# Invertibility and Robustness of Phaseless Reconstruction

arXiv: https://arxiv.org/abs/1308.4718 · HTML: https://mlsanity.com/paper/1308.4718/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Aug 2013.

## Built on by (most cited first, 3 of 3)

- [Permutation Invariant Representations with Applications to Graph Deep Learning](https://mlsanity.com/paper/2203.07546/) (2022)
- [Group-invariant max filtering](https://mlsanity.com/paper/2205.14039/) (2022)
- [Stability of sorting based embeddings](https://mlsanity.com/paper/2410.05446/) (2024)

## Abstract (arXiv)

This paper is concerned with the question of reconstructing a vector in a finite-dimensional real Hilbert space when only the magnitudes of the coefficients of the vector under a redundant linear map are known. We analyze various Lipschitz bounds of the nonlinear analysis map and we establish theoretical performance bounds of any reconstruction algorithm. We show that robust and stable reconstruction requires additional redundancy than the critical threshold.