# Sparse Sampling for Inverse Problems with Tensors

arXiv: https://arxiv.org/abs/1806.10976 · HTML: https://mlsanity.com/paper/1806.10976/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Jun 2018.

## Built on by (most cited first, 4 of 4)

- [Continuous Product Graph Neural Networks](https://mlsanity.com/paper/2405.18877/) (2024)
- [Second-Order Tensorial Partial Differential Equations on Graphs](https://mlsanity.com/paper/2509.02015/) (2025)
- [Meta-LinEXP3: Online-within-Online Learning for Adversarial Linear Contextual Bandits](https://mlsanity.com/paper/2609.09907/) (2026)
- [Signal Processing over Product DAGs: Causal Shifts and Filters](https://mlsanity.com/paper/2609.40275/) (2026)

## Abstract (arXiv)

We consider the problem of designing sparse sampling strategies for multidomain signals, which can be represented using tensors that admit a known multilinear decomposition. We leverage the multidomain structure of tensor signals and propose to acquire samples using a Kronecker-structured sensing function, thereby circumventing the curse of dimensionality. For designing such sensing functions, we develop low-complexity greedy algorithms based on submodular optimization methods to compute near-optimal sampling sets. We present several numerical examples, ranging from multi-antenna communications to graph signal processing, to validate the developed theory.