The ability to effectively store and transmit high-resolution images such as MRI and CT scans without losing quality is critical to modernizing medical imaging. Traditional compression methods risk losing essential medical image data, which requires perfect detail for diagnosis. Quantum algorithms use superposition and entanglement to compress faster while preserving important information. This research presents a Quantum-enhanced Artificial Neural Network (QANN) model that combines quantum feature extraction with classical neural network topologies to improve image compression. Our approach consists of converting standardized classical data into quantum states, controlling these states using parameterized quantum circuits, and measuring the resulting states to produce enhanced feature vectors. The quantum-enhanced features are fed into a traditional neural network for image compression. The experimental results clearly show that our QANN framework outperforms standard models in terms of accurate reconstructed images, reduced size, and increased space-saving percentage, especially when dealing with large and complicated datasets. The QANN model demonstrates how quantum computing can significantly enhance the effectiveness of medical image processing solutions. Kaggle brain CT and MRI datasets and COVID-CXNet chest x-ray images are used. The proposed QANN model improves peak signal-to-noise ratio (PSNR) and structural similarity index (SSIM). Using quantum technology, the image size is reduced for MRI (73.3 %), X-ray (74.1%), and CT-SCAN (71.8%) to save space.