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A theory of super-resolution from unregistered aliased sets of samples is described. The super-resolution problem is written as a set of polynomial equations and it is possible to reconstruct the signal by using Grobner basis methods.

A novel efficient space-frequency quantization (SFQ) compression algorithm designed by using directionlets was observed to outperform the standard SFQ, both in terms of mean-square error and visual quality.

The decay of the spectrum of the plenacoustic function is introduced and studied on both temporal and spatial frequency axes. Based on the support of the spectrum, the number and spacing between microphones needed to reconstruct the sound pressure field up to a certain temporal frequency is determined.

A lattice-based perfect reconstruction and critically sampled anisotropic multidirectional (M-DIR) wavelet transform (WT) with corresponding effective directional anisotropic basis functions (directionlets) in image processing is presented. It is shown that this novel transform provides an efficient tool for nonlinear approximation of images, achieving the approximation power O([N.sub.-1.55]).

A spatial adaptive algorithm for image interpolation which utilizes a wavelet transforms to get information about sharp differences in low-resolution image and perfectly applies interpolation which adapts to the image local smoothness or singularity characteristics. The recommended algorithm produced sharper images in comparison with various methods and higher complexity leads to better performance.

A 'true' two-dimensional transform is proposed that can capture the intrinsic geometrical structure in visual information. Some numerical experiment demonstrating the potential of contourlets in several image processing applications are shown.

The study describes some newly developed novel coding algorithms based on the tree-structured segmentation, which can easily achieve the correct asymptotic rate-distortion (R-D) behavior for piecewise polynomial images. The algorithm can achieve exponentially decaying asymptotic R-D behavior for the polygonal image model and hence is also capable of outperforms signals in the case of compression real images.

Sampling results for certain classes of 2-D signals that are not band limited but have a parametric representation with a finite number of degrees of freedom are presented. Potentials and limitations of the algorithms in the noisy case are also pointed.

The Laplacian pyramid (LP) is studied using frame theory , and it is shown that the usual reconstruction is suboptim al.

The dependency across scales of the wavelet coefficients generated by discontinuities is investigated and discussed.

A family of discrete orthonormal transforms for images is presented and discussed. It is based on the ridgelet idea.

Signals with finite rates of innovation, which permit uniform sampling after smoothing and reconstruction from samples, are examined. For signals such as streams of Diracs, nonuniform splines, and piecewise polynomials, exact reconstruction formulas were obtainable even though the signals are nonbandlimited.

A statistical approach to the texture-retrieval problem is discussed. Feature extraction (FE) and similarity measurement (SM) are combined in a modeling and classification scheme.

Multiwavelets and properties of approximation and smoothness associated with them are examined. Particular attention focuses on the issue of preservation of discrete-time polynomial signals by multifilterbanks.

Image recovery from multiple noisy copies is described.

An finite impulse response FIR cascade structure is proposed as an alternative framework for adaptive linear prediction. The application of this method is based on the least squares minimization in which the predictor used is composed of a cascade of small-order independently adapting linear filters instead of the conventional adaptive filters. Experimental results show that the FIR cascade structure effects a more speedy route to convergence.

A study was conducted on a framework that defines a coded image as belonging to the intersection of several convex sets. A set of tools to design a new class of encoders for image compression, based on a set decomposition and recombination of image features, has been developed. The findings indicate that these tools can modify the encoding process of block discreet cosine transform (DCT) coding in order to yield less blocking artifacts.

The class of frames in l2(Z), which are equivalent to perfect reconstruction oversampled filter banks, was studied. The required and sufficient conditions on a filter bank for implementing a frame or a tight frame expansion were determined, including the requisite and sufficient condition for perfect reconstruction using finite impulse response (FIR) filters after an FIR analysis. Then, nonsubsampled filter banks, which implement transforms similar to continuous-time transforms and permit very flexible design, were studied.

Tight Weyl-Heisenberg frames in l2(Z) were investigated utilizing filter bank theory methods. These frames are used in short-time Fourier analysis in discrete time and are closely related to paraunitary modulated filter banks. A complete parameterization of these frames with finite support in time was obtained. It was also shown that redundant Weyl-Heisenberg families permit the formation of windows with improved frequency selectivity over critically sampled ones.

The balanced multiwavelets method may be utilized in determining solutions to the problems of wavelets in signal processing applications. This method can also used as a tool to process images and sounds in an orthogonal linear finite impulse response environment. Although the innovative balance multiwavelets method yields important functions, the method is not comprehensive to deal on several problems of signal processing.

An adaptive quantization algorithm capable of learning the source distribution from the quantized data and adapting the quantize parameters using solid design methods is examined. The backward adaptive algorithm explicitly separates adaption into two parts, namely, source modeling and quantizer design. It can also be used for quantization schemes which rely on an underlying scalar quantizer.

A recursive segmentation-based image coding procedure utilizes binary space partitioning (BSP)-tree representations for effective compression of still images. The method follows a hierarchical scheme for encoding the partitioning lines of the BSP-tree. However, low-order polynomials can encode the BSP-tree cells and can represent image signals within these cells. An optimum pruning algorithm which reduces the bit-rate of the encoded BSP-tree with minimal distortion, and the simulation results for BSP-based coding method are presented.

An adaptive image processing technique uses spatially varying wavelet packets (WPs) through a double-tree structure to provide the best spatial segmentation and frequency decomposition for each image coding segment. The double-tree algorithm optimizes an operational rate-distortion cost function by jointly determining the spatial and frequency segmentations. The usefulness of the technique is demonstrated using a first-order entropy rate-measure-based coder. Only quadtree spatial segmentations and binary WP frequency decompositions are considered to avoid computational complexity.

Vector quantization (VQ) and subband decomposition provide an effective means of image compression. VQ helps in the conversion of the decomposed signal into bits. The conversion takes advantage of the flexible partitions of the higher dimensional vector spaces, and the inter and intraband correlation. A survey of the methods used since 1988 to study VQ applications to subband/wavelet transform coefficients is presented.

Two- and three-dimensional nonseparable wavelets, obtained from discrete-time bases by iterating filter banks, allow for the analyzation of single-input single-output periodically time-varying systems as if they were multiple-input multiple-output time-invariant systems. Three sampling lattices, quincunx, separable by two in two dimensions, and FCO, are designed using McClellan transformation or cascade structures and then analyzed using the technique. Solutions for previously impossible samplings, including linear phase and orthonormal filters, can be achieved by the multiple dimension systems.

The wavelet transform extreme and zero crossing representations are investigated within the framework of convex representations in l(2)(Z). The investigation involves the introduction of a wavelet zero-crossings representation of two-dimensional signals as convex multiscale representations. The investigation reveals that the extrema and the zero-crossing representations are capable of generating new algorithms.

Examination of the time domain description of the two channel orthogonal filter bank provides information on the construction of orthogonal time-varying filter banks. The examination enables construction of the orthogonal boundary filters that can be applied to finite-length or one-sided signals. This generates the subband tree structures that vary over time. Continuous time bases are obtained from the iteration of discrete-time-varying filter banks.

The advantages of adaptive thresholding, applied to JPEG and MPEG coding, are quantified by the newly developed optimal algorithm. Sweeping of Lagrange multipliers through the various positive values for standard quantization scales yields the R-D curves. Finer quantization scales that produce decent coding gain are obtained by the reference bit rate.

Efficient bit allocation in a dependent coding environment is performed by an operational rate-distortion (RD) framework, which is widely used for arbitrary quantizer systems. The method is an extension of the methods used for optimal bit allocation for independently coded blocks of signal. The new method obtains near-optimal and optimal solutions by exploiting the monotonicity exhibited by the dependent RD curves. This method is applicable to topical MPEG video and multiresolution coders.

A deterministic analysis of oversampled A/D conversion reveals that the set of bandlimited signals is convex and helps improve nonconsistent estimates. Classical linear decoding estimates are not consistent in all cases. Deterministic knowledge of quantized signals are used to suggest methods of improving simple ADC, predictive ADC, single-loop and multiloop Sigma-Delta modulation.

A Lagrangian optimization-based heuristic algorithm which used an operational rate-distortion framework exhibited a reduction in computational complexity related to buffer constrained quantization. These optimal fast algorithms were used in applications which did not depend on processing delay such as video on CD-ROM, workstation display and broadcasting.

An analysis of oversampled analog-to-digital converters reveals that, under specific conditions, reconstruction of the device yields a mean squared error (MSE) that is inversely proportional to the square of the oversampling ratio 'R'. The reduction in MSE occurs for specific R values with a reconstruction pattern which assumes that analog signals are periodic within inherent time steps. The device achieves MSE reduction when the reconstructed digital device reproduces the 'discrete time discrete amplitude' performance of its analog counterpart.

Time varying orthogonal tree structures provide arbitrary orthonormal tilings of the time-frequency plane under several conditions, including transitions. Boundary and transition filters aid the construction of arbitrary tilings. A double-tree algorithm that selects the ideal binary segmentation in time and frequency is constructed and used for compressing nonstationary signals.

Examination of the structure of orthogonal two channel filter banks and their relation with orthonormal bases of wavelets reveals that the continuous-time bases of wavelets can be derived by the perfect reconstruction of filter banks. The infinite impulsive response filters cause general wavelets of infinite support. The orthonormal wavelet bases are generated by completely constructed orthogonal two channel filter banks having rational filter banks.

The perfect reconstruction filter banks with rational sampling factors have N branches, and each has a sampling factor of pi divided by qi and pi plus qi equals one. Non-uniform divisions of the spectrum are allowed for by the extension of the well-known theory of filter banks with uniform band splitting. The theory is utilized in the analysis of speech and music. Filter banks are classified according to possible methods of construction.

Electronic experts have developed a new method for signal compression by decomposing wavelet packets on the model of an adaptive tree structure. Decomposition of a direct signal takes place by using wavelet packets as the basis of a given wavelet kernel to discover the best wavelet packet model. A layout that includes both rate and distortion is worked on to prune the tree, which denotes the entire collection of permissible wavelet packet basis, to arrive at the most suitable basis subtree which would reduce the coding bit rate for better target quality.

The design of three-dimensional perfect reconstruction filter banks for nonseparable subsampling by two of digital video sequences in three dimensions is studied. The scheme, which uses the face-centered orthorhombic sampling lattice, is compared to the quincunx sampling process based on interlacing that also performs splitting into two bands. Its superiority over the quincunx sampling method is demonstrated.

A study of the correlations between wavelets, filter banks and multiresolution signal analysis is presented. It contains a comparison of the wavelet transform and the short-timeFourier transform approaches to continuous-time and discrete-time signal analysis. Perfect reconstruction filter banks and continued fraction theory areutilized to obtain filter banks with a highly regular structures. They result in biorthogonal continuous wavelet bases with symmetries.

Astudy on adaptive identification of critically sampled, linear, multirate systems is presented. It starts by demonstrating that proper modelization necessitates adaptive cross-filters between subbands for both two-band and multiband cases. Two algorithms for adaptive filtering in subbands are then presented and analyzed. Although their convergence performance is not up to expectations, they may still be used for practical purposes.

Methods to rebuild a banlimited discrete-time signal from irregular samples at unknown sites, are reported.

An adaptive data-drive threshold for image denoising is presented, using wavelet soft-thresholding.

A spatially adaptive wavelet thresholding technique has introduced, based on context modeling.

The matching pursuit algorithm can be applied for the derivation of signal decompositions in terms of the elements of a dictionary of time-frequency atoms. The application of a structured overcomplete dictionary provides a signal model that is both parametric and signal adaptive. Matching pursuit was used in the derivation of signal expansions based on damped sinusoids. It was observed that expansions in terms of complex damped sinusoids can be efficiently derived by employing simple recursive filter banks.

A study was conducted to determine a solution to continuous-time local cosine bases (LCB) problems and to develop a theory of LCB that accommodates the deep connection associated with discrete and continuos time. The solution did not utilized any features of continuous time. It supported operators that correlate with compactly supported functions. The norm of folded products was then used to determine deviations from orthogonality.

The literature on gradient and differential microphone arrays makes a distinction between the two types, but it nevertheless shows how both types can be used to obtain the same directional responses. A more theoretically sound rationale for using delays in differential microphone arrays has not yet been given. A gradient analysis of the sound field viewed as a spatiotemporal phenomenon is presented, giving a theoretical interpretation of the working principles of gradient and differential microphone arrays. It is shown that both types of microphone arrays can be viewed as devices for approximately measuring spatiotemporal derivatives of the sound field. Furthermore the design of high-order differential microphone arrays using the aforementioned spatiotemporal gradient analysis is discussed. [ABSTRACT FROM AUTHOR]