基于高斯泼溅的低秩张量表示用于多维图像恢复
Gaussian Splatting-based Low-Rank Tensor Representation for Multi-Dimensional Image Recovery
用2D/1D高斯泼溅参数化张量奇异值分解中的潜变量张量与变换矩阵，为多维图像提供连续、紧凑且能捕捉局部高频信息的表示，可迁移到高光谱/视频等低层复原任务中替代固定基变换。
原文依据 we propose a Gaussian Splatting-based Low-rank tensor Representation (GSLR) framework, which compactly and continuously represents multi-dimensional images.
摘要译文
由模型翻译 · 术语统一 · 请对照原文核对关键结论张量奇异值分解（t-SVD）是一种有前景的多维图像表示工具，它将多维图像分解为潜变量张量和伴随的变换矩阵。然而，t-SVD方法存在两个关键局限：（1）潜变量张量的近似（如张量分解）较为粗糙，无法准确捕捉空间局部高频信息；（2）变换矩阵由固定基原子（如DFT中的复指数原子和DCT中的余弦原子）组成，无法精确捕捉沿模-3纤维的局部高频信息。为解决这两个局限，我们提出了基于高斯泼溅的低秩张量表示（GSLR）框架，该框架能够紧凑且连续地表示多维图像。具体而言，我们分别利用定制的2D高斯泼溅和1D高斯泼溅来生成潜变量张量和变换矩阵。在该表示框架下，2D和1D高斯泼溅不可或缺且互补，具有强大的表示能力，尤其对局部高频信息。为评估所提GSLR的表示能力，我们开发了一个基于GSLR的无监督多维图像恢复模型。在多维图像恢复上的大量实验表明，GSLR始终优于最优方法，特别是在捕捉局部高频信息方面。
英文原文摘要 1512 字符
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.