Notwithstanding ultrasound (US) B-Mode images, automatic diagnosis of benign and malignant breast cancers is still an unexplored area of study. In this study, a deep convolutional neural network architecture based on parametric imaging is proposed to categorize and identify breast tumors from breast ultrasound images. Here, an appropriate model for explaining the ultrasound image statistics within the Curvelet Transform domain is the Normal Inverse Gaussian (NIG) distribution. To categorize parametric images produced by locally calculated parameter values of the NIG distributions in various Curvelet sub-bands, the proposed convolutional neural network is used. 100 benign fibroadenomas and 100 malignant cases from a publicly accessible dataset of 780 breast US images are undertaken. The proposed technique yields 95.5%, 96.91%, 94.17%, 94%, and 97% accuracy, sensitivity, specificity, positive predictive value (PPV), and negative predictive value (NPV), respectively. Additionally, it is shown that the Proposed Method's accuracy exceeds a number of recently published findings.