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arXiv · 2608.00053

Fast Trainable Multilinear Bases for Image Compression

Shiwen An·Zhongyi Ni·Huanhai Zhou·Jin-Guo Liu
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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. In this work, we generalize these bases to isometric multilinear bases, allowing a small number of extra parameters (polylogarithmic in the image size), while preserving all three properties. We develop a scheme to train a better transformation for a given image dataset: we use isometric tensor networks, inspired by quantum many-body theory, to parameterize the basis, and train it with Riemannian optimization. We show that training consistently improves performance, as our parameterized bases can represent the traditional DFT and DCT-IV (a variant of the DCT). Evidence is shown across natural photographs and line drawings. On Quick Draw line-drawing compression, for example, the best trained basis outperforms the block cosine transform used in the JPEG format by $20\%$ in terms of compressed data size.

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Shiwen An, Zhongyi Ni, Huanhai Zhou, Jin-Guo Liu. 2026-08-29. Fast Trainable Multilinear Bases for Image Compression. https://arxiv.org/abs/2608.00053

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