A novel hybrid approach combining quantum computing with classical deep learning has proven effective for grayscale image compression and decompression. This method integrates a Variational Quantum Daubechies Wavelet Transform (V-QDWT) and a trainable Quantum Convolutional Neural Network (QCNN). The strategy enables image-adaptive multi-resolution analysis and entanglement-based feature reduction, encoding input images using a Normal Arbitrary Superposition State (NASS) representation for compact and scalable quantum storage.

For decompression, the system employs inverse QCNN and V-QDWT circuits to reconstruct coarse image features. Subsequently, a classical Super-Resolution Generative Adversarial Network (SRGAN) enhances perceptual quality. Experimental evaluations on benchmark grayscale datasets demonstrate that the quantum pipeline closely rivals classical JPEG2000 standards. Subsequent SRGAN refinement substantially pushes the boundaries of reconstruction, achieving superior structural fidelity with a PSNR of 30.0667 dB, an SSIM of 0.8744, and a Histogram Correlation of 0.9244.

This advance highlights the potential of combining variational quantum compression with classical deep learning to enable efficient, scalable, and perceptually aware image processing in quantum-enhanced computing environments. Histogram analysis and qualitative comparisons further validate the restoration of fine textures and intensity distributions, paving the way for future applications in visual data processing with enhanced quantum capabilities.