To reduce noise and enhance the contrast-to-noise ratio (CNR) of microcalcifications (MCs) in digital breast tomosynthesis (DBT), we conducted a study to investigate the feasibility of performing denoising on the projection views (PVs) using a deep convolutional neural network (DCNN) before reconstruction. We fine-tuned a modularized adaptive processing neural network (MAPNN) based on a pretrained model for CT image denoising. Four phantom DBTs containing over 700 simulated MCs of 3 nominal sizes were scanned with a DBT system that acquired 9 PVs within a 25° scan angle at two dose level settings to form the training and validation sets. Nine human subject DBTs were used as an independent test set. We trained the DCNN with low dose PVs as the input and the corresponding high dose PVs as the reference. We marked the MCs in the PVs and designed a loss function for DCNN training that balanced the effect of noise reduction and signal preservation. The loss function was a weighted sum of the perceptual loss, the adversarial loss and the CNR loss. A visual comparison of the DBT volumes reconstructed from the denoised PVs indicated that the proposed method could reduce noise and preserve the texture of the background without blurring subtle MC signals. A quantitative comparison showed a significant CNR improvement (p < 0.0001) in both the validation phantom and the human subject DBTs.