Signal alignment: A method based on non-convex optimization

We consider the problem of aligning two observations of a source signal. We propose a method that does not require to explicitly estimate the time-delay between the observations. The method relies on extracting a phase map that acts on the short time Fourier coefficients of one of the observations. We formulate the phase map extraction step as a simple non-convex minimization problem. We also discuss how the proposed method preserves the statistical properties of the unwanted noise, while aligning the source of interest in both observations.