A quality constrained compression algorithm based on Discrete Wavelet Transform (DWT) is proposed. The spatial-frequency decomposition property of DWT provides possibility for not only the new compression algorithm, but also a frequency-domain quality assessment method that can be executed in real-time. For this propose, a new quality metric in the wavelet domain called WNMSE is suggested, which assesses the quality of an image with the weighted sum of normalized mean square errors of the wavelet coefficients. The metric is consistent with the human judgment of visual quality as well as estimates the post-compression quality of an image efficiently. Based on the relationship among the statistic features, quantization step-sizes, and WNMSE value of a compressed image, we develop a Quality Constrained Quantization algorithm which can determine the quantization step-sizes for all the wavelet subbands for compressing the image to a desired visual quality accurately.

: We present a prototype implementation of a video coding and decoding algorithm suitable for wireless networks. Typical bursty errors of wireless networks are handled by a coding scheme which allows for graceful service degradation when the video data is received incompletely. This property is achieved by applying a coding scheme based on the wavelet transformation (WT) which yields a nonredundant multi-resolution representation. In addition, an interleaved segmentation and the introduction of redundancy for critical low frequency components of the coded video may be activated to reduce the visible loss to a minimum. The algorithms provide scalability over a wide range of video QoS parameters, namely image quality, frame rate, compression ratio and computational complexity. The tagged representation of the stream makes it possible to extract and discard particular information, like high resolution or color, from the video by just identifying and dropping tagged stream segment...

This paper chronicles more than 40 years of evolution in the design of such modems.

The Motion Picture Experts Group (MPEG)-1 audio compression algorithm is an International Organization for Standardization (ISO) standard for high fidelity audio compression. MPEG-1 provides three layers, with increasing degree of complexity of implementation and quality of compression. Layer I uses a 32 sub-band filter bank for decomposing the input signal into sub-sampled spectral components, for subsequent quantization and coding using rules of psychoacoustics. The filter bank is not a perfect reconstruction system. Layer III refines the spectral resolution of the Layer I by further processing its output using Modified Discrete Cosine Transform. This hybrid system suffers from several defects. In this paper, we rectify these problems using a unified filter bank that has temporal resolution and frequency selectivity identical to the hybrid system. In addition, it provides Perfect Reconstruction. A feasible design example is also presented.

In this paper, we briefly review the connection between subband coding, wavelet approximation and general cornpression problems. Wavelet or subband coding is successful in compression applications partly because of the good approximation properties of wavelets. First, we revisit some rate-distortion bounds for wavelet approximation of piecewise smooth functions. We contrast these results with rate-distortion bounds achievable using oracle based methods. We indicate that such bounds are achievable in practice using dynamic programming. Finally, we conclude with an outlook on open questions in the area of compression and representations.

The great challenge in signal processing is to devise computationally efficient and statisti-cally optimal algorithms for estimating signals from noisy background and understanding their contents. This thesis treats the problem of multiscale signal processing and shape analysis for an Inverse Synthetic Aperture Radar (ISAR) imaging system. To address some of the limita-tions of conventional techniques in radar image processing, an information theoretic approach for target motion estimation is first proposed. A wavelet based multiscale method for shape enhancement is subsequently derived and followed by a regression technique for shape recog-nition. Building on entropy-based divergence measures which have shown promising results in many areas of engineering and image processing, we introduce in this thesis a new generalized divergence measure, namely the Jensen-Rényi divergence. Upon establishing its properties such as convexity and its upper bound etc., we apply it to image registration for ISAR focusing as well as related problems in data fusion. Attempting to extend current approaches to signal estimation in a wavelet framework, which have generally relied on the assumption of normally distributed perturbations, we pro-

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Quadrature Mirror Filter (QMF) banks have been used in a variety of one-dimensional signal processing applications, and have been applied separably in two dimensions. As with most one-dimensional filters, separable extension to multiple dimensions produces a transform in which the orientation selectivity of some of the high-pass filters is poor. We describe generalized non-separable extensions of QMF banks to two and three dimensions, in which the orientation specificity of the high-pass filters is greatly improved. In particular, we discuss extensions to two dimensions with hexagonal symmetry, and three dimensional spatio-temporal extensions with rhombic-dodecahedral symmetry. Although these filters are conceived and designed on non-standard sampling lattices, they may be applied to rectangularly sampled images. As in one dimension, these transformations may be hierarchically cascaded to form a multi-scale “pyramid ” representation. We design a set of example filters and apply them to the problems of image compression, progressive transmission, orientation analysis, and motion analysis.

Multi–level numerical methods that obtain the exact solution of a linear system are presented. The methods are devised by combining ideas from the full multi–grid algorithm and perfect reconstruction filters. The problem is stated as whether a direct solver is possible in a full multi–grid scheme by avoiding smoothing iterations and using different coarse grids at each step. These coarse grids must form a partition of the fine grid and thus establishes a strong connection with domain decomposition methods. An important analogy is established between the conditions for direct solution in multi–grid solvers and perfect reconstruction in filter banks. Furthermore, simple solutions of these conditions for direct multi–grid solvers are found by using quadrature mirror filters. As a result, different configurations of direct multi–grid solvers are obtained and studied. Key words: multigrid, perfect reconstruction filter, domain decomposition, direct solver, aliasing