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Digital breast tomosynthesis (DBT) is a relatively new modality for breast imaging that can provide detailed assessment of dense tissue within the breast. In the domains of cancer diagnosis, radiogenomics, and resident education, it is important to accurately segment breast masses. However, breast mass segmentation is a very challenging task, since mass regions have low contrast difference between their neighboring tissues. Notably, the task might become more difficult in cases that were assigned BI-RADS 0 category since this category includes many lesions that are of low conspicuity and locations that were deemed to be overlapping normal tissue upon further imaging and were not sent to biopsy. Segmentation of such lesions is of particular importance in the domain of reader performance analysis and education. In this paper, we propose a novel deep learning-based method for segmentation of BI-RADS 0 lesions in DBT. The key components of our framework are an encoding path for local-to-global feature extraction, and a decoding patch to expand the images. To address the issue of limited training data, in the training stage, we propose to sample patches not only in mass regions but also in non-mass regions. We utilize a Dice-like loss function in the proposed network to alleviate the class-imbalance problem. The preliminary results on 40 subjects show promise of our method. In addition to quantitative evaluation of the method, we present a visualization of the results that demonstrate both the performance of the algorithm as well as the difficulty of the task at hand.