TT-net: Quantum Inspired Tensor Network Denoising in Conditional GANs

Image denoising is a fundamental challenge in computer vision, aiming to recover clean signals from degraded observations. Conditional generative adversarial networks have become a prominent approach for this task, utilizing a generator-discriminator setup to preserve fine visual details. Within these architectures, singular value decomposition has been incorporated as a linear algebra filtering step to process intermediate feature maps. However, standard implementations apply this decomposition to individual channels independently, preventing the network from directly evaluating cross-channel relationships.

This paper introduces TT-Net, a quantum-inspired model that replaces single-cut per-channel singular value decomposition with a two-cut tensor-train decomposition. This design enables the network to access cross-channel information directly during feature map filtering. The first cut reshapes the feature tensor to compare all channels simultaneously, discarding cross-channel variance while preserving shared patterns. The second cut operates on the retained remainder to capture spatial regularities across height and width dimensions. To maintain a fair evaluation against previous single-cut models, the authors introduce an adaptive thresholding scheme that preserves a comparable overall retained-energy target across both configurations.

Evaluated on the CIFAR-10 dataset across Gaussian, motion blur, and salt-and-pepper noise conditions, TT-Net consistently outperforms its single-cut predecessor, SVD-Net, in both peak signal-to-noise ratio and structural similarity index metrics. On Gaussian noise specifically, TT-Net also surpasses more heavily tuned state-of-the-art baselines like Pix2pix and EigenGAN. Analysis of training dynamics reveals that TT-Net exhibits a distinct stabilization pattern where the adversarial loss term saturates early, while reconstruction quality continues to improve steadily through the reconstruction loss components.