Fast Trainable Multilinear Bases for Image Compression
Abstract
The Discrete Fourier Transform (DFT), the Discrete Cosine Transform (DCT), and their block-wise variants underpin most deployed image and video codecs. Their effectiveness rests on three properties: their runtime is near-linear (up to a polylogarithmic factor) in the image size, they are exactly invertible, and they carry few to no parameters. We generalize these transforms to dataset-adaptive isometric multilinear bases that keep all three properties at the cost of a polylogarithmic number of parameters, by parameterizing each basis as an isometric tensor network, inspired by quantum many-body theory, and training one shared basis per image dataset with Riemannian optimization. Because the family contains the DFT and the DCT-IV (a variant of the DCT) as exact points, training can start from these transforms, and it improves on its starting point at the compression level it is trained for. We evaluate the bases on natural photographs and line drawings. On photographs, which the cosine basis already fits well, the best trained basis leads the DCT only under aggressive truncation. On Quick Draw line drawings, under a common codec at matched quality, the best trained basis stores each image in about 20% fewer bytes than the 8x8 block cosine transform of the Joint Photographic Experts Group (JPEG) format, not counting the one-off storage of the basis.
Related
- Regularized coordinate minimization for nonconvex composite optimization with application to quantized image compression
- Generative SDEs with Trainable Diffusion and Density-Based Losses
- Gibbs measures with multilinear forms
- Restriction estimates using multilinear Kakeya
- AT-SKM-Net: An Accelerated Trainable Sampling Kaczmarz-Motzkin Framework for Linear Hard-Constraint Feasibility on Dynamic Graphs
BibTeX
@misc{an2026fast,
title = {{Fast Trainable Multilinear Bases for Image Compression}},
author = {Shiwen An and Zhongyi Ni and Huanhai Zhou and Jin-Guo Liu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.00053},
eprint = {2608.00053},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.00053},
}
RIS
TY - UNPB
TI - Fast Trainable Multilinear Bases for Image Compression
AU - Shiwen An
AU - Zhongyi Ni
AU - Huanhai Zhou
AU - Jin-Guo Liu
PY - 2026
DA - 2026/10/11
PB - arXiv
DO - 10.48550/arxiv.2608.00053
UR - https://arxiv.org/abs/2608.00053
AB - The Discrete Fourier Transform (DFT), the Discrete Cosine Transform (DCT), and their block-wise variants underpin most deployed image and video codecs. Their effectiveness rests on three properties: their runtime is near-linear (up to a polylogarithmic factor) in the image size, they are exactly invertible, and they carry few to no parameters. We generalize these transforms to dataset-adaptive isometric multilinear bases that keep all three properties at the cost of a polylogarithmic number of parameters, by parameterizing each basis as an isometric tensor network, inspired by quantum many-body theory, and training one shared basis per image dataset with Riemannian optimization. Because the family contains the DFT and the DCT-IV (a variant of the DCT) as exact points, training can start from these transforms, and it improves on its starting point at the compression level it is trained for. We evaluate the bases on natural photographs and line drawings. On photographs, which the cosine basis already fits well, the best trained basis leads the DCT only under aggressive truncation. On Quick Draw line drawings, under a common codec at matched quality, the best trained basis stores each image in about 20% fewer bytes than the 8x8 block cosine transform of the Joint Photographic Experts Group (JPEG) format, not counting the one-off storage of the basis.
ER -