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The Karhunen-Loéve transform (KLT) is known to be optimal for high-rate transform coding of Gaussian vectors for both fixed-rate and variable-rate encoding. The KLT is also known to be suboptimal for some non-Gaussian models. This paper proves high-rate optimality of the KLT for variable-rate encoding of a broad class of non-Gaussian vectors: Gaussian vector-scale mixtures (GVSM), which extend the Gaussian scale mixture (GSM) model of natural signals. A key concavity property of the scalar GSM (same as the scalar GVSM) is derived to complete the proof. Optimality holds under a broad class of quadratic criteria, which include mean-squared error (MSE) as well as generalized f-divergence loss in estimation and binary classification systems. Finally, the theory is illustrated using two applications: signal estimation in multiplicative noise and joint optimization of classification/reconstruction systems. [ABSTRACT FROM AUTHOR]

Rates of reliable transmission of hidden information are derived for watermarking problems involving parallel Gaussian sources, which are often used to model host images and audio signals. Constraints are imposed on the average squared-error distortion that can be introduced by the information hider and by the attacker. When distortions are measured with respect to the original host data, the optimal covert and attack channels are two banks of Gaussian test channels. The solution to the watermarking game involves an optimal allocation of distortions by the information hider and by the attacker to the different channels. A fast algorithm is given for computing the optimal solution based on duality theory. For each channel, we derive analytical expressions for two asymptotic regimes: weak and strong host signals. Finally, we extend these results to the class of stationary Gaussian host signals with bounded, continuous spectral density. The analysis also provides an upper bound on watermarking capacity for non-Gaussian host signals. [ABSTRACT FROM AUTHOR]