Blind deconvolution of sources from the transmission responses of one-dimensional inhomogeneous continuous and discrete layered absorbing media

Abstract

Non-destructive testing and reconstruction of lossy non-uniform transmission lines require solving inverse scattering problems for inhomogeneous one-dimensional (1D) lossy media. Often the source waveform used to probe the medium is unknown, since it cannot be measured separately. This paper shows that the blind deconvolution problem of reconstructing both an unknown source and an unknown lossy 1D medium can be solved, provided the medium absorption is sufficiently large. We generalize the minimum-phase property of the transmission response to a more severe property for lossy media. We also show how partial knowledge of the source can be used to reconstruct low-loss and lossless 1D media. Both discrete and continuous 1D layered media are considered. Numerical examples are presented.