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A general distributed field reconstruction problem is studied by using a dense network of noisy one-bit randomized scalar quantizers in the presence of additive observation noise of unknown distribution. A general condition is derived for the optimization of the rate of decay of the mean squared error (MSE) upper-bound with sensor density.

A broad set of sufficient conditions that guarantees the existence of the maximum entropy (maxent) distribution consistent with specified bounds on certain generalized moments is derived. Most results in the literature are either focused on the minimum cross-entropy distribution or apply only to distributions with a bounded-volume support or address only equality constraints. The results of this work hold for general moment inequality constraints for probability distributions with possibly unbounded support, and the technical conditions are explicitly on the underlying generalized moment functions. An analytical characterization of the maxent distribution is also derived using results from the theory of constrained optimization in infinite-dimensional normed linear spaces. Several auxiliary results of independent interest pertaining to certain properties of convex coercive functions are also presented. Index Terms--Coercive functions, constrained optimization, convex analysis, cross-entropy, differential entropy, maximum entropy methods.

The novelty of reversing the order of encrypting and compressing the data without compromising either the compression efficiency or the information-theoretic security is described. It is proved that through the use of coding with side information principles, the reversal of order of encrypting and compressing the data is possible in some settings of interest, without loss of either optimal coding efficiency or perfect secrecy.

An equivalence is established between two models of signal estimation under modeling uncertainty. The methods are: set-theoretic estimation; and maximum entropy (maxent) MAP estimation.

Most motion-compensation methods dealt with in the literature make strong assumptions about the smoothness of the underlying motion field. For instance, block-matching algorithms assume a blockwise-constant motion field and are adequate for translational motion models; control-grid interpolation assumes a blockwise bilinear motion field and captures zooming and warping fairly well. Time-varying imagery, however, often contains both types of motion (as well as others), and hence exhibits a high degree of spatial variability of its motion-field smoothness properties. We develop a simple method to spatially adapt the smoothness of the motion field. The proposed method demonstrates substantial improvements in video quality over a wide range of bit rates. To this end, we introduce the notion of a motion field that is characterized by a set of labels. The labels provide the flexibility to adaptively switch between two different motion models locally. The individual motion models have very different smoothness properties. The switched framework for motion compensation performs significantly better than each of its constituent motion models, in terms of both visual quality and signal-to-noise ratio (0.3--0.7 dB on the average). Finally, we develop an extension of this method that enhances the overlapped block motion compensation scheme by allowing spatial adaptation of the window function. Index Terms--Block matching, interpolation methods, motion estimation, overlapped block motion compensation, video compression.