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Breast cancer is the second leading cause of cancer death among women worldwide. Nevertheless, it is also one of the most treatable malignances if detected early. Screening for breast cancer with digital mammography (DM) has been widely used. However it demonstrates limited sensitivity for women with dense breasts. An emerging technology in the field is contrast-enhanced digital mammography (CEDM), which includes a low energy (LE) image similar to DM, and a recombined image leveraging tumor neoangiogenesis similar to breast magnetic resonance imaging (MRI). CEDM has shown better diagnostic accuracy than DM. While promising, CEDM is not yet widely available across medical centers. In this research, we propose a Shallow-Deep Convolutional Neural Network (SD-CNN) where a shallow CNN is developed to derive "virtual" recombined images from LE images, and a deep CNN is employed to extract novel features from LE, recombined or "virtual" recombined images for ensemble models to classify the cases as benign vs. cancer. To evaluate the validity of our approach, we first develop a deep-CNN using 49 CEDM cases collected from Mayo Clinic to prove the contributions from recombined images for improved breast cancer diagnosis (0.86 in accuracy using LE imaging vs. 0.90 in accuracy using both LE and recombined imaging). We then develop a shallow-CNN using the same 49 CEDM cases to learn the nonlinear mapping from LE to recombined images. Next, we use 69 DM cases collected from the hospital located at Zhejiang University, China to generate "virtual" recombined images. Using DM alone provides 0.91 in accuracy, whereas SD-CNN improves the diagnostic accuracy to 0.95.