Deep learning techniques have been widely used for two-dimensional (2D) and three-dimensional (3D) computer vision problems, such as object detection, super-resolution (SR) and classification to name a few. Radar images suffer from poor resolution as compared to optical images, hence developing a high-accuracy model to solve computer vision problems, such as a classifier, is a challenge. This is because of the lack of high-frequency details in the input images which makes it difficult for the classifier model to generate accurate predictions. Ways of addressing this challenge include training the learning model with a large dataset or using a more complicated model, such as deeper layer architecture. However, employing such approaches might result in the overfitting of the model, where the model might not generalize well on previously unseen data. Also, generating a large dataset for training the model is a challenging task, especially in the case of radar images. An alternate solution for achieving high accuracy in radar classification problems is provided in this paper wherein a CNN-enabled super-resolution (SR) model is integrated with the classifier model. The SR model is trained to generate high-resolution (HR) millimeter-wave (mmW) images from any input low-resolution (LR) mmW images. These resolved images from the SR model will be used by the classifier model to classify the input images into appropriate classes, consisting of threat and non-threat objects. The training data for the dual CNN layers are generated using a numerical model of a near-field coded-aperture computational imaging (CI) system. This trained dual CNN model is tested with simulated data generated from the CI numerical model wherein a high classification accuracy of 95% and a fast inference time of 0.193 s are obtained, making it suitable for real-time automated threat classification applications. For fair comparison, the developed CNN model is also validated with experimentally generated reconstruction data, in which case, a classification accuracy of 94% is obtained.