Signal Estimation from Correlation Vectors with Structured Low-Rank Approximation

The paper focuses on the reconstruction of a multivariate signal from its noisy correlation vectors, a problem appearing in phase retrieval and blind channel identification. In the noiseless case, the signals can be retrieved from greatest common divisors of the polynomials associated to observed vectors. For the noisy case, by exploiting the properties of Sylvester matrices, we propose a new reconstruction approach that exploits all the available data and preserves matrix structure in the associated low-rank approximation problem. By doing so, we achieve an improvement of the reconstruction performance with respect to existing methods.