Blind Separation of Superimposed Shifted Images Using Parameterized Joint Diagonalization

• Published in: IEEE transactions on image processing 2008-03, Vol.17 (3), p.340-353
• Main Authors: Be'ery, E., Yeredor, A.
• Format: Article
• Language: English
• Subjects: Algorithms; Applied sciences; Approximate joint diagonalization; Approximation; Artificial Intelligence; Blind source separation; blind source separation (BSS); Blinds; Detection, estimation, filtering, equalization, prediction; Exact sciences and technology; Frequency estimation; Gain; Glass; Image Enhancement - methods; Image Interpretation, Computer-Assisted - methods; Image processing; image reflections; image separation; Imaging, Three-Dimensional - methods; Information, signal and communications theory; Layout; Mathematical analysis; Mathematical models; Miscellaneous; Movements; Optical attenuators; Optical polarization; Optical reflection; Pattern Recognition, Automated - methods; Photography - methods; Reproducibility of Results; Sensitivity and Specificity; Separation; Signal and communications theory; Signal processing; Signal Processing, Computer-Assisted; Signal, noise; Source separation; spatial shifts; Subtraction Technique; Telecommunications and information theory; Vectors; Windows
• ISSN: 1057-7149; 1941-0042
• DOI: 10.1109/TIP.2007.915548

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.