Problem
Research questions and friction points this paper is trying to address.
image inpainting
quantum-inspired tensor-network circuits
trainable transforms
Quantum-Inspired Trainable and Parameter-Efficient Tensor Networks for Image Inpainting
🤖 AI Summary
本文提出量子启发的张量网络电路用于图像修复，通过可训练变换和无约束梯度优化方法，以较少参数实现高效学习和泛化性能。
📝 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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
quantum-inspired tensor-network circuits
diagonal quantum Fourier transform (QFT) relaxation
unconstrained gradient-based phase optimization
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