Image Reconstruction Through Adaptive Quantum Feature Representation Using Variational Autoencoders

Image reconstruction and generation have become fundamental tasks in computer vision and quantum-inspired machine learning. Existing quantum-inspired variational autoencoders have demonstrated promising capabilities; however, they often suffer from limited local feature representation, unstable optimization, and performance degradation under noisy environments. This paper proposes quantum-inspired feature-preserving reconstruction variational autoencoder (QFR-VAE), which integrates adaptive handcrafted feature extraction with quantum-inspired latent representation learning. First, it extracts informative local descriptors from overlapping image patches. Then, it employs a differentiable soft gating mechanism before quantum-inspired single-qubit encoding, retaining the full spatial resolution of the input. The encoded representation is then learned using a convolutional variational autoencoder optimized with a composite objective. The proposed model was assessed on the MNIST and Fashion-MNIST datasets under both ideal and depolarizing noisy environments using FID, SSIM, PSNR, and LPIPS. Under ideal environments, it obtained an FID of 24.03, an SSIM of 0.9568, a PSNR of 22.74 dB, and an LPIPS of 0.0539 on MNIST. Whereas for Fashion-MNIST, it achieved an FID of 38.06, an SSIM of 0.8501, a PSNR value 20.66 dB, and an LPIPS of 0.1431. A component study isolating each element of the proposed framework was introduced to show that the single-qubit readout performs comparably to a classical mapping that matches its parameter account.