Abstract
Compressive imaging (CI) reconstruction, such as snapshot compressive imaging (SCI) and compressive sensing magnetic resonance imaging (MRI), aims to recover high-dimensional images from low-dimensional compressed measurements. This process critically relies on learning an accurate representation of the underlying high-dimensional image. However, existing unsupervised representations may struggle to achieve a desired balance between representation ability and efficiency. To overcome this limitation, we propose Tensor Decomposed multi-resolution Grid encoding (GridTD), an unsupervised continuous representation framework for CI reconstruction. GridTD optimizes a lightweight neural network and the input tensor decomposition model whose parameters are learned via multi-resolution hash grid encoding. It inherently enjoys the hierarchical modeling ability of multi-resolution grid encoding and the compactness of tensor decomposition, enabling effective and efficient reconstruction of high-dimensional images. Theoretical analyses for the algorithm's Lipschitz property, generalization error bound, and fixed-point convergence reveal the intrinsic superiority of GridTD as compared with existing continuous representation models. Extensive experiments across diverse CI tasks, including video SCI, spectral SCI, and compressive dynamic MRI reconstruction, consistently demonstrate the superiority of GridTD over existing methods, positioning GridTD as a versatile and state-of-the-art CI reconstruction method.
Abstract (translated)
压缩成像（CI）重建技术，如快照压缩成像（SCI）和压缩感知磁共振成像（MRI），旨在从低维压缩测量中恢复高维度图像。这一过程关键在于准确学习底层高维图像的表示形式。然而，现有的无监督表示方法可能难以在表征能力和效率之间取得理想的平衡。为克服这一限制，我们提出了一种针对CI重建的无监督连续表示框架——张量分解多分辨率网格编码（GridTD）。GridTD通过多层次哈希网格编码优化轻量级神经网络和输入张量分解模型，并从中学习参数。它天然具备多层次网格编码的层次建模能力和张量分解的紧凑性，能够有效地实现高维图像重建。 算法的Lipschitz性质、泛化误差界限以及固定点收敛性的理论分析揭示了GridTD与现有连续表示模型相比所具有的内在优越性。在包括视频SCI、光谱SCI和压缩动态MRI重建等多样的CI任务中进行的广泛实验，一致地证明了GridTD优于现有的方法，并将GridTD定位为一种通用且先进的CI重建技术。
URL
https://arxiv.org/abs/2507.07707
