Quantum-Inspired Trainable and Parameter-Efficient Tensor Networks for Image Inpainting

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.

5 pages, 3 figures, 1 table. Submitted to ICASSP 2027

Image and Video Processing (eess.IV); Computer Vision and Pattern Recognition (cs.CV); Machine Learning (cs.LG)

arXiv:2609.17298 [eess.IV]

(or arXiv:2609.17298v1 [eess.IV] for this version)

https://doi.org/10.48550/arXiv.2609.17298 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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