Wavelets and Subband Coding

First published in 1995, Wavelets and Subband Coding offered a unified view of the exciting field of wavelets and their discrete-time cousins, filter banks, or subband coding. The book developed the theory in both continuous and discrete time, and presented important applications. During the past decade, it filled a useful need in explaining a new view of signal processing based on flexible time-frequency analysis and its applications. Since 2007, the authors now retain the copyright and allow open access to the book

Discrete Wavelet Transforms

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

Fourier Transform

The application of Fourier transform (FT) in signal processing and physical sciences has increased in the past decades. Almost all the textbooks on signal processing or physics have a section devoted to the FT theory. For this reason, this book focuses on signal processing and physical sciences. The book chapters are related to fast hybrid recursive FT based on Jacket matrix, acquisition algorithm for global navigation satellite system, determining the sensitivity of output parameters based on FFT, convergence of integrals of products based on Riemann-Lebesgue Lemma function, extending the real and complex number fields for treating the FT, nonmaterial structure, Gabor transform, and chalcopyrite bioleaching. The book provides applications oriented to signal processing and physics written primarily for engineers, mathematicians, physicians and graduate students, will also find it useful as a reference for their research activities

Performance and Microarchitectural Analysis for Image Quality Assessment

This thesis presents performance analysis for five matured Image Quality Assessment algorithms: VSNR, MAD, MSSIM, BLIINDS, and VIF, using the VTune ... from Intel. The main performance parameter considered is execution time. First, we conduct Hotspot Analysis to find the most time consuming sections for the five algorithms. Second, we perform Microarchitecural Analysis to analyze the behavior of the algorithms for Intel's Sandy Bridge microarchitecture to find architectural bottlenecks. Existing research for improving the performance of IQA algorithms is based on advanced signal processing techniques. Our research focuses on the interaction of IQA algorithms with the underlying hardware and architectural resources. We propose techniques to improve performance using coding techniques that exploit the hardware resources and consequently improve the execution time and computational performance. Along with software tuning methods, we also propose a generic custom IQA hardware engine based on the microarchitectural analysis and the behavior of these five IQA algorithms with the underlying microarchitectural resources.School of Electrical & Computer Engineerin

A generalized, parametric PR-QMF/wavelet transform design approach for multiresolution signal decomposition

This dissertation aims to emphasize the interrelations and the linkages of the theories of discrete-time filter banks and wavelet transforms. It is shown that the Binomial-QMF banks are identical to the interscale coefficients or filters of the compactly supported orthonormal wavelet transform bases proposed by Daubechies. A generalized, parametric, smooth 2-band PR-QMF design approach based on Bernstein polynomial approximation is developed. It is found that the most regular compact support orthonormal wavelet filters, coiflet filters are only the special cases of the proposed filter bank design technique. A new objective performance measure called Non-aliasing Energy Ratio(NER) is developed. Its merits are proven with the comparative performance studies of the well known orthonormal signal decomposition techniques. This dissertation also addresses the optimal 2-band PR-QMF design problem. The variables of practical significance in image processing and coding are included in the optimization problem. The upper performance bounds of 2-band PR-QMF and their corresponding filter coefficients are derived. It is objectively shown that there are superior filter bank solutions available over the standard block transform, DCT. It is expected that the theoretical contributions of this dissertation will find its applications particularly in Visual Signal Processing and Coding

Data compression and harmonic analysis

In this paper we review some recent interactions between harmonic analysis and data compression. The story goes back of course to Shannon’

A Panorama on Multiscale Geometric Representations, Intertwining Spatial, Directional and Frequency Selectivity

The richness of natural images makes the quest for optimal representations in image processing and computer vision challenging. The latter observation has not prevented the design of image representations, which trade off between efficiency and complexity, while achieving accurate rendering of smooth regions as well as reproducing faithful contours and textures. The most recent ones, proposed in the past decade, share an hybrid heritage highlighting the multiscale and oriented nature of edges and patterns in images. This paper presents a panorama of the aforementioned literature on decompositions in multiscale, multi-orientation bases or dictionaries. They typically exhibit redundancy to improve sparsity in the transformed domain and sometimes its invariance with respect to simple geometric deformations (translation, rotation). Oriented multiscale dictionaries extend traditional wavelet processing and may offer rotation invariance. Highly redundant dictionaries require specific algorithms to simplify the search for an efficient (sparse) representation. We also discuss the extension of multiscale geometric decompositions to non-Euclidean domains such as the sphere or arbitrary meshed surfaces. The etymology of panorama suggests an overview, based on a choice of partially overlapping "pictures". We hope that this paper will contribute to the appreciation and apprehension of a stream of current research directions in image understanding.Comment: 65 pages, 33 figures, 303 reference

Channelization for Multi-Standard Software-Defined Radio Base Stations

As the number of radio standards increase and spectrum resources come under more pressure, it becomes ever less efficient to reserve bands of spectrum for exclusive use by a single radio standard. Therefore, this work focuses on channelization structures compatible with spectrum sharing among multiple wireless standards and dynamic spectrum allocation in particular. A channelizer extracts independent communication channels from a wideband signal, and is one of the most computationally expensive components in a communications receiver. This work specifically focuses on non-uniform channelizers suitable for multi-standard Software-Defined Radio (SDR) base stations in general and public mobile radio base stations in particular. A comprehensive evaluation of non-uniform channelizers (existing and developed during the course of this work) shows that parallel and recombined variants of the Generalised Discrete Fourier Transform Modulated Filter Bank (GDFT-FB) represent the best trade-off between computational load and flexibility for dynamic spectrum allocation. Nevertheless, for base station applications (with many channels) very high filter orders may be required, making the channelizers difficult to physically implement. To mitigate this problem, multi-stage filtering techniques are applied to the GDFT-FB. It is shown that these multi-stage designs can significantly reduce the filter orders and number of operations required by the GDFT-FB. An alternative approach, applying frequency response masking techniques to the GDFT-FB prototype filter design, leads to even bigger reductions in the number of coefficients, but computational load is only reduced for oversampled configurations and then not as much as for the multi-stage designs. Both techniques render the implementation of GDFT-FB based non-uniform channelizers more practical. Finally, channelization solutions for some real-world spectrum sharing use cases are developed before some final physical implementation issues are considered

Directional multiresolution image representations

Efficient representation of visual information lies at the foundation of many image processing tasks, including compression, filtering, and feature extraction. Efficiency of a representation refers to the ability to capture significant information of an object of interest in a small description. For practical applications, this representation has to be realized by structured transforms and fast algorithms. Recently, it has become evident that commonly used separable transforms (such as wavelets) are not necessarily best suited for images. Thus, there is a strong motivation to search for more powerful schemes that can capture the intrinsic geometrical structure of pictorial information. This thesis focuses on the development of new "true" two-dimensional representations for images. The emphasis is on the discrete framework that can lead to algorithmic implementations. The first method constructs multiresolution, local and directional image expansions by using non-separable filter banks. This discrete transform is developed in connection with the continuous-space curvelet construction in harmonic analysis. As a result, the proposed transform provides an efficient representation for two-dimensional piecewise smooth signals that resemble images. The link between the developed filter banks and the continuous-space constructions is set up in a newly defined directional multiresolution analysis. The second method constructs a new family of block directional and orthonormal transforms based on the ridgelet idea, and thus offers an efficient representation for images that are smooth away from straight edges. Finally, directional multiresolution image representations are employed together with statistical modeling, leading to powerful texture models and successful image retrieval systems