The task-based framework, previously developed for beamformer comparison [Nguyen, Prager, and Insana, J. Acoust. Soc. Am. 140, 1048–1059 (2016)], is extended to design a new beamformer with potential applications in breast cancer diagnosis. The beamformer is based on a better approximation of the Bayesian strategy. It is a combination of the Wiener-filtered beamformer and an iterative process that adapts the generated image to specific features of the object. Through numerical studies, the new method is shown to outperform other beamformers drawn from the framework, but at an increase in computational cost. It requires a preprocessing step where the scattering field is segmented into regions with distinct statistical properties. Segmentation errors become a major limitation to the beamformer performance. All the beamformers under investigation are tested using data obtained from an instrumented ultrasound machine. They are implemented using a new time delay calculation, recently developed in the pixel-based beamforming studies presented here, which helps to overcome the challenge posed by the shift-variant nature of the imaging system. The efficacy of each beamformer is evaluated based on the quality of generated images in the context of the task-based framework. The in vitro results confirm the conclusions drawn from the simulations.