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Fundamental performance bounds for statistical estimation of parametric surfaces embedded in [R.sup.3], in which the reconstruction of the shape of binary or homogenous objects could be represented by asymptotic global confidence regions that facilitate geometric inference and optimization of the imaging system is derived. Simulation results reveal the tightness of the resulting bound and the efficiency of the three-dimensional global confidence region approach.

A joint hashing/watermarking scheme is developed in which a short hash of the host signal is available to a detector and potential applications include content tracking on public networks and forensic identification. The joint hashing/watermarking scheme outperforms the traditional hashless watermarking technique.

A game-theoretic formulation of the watermark embedding problems is presented. Its solution is derived for Gaussian signals, spread-spectrum watermarks, and attacks.

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.

A general method is described for computing Cramer-Rao bounds for parametric shape estimation in linear inverse problems, such as computed tomography.

A model for image watermarking and data hiding is proposed. New theoretical results are used to characterize the capacity of data-hiding and image watermarking systems.

An information-theoretic analysis of statistical dependencies between image wavelet coefficients is presented. Dependencies are measured using mutual information.

A study was conducted to evaluate the efficiency of the design of signal-adapted finite impulse response (FIR) paraunitary filter banks which are based on the energy compaction criterion. The innovative filter banks' optimal filters can be utilized in solving linear semi-infinite programming problems. However, the method of designing such optimal filter banks may not be appropriate in multidimensional FIR filter banks due to lack of spectral factorization.

The image sequences in many image processing and computer vision applications have problems associated with the accurate modeling and estimation of motion. The use of multiscale models is proposed as a first step towards representing, computing and encoding motion fields. A systematic approach to motion field estimation and coding is presented.

This study shows that designing an orthogonal FIR, quadrature-mirror filter (QMF) bank to maximize the coding gain is much simpler that the previous operation. The coding gain depends on the product filter which leads to a stable class of linear optimization problem termed as linear semi-infinite programming (SIP). The original filter is obtained by deflation and spectral factorization of the product filter. A comprehensive analysis of the SIP problem is also presented using numerical algorithm.

A novel technique enhances nonorthogonal multiresolution transforms for image encoding by minimizing the L(super 2) reconstruction error. This is done on the possible set of encoded images. A multiscale relaxation algorithm computes the suboptimal solutions by using intra- and inter-scale noise feedback filters, and this maximizes the signal-to-noise ratio. The coding problem involves high-dimensional discrete optimization.

The logarithm of an unknown power spectrum S(f) of a stationary random process is represented by a nonparametric method based on wavelet representation. The estimation of S(f) of a stationary random process is a nonparametric statistical estimation problem. The statistically significant constituents of the logarithm of S(f) at different resolution levels are captured by this approach. The proposed wavelet thresholding technique helps solve the nonparametric statistical estimation problem.

We present new methods for computing fundamental performance limits for two-dimensional (2-D) parametric shape estimation in nonlinear inverse scattering problems with an application to passive radar imaging. We evaluate Cramer-Rao lower bounds (CRB) on shape estimation accuracy using the domain derivative technique from nonlinear inverse scattering theory. The CRB provides an unbeatable performance limit for any unbiased estimator, and under fairly mild regularity conditions is asymptotically achieved by the maximum likelihood estimator (MLE). The resultant CRBs are used to define an asymptotic global confidence region, centered around the true boundary, in which the boundary estimate lies with a prescribed probability. These global confidence regions conveniently display the uncertainty in various geometric parameters such as shape, size, orientation, and position of the estimated target and facilitate geometric inferences. Numerical simulations are performed using the layer approach and the Nystrom method for computation of domain derivatives and using Fourier descriptors for target shape parameterization. This analysis demonstrates the accuracy and generality of the proposed methods. Index Terms--Cramer-Rao bounds, Fourier descriptors, global confidence regions, nonlinear inverse scattering, passive radar imaging, shape 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.

A new method for image denoising is proposed, based on complexity regularization, as an alternative to L2, l1 and Besov regularization techniques.

Research describing the design of subband coders is presented. In particular the coders are optimized for rate distortion and the use of scalar quantizers and computational algorithms is developed.

We consider the problems of motion-compensated frame interpolation (MCFI) and bidirectional prediction in a video coding environment. These applications generally require good motion estimates at the decoder. In this paper, we use a multiscale optical-flow-based motion estimator that provides smooth, natural motion fields under bit-rate constraints. These motion estimates scale well with change in temporal resolution and provide considerable flexibility in the design and operation of coders and decoders. In the MCFI application, this estimator provides excellent interpolated frames that are superior to those of conventional motion estimators, both visually and in terms of peak signal-to-noise ratio (PSNR). We also consider the effect of occlusions in the bidirectional prediction application and introduce a dense label field that complements our motion estimator. This label field enables us to adaptively weight the forward and backward predictions and gives us substantial visual and PSNR improvements in the covered/uncovered regions of the sequence. Index Terms - Bidirectional prediction, frame interpolation, motion compensation, motion estimation, video compression.

A new-best basis design, in which filter banks, subband tree structure and quantizers are chosen to optimize rate-distortion performance, is presented. The new design integrated two different but complementary approaches to best-basis design. One method involves the use of fast algorithms to determine the best bases in an operational rate-distortion sense, while the other method involves the design of filter banks that optimize energy compaction for a single signal or a class of signals.