Quantum-inspired tensor networks improve image completion with fewer parameters
Quantum-Inspired Trainable and Parameter-Efficient Tensor Networks for Image Inpainting
Computer Vision and Pattern RecognitionMachine Learning
Summary
Image inpainting means filling in missing parts of pictures in a smart way. This paper shows a new technique inspired by quantum computing that uses special mathematical tools called tensor networks to do image inpainting efficiently. The method learns to fill in images by training on examples, and it can work quickly and well without needing lots of tuning or many parameters. It also keeps certain mathematical properties that help it stay accurate during learning.
What this means in practice
- •For image processing engineers: Develop image completion tools that run efficiently with fewer parameters, improving recovery of missing pixels under fixed sampling patterns.
- •For computer vision developers: Integrate tensor-network-based inpainting methods that generalize well from training data to fill occluded or corrupted image regions.
Authors
Shiwen An, Konstantinos Slavakis
Abstract
This work introduces quantum-inspired tensor-network circuits as trainable transforms for image inpainting. Among the proposed architectures, the diagonal quantum Fourier transform (QFT) relaxation is invertible with $O(N^2 \log N)$ computational cost for $N\times N$ images, inherently preserving minimum coherence throughout training via its circuit structure and eliminating the need for explicit coherence penalties. Unconstrained gradient-based phase optimization (Riemannian-optimization free) enables efficient learning from randomly sampled training data, allowing the learned transform to generalize to test images observed through fixed sampling masks. Numerical tests show that the learned models outperform fixed transforms and per-image optimization while matching the performance of much larger unitary architectures, yet with far fewer parameters.