In this paper, a novel U-Net-based method for robust adherent cell segmentation for quantitative phase microscopy image is designed and optimised. We designed and evaluated four specific post-processing pipelines. To increase the transferability to different cell types, non-deep learning transfer with adjustable parameters is used in the post-processing step. Additionally, we proposed a self-supervised pretraining technique using nonlabelled data, which is trained to reconstruct multiple image distortions and improved the segmentation performance from 0.67 to 0.70 of object-wise intersection over union. Moreover, we publish a new dataset of manually labelled images suitable for this task together with the unlabelled data for self-supervised pretraining.