# Multi-dimensional Signal Recovery using Low-rank Deconvolution

arXiv: https://arxiv.org/abs/2305.02264 · HTML: https://mlsanity.com/paper/2305.02264/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 23 references that are in the map.
- First posted on arXiv 3 May 2023.

## Builds on (most cited first, 3 of 3)

- [Nonconvex Low-Rank Tensor Completion from Noisy Data](https://mlsanity.com/paper/1911.04436/) (2019)
- [Convolutional Dictionary Learning: A Comparative Review and New Algorithms](https://mlsanity.com/paper/1709.02893/) (2017)
- [Convolutional Dictionary Learning via Local Processing](https://mlsanity.com/paper/1705.03239/) (2017)

## Built on by (most cited first, 1 of 1)

- [Fast Unsupervised Tensor Restoration via Low-rank Deconvolution](https://mlsanity.com/paper/2406.10679/) (2024)

## Abstract (arXiv)

In this work we present Low-rank Deconvolution, a powerful framework for low-level feature-map learning for efficient signal representation with application to signal recovery. Its formulation in multi-linear algebra inherits properties from convolutional sparse coding and low-rank approximation methods as in this setting signals are decomposed in a set of filters convolved with a set of low-rank tensors. We show its advantages by learning compressed video representations and solving image in-painting problems.