# Compressive Imaging Reconstruction via Tensor Decomposed Multi-Resolution Grid Encoding

arXiv: https://arxiv.org/abs/2507.07707 · HTML: https://mlsanity.com/paper/2507.07707/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 31 of its 54 references that are in the map.
- First posted on arXiv 10 Jul 2025.

## Builds on (most cited first, 30 of 31)

- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Plug-and-Play ADMM for Image Restoration: Fixed Point Convergence and Applications](https://mlsanity.com/paper/1605.01710/) (2016)
- [NeRP: Implicit Neural Representation Learning with Prior Embedding for Sparsely Sampled Image Reconstruction](https://mlsanity.com/paper/2108.10991/) (2021)
- [Mask-guided Spectral-wise Transformer for Efficient Hyperspectral Image Reconstruction](https://mlsanity.com/paper/2111.07910/) (2021)
- [Convolutional Recurrent Neural Networks for Dynamic MR Image Reconstruction](https://mlsanity.com/paper/1712.01751/) (2017)
- [Rank Minimization for Snapshot Compressive Imaging](https://mlsanity.com/paper/1807.07837/) (2018)
- [Blind Video Temporal Consistency via Deep Video Prior](https://mlsanity.com/paper/2010.11838/) (2020)
- [MST++: Multi-stage Spectral-wise Transformer for Efficient Spectral Reconstruction](https://mlsanity.com/paper/2204.07908/) (2022)
- [Time-Dependent Deep Image Prior for Dynamic MRI](https://mlsanity.com/paper/1910.01684/) (2019)
- [Coarse-to-Fine Sparse Transformer for Hyperspectral Image Reconstruction](https://mlsanity.com/paper/2203.04845/) (2022)
- [HDNet: High-resolution Dual-domain Learning for Spectral Compressive Imaging](https://mlsanity.com/paper/2203.02149/) (2022)
- [Coded aperture compressive temporal imaging](https://mlsanity.com/paper/1302.2575/) (2013)
- [Plug-and-Play Algorithms for Video Snapshot Compressive Imaging](https://mlsanity.com/paper/2101.04822/) (2021)
- [HIR-Diff: Unsupervised Hyperspectral Image Restoration Via Improved Diffusion Models](https://mlsanity.com/paper/2402.15865/) (2024)
- [OCMR (v1.0)--Open-Access Multi-Coil k-Space Dataset for Cardiovascular Magnetic Resonance Imaging](https://mlsanity.com/paper/2008.03410/) (2020)
- [Spatiotemporal implicit neural representation for unsupervised dynamic MRI reconstruction](https://mlsanity.com/paper/2301.00127/) (2022)
- [Self-supervised Neural Networks for Spectral Snapshot Compressive Imaging](https://mlsanity.com/paper/2108.12654/) (2021)
- [Neural Implicit k-Space for Binning-free Non-Cartesian Cardiac MR Imaging](https://mlsanity.com/paper/2212.08479/) (2022)
- [DDS2M: Self-Supervised Denoising Diffusion Spatio-Spectral Model for Hyperspectral Image Restoration](https://mlsanity.com/paper/2303.06682/) (2023)
- [Deep Low-rank plus Sparse Network for Dynamic MR Imaging](https://mlsanity.com/paper/2010.13677/) (2020)
- [Unsupervised Deep Learning Methods for Biological Image Reconstruction and Enhancement](https://mlsanity.com/paper/2105.08040/) (2021)
- [Implicit Neural Networks with Fourier-Feature Inputs for Free-breathing Cardiac MRI Reconstruction](https://mlsanity.com/paper/2305.06822/) (2023)
- [Hyperspectral Denoising Using Unsupervised Disentangled Spatio-Spectral Deep Priors](https://mlsanity.com/paper/2102.12310/) (2021)
- [Learning Nonlocal Sparse and Low-Rank Models for Image Compressive Sensing](https://mlsanity.com/paper/2203.09656/) (2022)
- [Understanding Untrained Deep Models for Inverse Problems: Algorithms and Theory](https://mlsanity.com/paper/2502.18612/) (2025)

## Abstract (arXiv)

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.