# Phase retrieval for wavelet transforms

arXiv: https://arxiv.org/abs/1512.07024 · HTML: https://mlsanity.com/paper/1512.07024/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Dec 2015.

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

- [One-Bit Quadratic Compressed Sensing: From Sample Abundance to Linear Feasibility](https://mlsanity.com/paper/2303.09594/) (2023)

## Abstract (arXiv)

We describe a new algorithm to solve a particular phase retrieval problem, that has wide applications in audio processing: the reconstruction of a function from its scalogram, that is from the modulus of its wavelet transform. It is a multiscale iterative algorithm. To efficiently propagate phase information from low to high frequencies, it uses an equivalent formulation of the phase retrieval problem that involves the holomorphic extension of the wavelet transform. Our numerical results, on audio and non-audio signals, show that reconstruction is precise and stable to noise. The algorithm has a linear complexity in the size of the signal, up to logarithmic factors, and can thus be used on large signals.