Image Compression Using Quantum Wavelet Transform and Quantum Convolutional Networks

Abstract

This paper presents a hybrid quantum-classical framework for grayscale image compression and decompression, leveraging the strengths of quantum computing and deep learning. The compression pipeline integrates a Variational Quantum Daubechies Wavelet Transform (V-QDWT) and a trainable Quantum Convolutional Neural Network (QCNN) optimized end-to-end to achieve efficient, image-adaptive multi-resolution analysis and entanglement-based feature reduction. Input images are encoded using the Normal Arbitrary Superposition State (NASS) representation, enabling compact and scalable quantum storage. For decompression, we implement inverse QCNN and V-QDWT circuits to reconstruct coarse image features natively, followed by a classical Super-Resolution Generative Adversarial Network (SRGAN) to enhance perceptual quality. Experimental evaluations on benchmark grayscale datasets demonstrate the efficacy of our hybrid approach. By jointly training the quantum layers, the base quantum pipeline closely rivals classical JPEG2000 standards. Subsequent SRGAN refinement substantially pushes the boundaries of the reconstruction, achieving superior structural fidelity (PSNR: 30.0667 dB, SSIM: 0.8744, Histogram Correlation: 0.9244). Histogram analysis and qualitative comparisons further validate the restoration of fine textures and intensity distributions. Our findings highlight 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.