On signal reconstruction without noisy phase

TL;DR

This paper introduces new Parseval frames enabling signal reconstruction solely from coefficient magnitudes, eliminating the need for phase information, thus confirming a longstanding conjecture in speech processing.

Contribution

The authors develop novel Parseval frames that allow phase-free signal reconstruction, advancing the theoretical understanding of phase retrieval in signal processing.

Findings

Reconstruction is possible without phase information.

New classes of Parseval frames are constructed.

The approach confirms a longstanding speech processing conjecture.

Abstract

We construct new classes of Parseval frames for a Hilbert space which allow signal reconstruction from the absolute value of the frame coefficients. As a consequence, signal reconstruction can be done without using noisy phase or its estimation. This verifies a longstanding conjecture of the speech processing community.