  Phase aberration is one of the primary sources of image quality degradation
in ultrasound, which is induced by spatial variations in sound speed across the
heterogeneous medium. This effect disrupts transmitted waves and prevents
coherent summation of echo signals, resulting in suboptimal image quality. In
real experiments, obtaining non-aberrated ground truths can be extremely
challenging, if not infeasible. It hinders the performance of deep
learning-based phase aberration correction techniques due to sole reliance on
simulated data and the presence of domain shift between simulated and
experimental data. Here, for the first time, we propose a deep learning-based
method that does not require reference data to compensate for the phase
aberration effect. We train a network wherein both input and target output are
randomly aberrated radio frequency (RF) data. Moreover, we demonstrate that a
conventional loss function such as mean square error is inadequate for training
the network to achieve optimal performance. Instead, we propose an adaptive
mixed loss function that employs both B-mode and RF data, resulting in more
efficient convergence and enhanced performance. Source code is available at
\url{http://code.sonography.ai}.
