4 research outputs found

    Wavelets and multirate filter banks : theory, structure, design, and applications

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    Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering, 2004.Includes bibliographical references (p. 219-230) and index.Wavelets and filter banks have revolutionized signal processing with their ability to process data at multiple temporal and spatial resolutions. Fundamentally, continuous-time wavelets are governed by discrete-time filter banks with properties such as perfect reconstruction, linear phase and regularity. In this thesis, we study multi-channel filter bank factorization and parameterization strategies, which facilitate designs with specified properties that are enforced by the actual factorization structure. For M-channel filter banks (M =/> 2), we develop a complete factorization, M-channel lifting factorization, using simple ladder-like structures as predictions between channels to provide robust and efficient implementation; perfect reconstruction is structurally enforced, even under finite precision arithmetic and quantization of lifting coefficients. With lifting, optimal low-complexity integer wavelet transforms can thus be designed using a simple and fast algorithm that incorporates prescribed limits on hardware operations for power-constrained environments. As filter bank regularity is important for a variety of reasons, an aspect of particular interest is the structural imposition of regularity onto factorizations based on the dyadic form uvt. We derive the corresponding structural conditions for regularity, for which M-channel lifting factorization provides an essential parameterization. As a result, we are able to design filter banks that are exactly regular and amenable to fast implementations with perfect reconstruction, regardless of the choice of free parameters and possible finite precision effects. Further constraining u = v ensures regular orthogonal filter banks,(cont.) whereas a special dyadic form is developed that guarantees linear phase. We achieve superior coding gains within 0.1% of the optimum, and benchmarks conducted on image compression applications show clear improvements in perceptual and objective performance. We also consider the problem of completing an M-channel filter bank, given only its scaling filter. M-channel lifting factorization can efficiently complete such biorthogonal filter banks. On the other hand, an improved scheme for completing paraunitary filter banks is made possible by a novel order-one factorization which allows greater design flexibility, resulting in improved frequency selectivity and energy compaction over existing state of the art methods. In a dual setting, the technique can be applied to transmultiplexer design to achieve higher-rate data transmissions.by Ying-Jui Chen.Ph.D

    Discrete Wavelet Transforms

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    The discrete wavelet transform (DWT) algorithms have a firm position in processing of signals in several areas of research and industry. As DWT provides both octave-scale frequency and spatial timing of the analyzed signal, it is constantly used to solve and treat more and more advanced problems. The present book: Discrete Wavelet Transforms: Algorithms and Applications reviews the recent progress in discrete wavelet transform algorithms and applications. The book covers a wide range of methods (e.g. lifting, shift invariance, multi-scale analysis) for constructing DWTs. The book chapters are organized into four major parts. Part I describes the progress in hardware implementations of the DWT algorithms. Applications include multitone modulation for ADSL and equalization techniques, a scalable architecture for FPGA-implementation, lifting based algorithm for VLSI implementation, comparison between DWT and FFT based OFDM and modified SPIHT codec. Part II addresses image processing algorithms such as multiresolution approach for edge detection, low bit rate image compression, low complexity implementation of CQF wavelets and compression of multi-component images. Part III focuses watermaking DWT algorithms. Finally, Part IV describes shift invariant DWTs, DC lossless property, DWT based analysis and estimation of colored noise and an application of the wavelet Galerkin method. The chapters of the present book consist of both tutorial and highly advanced material. Therefore, the book is intended to be a reference text for graduate students and researchers to obtain state-of-the-art knowledge on specific applications

    Integer fast lapped biorthogonal transform via applications of DCT matrices and dyadic-valued factors for lifting coefficient blocks

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