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Digital mammography is still the most common imaging tool for breast cancer screening. Although the benefits of using digital mammography for cancer screening outweigh the risks associated with the x-ray exposure, the radiation dose must be kept as low as possible while maintaining the diagnostic utility of the generated images, thus minimizing patient risks. Many studies investigated the feasibility of dose reduction by restoring low-dose images using deep neural networks. In these cases, choosing the appropriate training database and loss function is crucial and impacts the quality of the results. In this work, a modification of the ResNet architecture, with hierarchical skip connections, is proposed to restore low-dose digital mammography. We compared the restored images to the standard full-dose images. Moreover, we evaluated the performance of several loss functions for this task. For training purposes, we extracted 256,000 image patches from a dataset of 400 images of retrospective clinical mammography exams, where different dose levels were simulated to generate low and standard-dose pairs. To validate the network in a real scenario, a physical anthropomorphic breast phantom was used to acquire real low-dose and standard full-dose images in a commercially avaliable mammography system, which were then processed through our trained model. An analytical restoration model for low-dose digital mammography, previously presented, was used as a benchmark in this work. Objective assessment was performed through the signal-to-noise ratio (SNR) and mean normalized squared error (MNSE), decomposed into residual noise and bias. Results showed that the perceptual loss function (PL4) is able to achieve virtually the same noise levels of a full-dose acquisition, while resulting in smaller signal bias compared to other loss functions.