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This research proposes trainable multilinear bases that integrate quantum-inspired tensor networks to enhance image compression efficiency while maintaining near-linear computational costs and invertibility. By optimizing these parameters on specific datasets, the method achieves significant storage reductions compared to standard transforms like JPEG's DCT without sacrificing reconstruction quality. The work bridges classical signal processing with advanced machine learning techniques rooted in many-body physics principles.
Fast Trainable Multilinear Bases for Image Compression
arXiv:2608.00053v1 Announce Type: cross Abstract: The Discrete Fourier Transform, the Discrete Cosine Transform, and their block-wise variants underpin most deployed image and video codecs. Their effectiveness rests on three properties: they run in near-linear time (linear up to a polylogarithmic factor), 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. Given an image dataset, we develop a systematic framework that searches this family for the basis compressing the dataset most effectively: the basis is parameterized as an isometric tensor network, inspired by quantum many-body theory, and trained with Riemannian optimization on the manifold of unitary matrices. Across natural photographs and line drawings, the trained bases consistently improve on their fixed, non-parametric counterparts. On Quick Draw line-drawing compression, they store images in roughly $20\%$ fewer bytes than JPEG's $8 \times 8$ block cosine transform at the same reconstruction quality.
Abstract:The Discrete Fourier Transform, the Discrete Cosine Transform, and their block-wise variants underpin most deployed image and video codecs. Their effectiveness rests on three properties: they run in near-linear time (linear up to a polylogarithmic factor), 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. Given an image dataset, we develop a systematic framework that searches this family for the basis compressing the dataset most effectively: the basis is parameterized as an isometric tensor network, inspired by quantum many-body theory, and trained with Riemannian optimization on the manifold of unitary matrices. Across natural photographs and line drawings, the trained bases consistently improve on their fixed, non-parametric counterparts. On Quick Draw line-drawing compression, they store images in roughly $20\%$ fewer bytes than JPEG's $8 \times 8$ block cosine transform at the same reconstruction quality.
Image and Video Processing (eess.IV); Computer Vision and Pattern Recognition (cs.CV); Machine Learning (cs.LG); Optimization and Control (math.OC); Quantum Physics (quant-ph)
arXiv:2608.00053 [eess.IV]
(or arXiv:2608.00053v1 [eess.IV] for this version)
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