Sparse spectral factorization: Unicity and reconstruction algorithms

Spectral factorization is a classical tool in signal processing and communications. It also plays a critical role in X-ray crystallography, in the context of phase retrieval. In this work, we study the problem of sparse spectral factorization, aiming to recover a one-dimensional sparse signal from its autocorrelation. We present a sufficient condition for the recovery to be unique, and propose an iterative algorithm that can obtain the original signal (up to a sign change, time-shift and time-reversal). Numerical simulations verify the effectiveness of the proposed algorithm.

• Type: Journal
• Year: 2011
• Where: ICASSP
• Authors: Yue M. Lu, Martin Vetterli
• Keywords: ICASSP 2011, One-dimensional Sparse Signal, Signal Processing, Sparse Spectral Factorization, Spectral Factorization