This study presents a Quantum-enhanced Artificial Neural Network (QANN) model for medical image compression, preserving essential details in MRI, CT, and X-ray scans. The approach converts classical data into quantum states, manipulates them via parameterized quantum circuits, and measures outcomes to produce enhanced feature vectors, which are then input into a classical neural network. QANN improves reconstructed image quality, reduces file size, and increases storage efficiency, achieving size reductions of 73.3% for MRI, 74.1% for X-ray, and 71.8% for CT scans. The framework demonstrates how quantum computing can enhance medical image processing and optimize healthcare data management.