Gaussian Splatting-based Low-Rank Tensor Representation for Multi-Dimensional Image Recovery

TL;DR

This paper introduces GSLR, a novel tensor representation method using Gaussian splatting that effectively captures local high-frequency details in multi-dimensional images, surpassing existing techniques.

Contribution

The paper proposes a Gaussian splatting-based low-rank tensor framework that improves local high-frequency information capture in multi-dimensional image representation.

Findings

GSLR outperforms state-of-the-art methods in image recovery tasks.

GSLR effectively captures local high-frequency details.

The method demonstrates superior representation capability for multi-dimensional images.

Abstract

Tensor singular value decomposition (t-SVD) is a promising tool for multi-dimensional image representation, which decomposes a multi-dimensional image into a latent tensor and an accompanying transform matrix. However, two critical limitations of t-SVD methods persist: (1) the approximation of the latent tensor (e.g., tensor factorizations) is coarse and fails to accurately capture spatial local high-frequency information; (2) The transform matrix is composed of fixed basis atoms (e.g., complex exponential atoms in DFT and cosine atoms in DCT) and cannot precisely capture local high-frequency information along the mode-3 fibers. To address these two limitations, we propose a Gaussian Splatting-based Low-rank tensor Representation (GSLR) framework, which compactly and continuously represents multi-dimensional images. Specifically, we leverage tailored 2D Gaussian splatting and 1D Gaussian splatting to generate the latent tensor and transform matrix, respectively. The 2D and 1D Gaussian splatting are indispensable and complementary under this representation framework, which enjoys a powerful representation capability, especially for local high-frequency information. To evaluate the representation ability of the proposed GSLR, we develop an unsupervised GSLR-based multi-dimensional image recovery model. Extensive experiments on multi-dimensional image recovery demonstrate that GSLR consistently outperforms state-of-the-art methods, particularly in capturing local high-frequency information.