Tensor recovery improved with shared-factor-conditioned diffusion model
Shared-Factor-Conditioned Diffusion for Low-Rank Tensor Recovery
Computer Vision and Pattern RecognitionArtificial Intelligence
Summary
Tensors are like multi-dimensional grids of data found in images, videos, and other complex datasets. Recovering missing or corrupted parts of these tensors is important but challenging. The authors present DiffTR, a new method that learns common patterns in the data to help restore missing or noisy pieces across different types of tensor data. This method can handle various tasks like filling in gaps, reducing noise, and increasing resolution by using a flexible approach rooted in diffusion models. Their technique works well for different data types, including images and videos, and data corrupted in different ways.
What this means in practice
- •For image processing teams: Enable enhanced image and video restoration and super-resolution by recovering missing or noisy pixel data using a single flexible diffusion-based model.
- •For remote sensing analysts: Improve reconstruction of high-resolution hyperspectral images from low-resolution noisy measurements using a prior learned from lower quality data.
Authors
Zhengyun Cheng, Guanwen Zhang, Wei Zhou
Abstract
Tensor recovery spans heterogeneous data structures and observation processes, calling for a representation that can adapt across modalities and tasks. We propose DiffTR, an unsupervised framework that unifies tensor completion, denoising, and hyperspectral super-resolution through coordinate-conditioned diffusion. Shared factors indexed by tensor coordinates condition a compact score network, and score matching jointly learns the factors and an implicit tensor representation from the available observations. Scalar and vector-valued outputs accommodate individual entries and entire tubes, enabling a common formulation for tabular tensors, images, and videos. The framework separates representation learning from task-specific observation modeling: reverse diffusion recovers missing values; estimation via Tweedie's formula, soft thresholding, and optional spatial consistency support mixed-noise denoising; and measurement-guided sampling transfers a prior learned from low-resolution hyperspectral observations to high-resolution reconstruction, followed by post-sampling refinement with data consistency and spectral subspace regularization. This separation makes the representation compatible with different corruption models and permits task-specific constraints to be incorporated within the same recovery framework. Experiments across multiple tensor modalities and recovery tasks demonstrate competitive reconstruction quality and the flexibility of a unified conditional generative representation. The code is available at https://github.com/CZY-Code/DiffTR