We have applied the Radon Cumulative Distribution Transform (RCDT) as an image transformation to highlight the subtle difference between left and right mammograms to detect mammographically occult (MO) cancer in women with dense breasts and negative screening mammograms. We developed deep convolutional neural networks (CNNs) as classifiers for estimating the probability of having MO cancer. We acquired screening mammograms of 333 women (97 unilateral MO cancer) with dense breasts and at least two consecutive mammograms and used the immediate prior mammograms, which radiologists interpreted as negative. We used fivefold cross validation to divide our dataset into a training and independent test sets with ratios of 0.8:0.2. We set aside 10% of the training set as a validation set. We applied RCDT on the left and right mammograms of each view. We applied inverse Radon transform to represent the resulting RCDT images in the image domain. We then fine-tuned a VGG16 network pretrained on ImageNet using the resulting images per each view. The CNNs achieved mean areas under the receiver operating characteristic (AUC) curve of 0.73 (standard error, SE = 0.024) and 0.73 (SE = 0.04) for the craniocaudal and mediolateral oblique views, respectively. We combined the scores from two CNNs by training a logistic regression classifier and it achieved a mean AUC of 0.81 (SE = 0.032). In conclusion, we showed that inverse Radon-transformed RCDT images contain information useful for detecting MO cancers and that deep CNNs could learn such information.