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Information-theoretic analyses for data hiding prescribe embedding the hidden data in the choice of quantizer for the host data. In this paper, we propose practical realizations of this prescription for data hiding in images, with a view to hiding large volumes of data with low perceptual degradation. The hidden data can be recovered reliably under attacks, such as compression and limited amounts of image tampering and image resizing. The three main findings are as follows. 1) In order to limit perceivable distortion while hiding large amounts of data, hiding schemes must use image-adaptive criteria in addition to statistical criteria based on information theory. 2) The use of local criteria to choose where to hide data can potentially cause desynchronization of the encoder and decoder. This synchronization problem is solved by the use of powerful, but simple-to-implement, erasures and errors correcting codes, which also provide robustness against a variety of attacks. 3) For simplicity, scalar quantization-based hiding is employed, even though information-theoretic guidelines prescribe vector quantization-based methods. However, an information-theoretic analysis for an idealized model is provided to show that scalar quantization-based hiding incurs approximately only a 2-dB penalty in terms of resilience to attack.

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We develop an algorithm for the solution of indefinite least-squares problems. Such problems arise in robust estimation, filtering, and control, and numerically stable solutions have been lacking. The algorithm developed herein involves the QR factorization of the coefficient matrix and is provably numerically stable.

We define the class of sequentially semi-separable matrices in this paper. Essentially this is the class of matrices which have low numerical rank on their off diagonal blocks. Examples include banded matrices, semi-separable matrices, their sums as well as inverses of these sums. Fast and stable algorithms for solving linear systems of equations involving such matrices and computing Moore-Penrose inverses are presented. Supporting numerical results are also presented. In addition, fast algorithms to construct and update this matrix structure for any given matrix are presented. Finally, numerical results that show that the coefficient matrices resulting from global spectral discretizations of certain integral equations indeed have this matrix structure are given.

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