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Abstract: In this paper, we identify and study an important patient privacy protection problem related to medical images. Following Health Insurance Portability and Accountability Act (HIPAA) mandate on privacy protection of patients'' medical records, efforts have been devoted to guaranteeing the confidentiality of data and medical images during storage and transmission via an untrustworthy channel. However, to our knowledge, there has not been any effort towards protecting against unauthorized release of images by an authorized recipient. In this paper, we study the problem of tracing illegally distributed medical images in a group communication environment and identify a set of design requirements that must be met. We propose a fingerprint model suitable for many-to-many multicast, that is computationally efficient and scalable in user storage and key update communication. Simulation results also show that our scheme is highly robust to typical medical image processing and collusion attacks, while yielding high quality watermarked images. [Copyright &y& Elsevier]

This paper studies the problem of selecting a submatrix of a positive definite matrix in order to achieve a desired bound on the smallest eigenvalue of the submatrix. Maximizing this smallest eigenvalue has applications to selecting input nodes in order to guarantee consensus of networks with negative edges as well as maximizing the convergence rate of distributed systems. We develop a submodular optimization approach to maximizing the smallest eigenvalue by first proving that positivity of the eigenvalues of a submatrix can be characterized using the probability distribution of the quadratic form induced by the submatrix. We then exploit that connection to prove that positive-definiteness of a submatrix can be expressed as a constraint on a submodular function. We prove that our approach results in polynomial-time algorithms with provable bounds on the size of the submatrix. We also present generalizations to non-symmetric matrices, alternative sufficient conditions for the smallest eigenvalue to exceed a desired bound that are valid for Laplacian matrices, and a numerical evaluation. [ABSTRACT FROM AUTHOR]