Quantum-Inspired Tensor Networks Enhance Image Denoising

Tensor Network methods, originally developed for quantum physics simulations, are finding increasing applications in machine learning. Among these, Tensor Trains (also known as Matrix Product States) have shown promise, often leveraging Singular Value Decomposition (SVD) for their operations. While some conditional GAN architectures for image denoising incorporate SVD as a single-cut decomposition step on generator feature maps, this approach limits their ability to access information across different channels. Researchers have introduced TT-Net, a novel quantum-inspired approach that replaces the per-channel SVD denoising block with a two-cut tensor-train decomposition. This key innovation allows TT-Net to directly access cross-channel information, a capability absent in contemporary alternatives. This cross-channel access is hypothesized to improve denoising quality. In controlled experiments, TT-Net consistently outperformed SVD-Net in terms of PSNR and SSIM across various noise types, including Gaussian, motion blur, and salt-and-pepper. Furthermore, for Gaussian noise, TT-Net even surpassed EigenGAN and the state-of-the-art Pix2pix method, which does not rely on linear algebra decompositions. The study highlights how quantum-inspired tools can serve as practical feature filters in deep learning applications, though it also notes an open question regarding the adversarial component's contribution as reconstruction quality improved even when adversarial loss saturated.