Blind Separation of Superimposed Shifted Images Using Parameterized Joint Diagonalization

We consider the blind separation of source images from linear mixtures thereof, involving different relative spatial shifts of the sources in each mixture. Such mixtures can be caused, e.g., by the presence of a semi-reflective medium (such as a window glass) across a photographed scene, due to slight movements of the medium (or of the sources) between snapshots. Classical separation approaches assume either a static mixture model or a fully convolutive mixture model, which are, respectively, either under-or over-parameterized for this problem. In this paper, we develop a specially parameterized scheme for approximate joint diagonalization of estimated spectrum matrices, aimed at estimating the succinct set of mixture parameters: the static (gain) coefficients and the shift values. The estimated parameters are, in turn, used for convenient frequency-domain separation. As we demonstrate using both synthetic mixtures and real-life photographs, the advantage of the ability to incorporate spatial shifts is twofold: Not only does it enable separation when such shifts are present, but it also warrants deliberate introduction of such shifts as a simple source of added diversity whenever the static mixing coefficients form a singular matrix - thereby enabling separation in otherwise inseparable scenes.