Introduction to a Transient World. Fourier Kingdom. Discrete Revolution. Time Meets Frequency. Frames. Wavelet Zoom. Wavelet Bases. Wavelet Packet and Local Cosine Bases. An Approximation Tour. Estimations are Approximations. Transform Coding. Appendix A: Mathematical Complements. Appendix B: Software Toolboxes.

http://ahvazdownload.persiangig.com/document/article/39.pdf

A wavelet tour of signal processing

A multiscale Canny edge detection is equivalent to finding the local maxima of a wavelet transform. The authors study the properties of multiscale edges through the wavelet theory. For pattern recognition, one often needs to discriminate different types of edges. They show that the evolution of wavelet local maxima across scales characterize the local shape of irregular structures. Numerical descriptors of edge types are derived. The completeness of a multiscale edge representation is also studied. The authors describe an algorithm that reconstructs a close approximation of 1-D and 2-D signals from their multiscale edges. For images, the reconstruction errors are below visual sensitivity. As an application, a compact image coding algorithm that selects important edges and compresses the image data by factors over 30 has been implemented. >

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Characterization of Signals From Multiscale Edges

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.

Wavelets and Subband Coding

A review of vector quantization techniques used for encoding digital images is presented. First, the concept of vector quantization is introduced, then its application to digital images is explained. Spatial, predictive, transform, hybrid, binary, and subband vector quantizers are reviewed. The emphasis is on the usefulness of the vector quantization when it is combined with conventional image coding techniques, or when it is used in different domains. >

Image coding using vector quantization: a review

The authors introduce a directionally oriented 2-D filter bank with the property that the individual channels may be critically sampled without loss of information. The passband regions of the component filters are wedge-shaped and thus provide directional information. It is shown that these filter bank outputs may be maximally decimated to achieve a minimum sample representation in a way that permits the original signal to be exactly reconstructed. The authors discuss the theory for directional decomposition and reconstruction. In addition, implementation issues are addressed where realizations based on both recursive and nonrecursive filters are considered. >

A filter bank for the directional decomposition of images: theory and design

The digital representation of an image requires a very large number of bits. The goal of image coding is to reduce this number, as much as possible, and reconstruct a faithful duplicate of the original picture. Early efforts in image coding, solely guided by information theory, led to a plethora of methods. The compression ratio, starting at 1 with the first digital picture in the early 1960s, reached a saturation level around 10:1 a couple of years ago. This certainly does not mean that the upper bound given by the entropy of the source has also been reached. First, this entropy is not known and depends heavily on the model used for the source, i.e., the digital image. Second, the information theory does not take into account what the human eye sees and how it sees. Recent progress in the study of the brain mechanism of vision has opened new vistas in picture coding. Directional sensitivity of the neurones in the visual pathway combined with the separate processing of contours and textures has led to a new class of coding methods capable of achieving compression ratios as high as 70:1. Image quality, of course, remains as an important problem to be investigated. This class of methods, that we call second generation, is the subject of this paper. Two groups can be formed in this class: methods using local operators and combining their output in a suitable way and methods using contour-texture descriptions. Four methods, two in each class, are described in detail. They are applied to the same set of original pictures to allow a fair comparison of the quality in the decoded pictures. If more effort is devoted to this subject, a compression ratio of 100:1 is within reach.

A. Ikonomopoulos

Papers

Second-generation image-coding techniques

High compression image coding via directional filtering

Compression d'images : Méthodes de la deuxième génération