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An information-theoretic model for image watermarking and data hiding is presented in this paper. Previous theoretical results are used to characterize the fundamental capacity limits of image watermarking and data-hiding systems. Capacity is determined by the statistical model used for the host image, by the distortion constraints on the data hider and the attacker, and by the information available to the data hider, to the attacker, and to the decoder. We consider autoregressive, block-DCT, and wavelet statistical models for images and compute data-hiding capacity for compressed and uncompressed host-image sources. Closed-form expressions are obtained under sparse-model approximations. Models for geometric attacks and distortion measures that are invariant to such attacks are considered.

We study the design of signal{adapted FIR paraunitary lter banks, using energy compaction as the adaptation criterion. We present some important properties that globally optimal solutions to this optimization problem satisfy. In particular, we show that the optimal lters in the rst channel of the lter bank are spectral factors of the solution to a linear semi{in nite programming (SIP) problem. The remaining lters are related to the rst through a matrix eigenvector decomposition. We discuss uniqueness and sensitivity issues. The SIP problem is solved using a discretization method and a standard simplex agorithm. We also show how regularity constraints may be incorporated into the design problem so as to obtain globally optimal (in the energy compaction sense) lter banks with speci ed regularity. We also consider a problem in which the polyphase matrix implementation of the lter bank is constrained to be DCT{based. Such constraints may also be incorporated into our optimization algorithm, so we are able to obtain globally optimal lter banks subject to regularity and/or computational complexity constraints. Numerous experiments are presented to illustrate the main features that distinguish adapted and nonadapted lters, as well as the e ects of the various constraints. The conjecture that energy compaction and coding gain optimization are equivalent design criteria, is shown not to hold for FIR lter banks.

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