Ambiguities on convolutions with applications to phase retrieval

Kurzfassung/Abstract

In this work we characterize all ambiguities of the convolution on two fixed finite-dimensional complex vector spaces. It will be shown that the convolution ambiguities correspond to factorization ambiguities in the z-domain, which are generated by swapping their zeros. We use this polynomial description to show a deterministic version of a recently introduced masked Fourier phase retrieval design. A semidefinite program can be used to recover exactly the noise-free input signals if they share no common factors. Then, we reformulate the problem as a deterministic blind deconvolution with knowledge of their autocorrelations. Moreover, numerically simulations show robustness against additive noise.