Research map / Image generation / Image restoration

Deep Rank-One Tensor Functional Factorization for Multi-Dimensional Data Recovery

AAAI 2025 · Image generation › Image restoration · approach: Inverse imaging with learned priors · 4 citations (OpenAlex)

Read the paperCheck your idea against 108,967 papers

AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.

Proposes DRO-TFF, a deep rank-one tensor functional factorization combining spatial rank-one factors, a deep mode-3 transform, and INR-parameterized factors, for multi-dimensional data recovery with far fewer parameters.

Problem

Compactly and effectively representing multi-dimensional data (color images, videos, hyperspectral images) for recovery tasks such as inpainting, denoising, and mixed-noise removal, without redundant parameters or underused data priors.

Approach

Replaces per-slice low-rank factorizations with a rank-one face-wise product re-weighted by a transform matrix, extends that transform to a deep LeakyReLU network, and parameterizes factors with sinusoidal INRs so the representation inherits low-rankness and Lipschitz smoothness.

Key results

• Image/video inpainting at SR=0.1: DRO-TFF reaches 24.631 PSNR on color images vs 23.519 for LRTFR, using 0.2M parameters.
• Hyperspectral image denoising at SD=0.1 averages 42.184 PSNR (SSIM 0.980), above LRTFR's 40.059 and DDS2M's 40.323, with 0.1M parameters vs 27.2M for DDS2M.
• Ablations show removing the deep transform (RO-TFF) drops inpainting PSNR from 37.601 to 30.279 on Oil Painting-based tests.

Measured effects reported in the paper

Surprising findings

• The method uses roughly 0.1M parameters while outperforming diffusion model HIR-Diff (391M parameters) on denoising and mixed-noise removal.

Limitations

• Mixed-noise results rely on ADMM with manually tuned hyperparameters (gamma, mu, beta) set per task.
• Runtime is not always lowest; e.g., DRO-TFF is slower than HLRTF and LRTFR on some tasks in the tables.

Experimental setup

Datasets: House Tree Jelly Beans Feathers Flowers Thread Spools News Carphone Hall Monitor Face Fake and Real Peppers Egyptian Statue

Benchmarks: House Tree Jelly Beans Feathers Flowers Thread Spools News Carphone Hall Monitor Face Fake and Real Peppers Egyptian Statue

Metrics: PSNR SSIM

Baselines: FTNN FCTN HLRTF LRTFR DDS2M S2DIP DS2DP HIR-Diff

Builds on: implicit neural representations (SIREN) deep image prior tensor train tensor ring total variation

Closest papers by meaning

• HLRTF: Hierarchical Low-Rank Tensor Factorization for Inverse Problems in Multi-Dimensional Imaging (CVPR 2022 · similarity 0.90)
• Learning Tensor Low-Rank Prior for Hyperspectral Image Reconstruction (CVPR 2021 · similarity 0.89)
• Robust Tensor Factorization With Unknown Noise (CVPR 2016 · similarity 0.88)
• DiffATS: Diffusion in Aligned Tensor Space (NeurIPS 2026 · similarity 0.87)
• Distribution-Aware Tensor Decomposition for Compression of Convolutional Neural Networks (NeurIPS 2025 · similarity 0.87)
• OTLRM: Orthogonal Learning-based Low-Rank Metric for Multi-Dimensional Inverse Problems (AAAI 2025 · similarity 0.86)