Computed tomography (CT) combined with deep learning (DL) has recently shown great potential in biomedical imaging. Complex DL models with varying architectures inspired by the human brain are improving imaging software and aiding diagnosis. However, the accuracy of these DL models heavily relies on the datasets used for training, which often contain low-quality CT images from low-dose CT (LDCT) scans. Moreover, in contrast to the neural architecture of the human brain, DL models today are dense and complex, resulting in a significant computational footprint. Therefore, in this work, we propose sparse optimizations to minimize the complexity of the DL models and leverage architecture-aware optimization to reduce the total training time of these DL models. To that end, we leverage a DL model called DenseNet and Deconvolution Network (DDNet). The model enhances LDCT chest images into high-quality (HQ) ones but requires many hours to train. To further improve the quality of final HQ images, we first modified DDNet's architecture with a more robust multi-level VGG (ML-VGG) loss function to achieve state-of-the-art CT image enhancement. However, improving the loss function results in increased computational cost. Hence, we introduce sparse optimizations to reduce the complexity of the improved DL model and then propose architecture-aware optimizations to efficiently utilize the underlying computing hardware to reduce the overall training time. Finally, we evaluate our techniques for performance and accuracy using state-of-the-art hardware resources.