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Background The limitations of traditional computer-aided detection (CAD) systems for mammography, the extreme importance of early detection of breast cancer and the high impact of the false diagnosis of patients drive researchers to investigate deep learning (DL) methods for mammograms (MGs). Recent breakthroughs in DL, in particular, convolutional neural networks (CNNs) have achieved remarkable advances in the medical fields. Specifically, CNNs are used in mammography for lesion localization and detection, risk assessment, image retrieval, and classification tasks. CNNs also help radiologists providing more accurate diagnosis by delivering precise quantitative analysis of suspicious lesions. Results In this survey, we conducted a detailed review of the strengths, limitations, and performance of the most recent CNNs applications in analyzing MG images. It summarizes 83 research studies for applying CNNs on various tasks in mammography. It focuses on finding the best practices used in these research studies to improve the diagnosis accuracy. This survey also provides a deep insight into the architecture of CNNs used for various tasks. Furthermore, it describes the most common publicly available MG repositories and highlights their main features and strengths. Conclusions The mammography research community can utilize this survey as a basis for their current and future studies. The given comparison among common publicly available MG repositories guides the community to select the most appropriate database for their application(s). Moreover, this survey lists the best practices that improve the performance of CNNs including the pre-processing of images and the use of multi-view images. In addition, other listed techniques like transfer learning (TL), data augmentation, batch normalization, and dropout are appealing solutions to reduce overfitting and increase the generalization of the CNN models. Finally, this survey identifies the research challenges and directions that require further investigations by the community. Electronic supplementary material The online version of this article (10.1186/s12859-019-2823-4) contains supplementary material, which is available to authorized users.

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