# New Conditions for Sparse Phase Retrieval

arXiv: https://arxiv.org/abs/1310.1351 · HTML: https://mlsanity.com/paper/1310.1351/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Oct 2013.

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

- [Low Complexity Regularized Phase Retrieval](https://mlsanity.com/paper/2407.16413/) (2024)

## Abstract (arXiv)

We consider the problem of sparse phase retrieval, where a k-sparse signal bf x ∈ mathbb Rn textrm (or  mathbb Cntextrm) is measured as bf y = |bf Ax|, where bf A ∈ mathbb Rm × n textrm (or  mathbb Cm × ntextrm respectively) is a measurement matrix and |·| is the element-wise absolute value. For a real signal and a real measurement matrix bf A, we show that m = 2k measurements are necessary and sufficient to recover bf x uniquely. For complex signal bf x ∈ mathbb Cn and bf A ∈ mathbb Cm × n, we show that m = 4k-2 phaseless measurements are sufficient to recover bf x. It is known that the multiplying constant 4 in m = 4k-2 cannot be improved.