# Deconvolution with a Box

arXiv: https://arxiv.org/abs/2407.11685 · HTML: https://mlsanity.com/paper/2407.11685/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 0 of its 4 references that are in the map.
- First posted on arXiv 16 Jul 2024.

## Built on by (most cited first, 2 of 2)

- [Super-Resolution with Structured Motion](https://mlsanity.com/paper/2505.15961/) (2025)
- [Multiscale Super Resolution without Image Priors](https://mlsanity.com/paper/2604.21810/) (2026)

## Abstract (arXiv)

Deconvolution with a box (square wave) is a key operation for super-resolution with pixel-shift cameras. In general convolution with a box is not invertible. However, we can obtain perfect reconstructions of sparse signals using convex optimization. We give a direct proof that improves on the reconstruction bound that follows from previous results. We also show our bound is tight and matches an information theoretic limit.