This study proposes an optimal approach to reduce noise in mammographic images and to identify salt-and-pepper, Gaussian, Poisson, and impact noises to determine the exact mass detection operation after these noise reductions. It therefore offers a method for noise reduction operations called quantum wavelet transform filtering and a method for precision mass segmentation called the image morphological operations in mammographic images based on the classification with an atrous pyramid convolutional neural network (APCNN) as a deep learning model. The hybrid approach called a QWT-APCNN is evaluated in terms of criteria compared with previous methods such as peak signal-to-noise ratio (PSNR) and mean-squared error (MSE) in noise reduction and accuracy of detection for mass area recognition. The proposed method presents more performance of noise reduction and segmentation in comparison with state-of-the-art methods. In this paper, we used the APCNN based on the convolutional neural network (CNN) as a new deep learning method, which is able to extract features and perform classification simultaneously, but it is intended as far as possible, empirically for the purpose of this research to be able to determine breast cancer and then identify the exact area of the masses and then classify them according to benign, malignant, and suspicious classes. The obtained results presented that the proposed approach has better performance than others based on some evaluation criteria such as accuracy with 98.57%, sensitivity with 90%, specificity with 85%, and also ROC and AUC with a rate of 86.77.