SPARSE SPECTRAL FACTORIZATION: UNICITY AND RECONSTRUCTION ALGORITHMS
Compressed Sensing and Sparse Representation of Signals
Presented by: Juri Ranieri, Author(s): Yue Lu, Harvard University, United States; Martin Vetterli, Ecole Polytechnique Fédérale de Lausanne, Switzerland
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.