-D matched filtering along axial lines shows no advantage over delay-andsum, suggesting an important role for incorporating correlations across different aperture windows in beamforming. We also show that a post-compression processing before the computation of an envelope is necessary to pass the diagnostic information in the beamformed radio-frequency signal to the final envelope image.