Compressive Imaging Reconstruction via Tensor Decomposed Multi-Resolution Grid Encoding

TL;DR

This paper introduces GridTD, a novel unsupervised tensor decomposed multi-resolution grid encoding framework that enhances high-dimensional image reconstruction in compressive imaging by balancing representation capacity and efficiency.

Contribution

The paper proposes GridTD, a new continuous representation method combining tensor decomposition and multi-resolution grid encoding for improved compressive imaging reconstruction.

Findings

Outperforms existing methods in diverse CI tasks

Provides theoretical analysis of Lipschitz property and convergence

Achieves efficient high-dimensional image reconstruction

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.