Multiresolution representations are effective for analyzing the information content of images. The properties of the operator which approximates a signal at a given resolution were studied. It is shown that the difference of information between the approximation of a signal at the resolutions 2/sup j+1/ and 2/sup j/ (where j is an integer) can be extracted by decomposing this signal on a wavelet orthonormal basis of L/sup 2/(R/sup n/), the vector space of measurable, square-integrable n-dimensional functions. In L/sup 2/(R), a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi (x). This decomposition defines an orthogonal multiresolution representation called a wavelet representation. It is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters. Wavelet representation lies between the spatial and Fourier domains. For images, the wavelet representation differentiates several spatial orientations. The application of this representation to data compression in image coding, texture discrimination and fractal analysis is discussed. >

/pdf/a-theory-for-multiresolution-signal-decomposition-the-530tw5pzq7.pdf

A theory for multiresolution signal decomposition: the wavelet representation

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

We construct orthonormal bases of compactly supported wavelets, with arbitrarily high regularity. The order of regularity increases linearly with the support width. We start by reviewing the concept of multiresolution analysis as well as several algorithms in vision decomposition and reconstruction. The construction then follows from a synthesis of these different approaches.

/pdf/orthonormal-bases-of-compactly-supported-wavelets-2h5ewm1jh3.pdf

Orthonormal bases of compactly supported wavelets

A scheme for image compression that takes into account psychovisual features both in the space and frequency domains is proposed. This method involves two steps. First, a wavelet transform used in order to obtain a set of biorthogonal subclasses of images: the original image is decomposed at different scales using a pyramidal algorithm architecture. The decomposition is along the vertical and horizontal directions and maintains constant the number of pixels required to describe the image. Second, according to Shannon's rate distortion theory, the wavelet coefficients are vector quantized using a multiresolution codebook. To encode the wavelet coefficients, a noise shaping bit allocation procedure which assumes that details at high resolution are less visible to the human eye is proposed. In order to allow the receiver to recognize a picture as quickly as possible at minimum cost, a progressive transmission scheme is presented. It is shown that the wavelet transform is particularly well adapted to progressive transmission. >

/pdf/image-coding-using-wavelet-transform-426c6qtjbf.pdf

Image coding using wavelet transform

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

In recent years, tree-structured analysis/reconstruction systems have been extensively studied for use in subband coders for speech. In such systems, it is important that the individual channel signals be decimated in such a way that the number of samples coded and transmitted does not exceed the number of samples in the original speech signal. Under this constraint, the systems presented in the past have sought to remove the aliasing distortion while minimizing the overall analysis/reconstruction distortion. In this paper, it is shown that it is possible to design tree-structured analysis/reconstruction systems which meet the sampling rate condition and which also result in exact reconstruction of the input signal. This paper develops the conditions for exact reconstruction and presents a general method for designing the corresponding high quality analysis and reconstruction filters.

A procedure for designing exact reconstruction filter banks for tree-structured subband coders

The authors present a new time-domain approach for the analysis and design of a broad class of general analysis/synthesis systems based on M-band filter banks. They derive a set of time-domain conditions for reconstruction which can be used directly in a filter bank design procedure. The general and unrestricted nature of this framework allows for the design of many useful banks. In addition to the complete derivation of the time-domain conditions, they also describe the associated filter bank design procedure and a number of design examples are included. >

Time-domain filter bank analysis: a new design theory

This paper describes our enhanced mixed excitation linear prediction (MELP) speech coder which is a candidate for the new U.S. Federal Standard at 2.4 kbits/s. The new coder is based on the MELP model, and it uses a number of enhancements as well as efficient quantization algorithms to improve performance while maintaining a low bit rate. In addition, the coder has been optimized for performance in acoustic background noise and in channel errors, as well as for efficient real-time implementation. Listening tests confirm that the enhanced 2.4 kbit/s MELP coder performs as well as the higher bit rate 4.8 kbit/s FS1016 CELP standard.

A 2.4 kbit/s MELP coder candidate for the new U.S. Federal Standard

This paper presents a new formalism for the description of analysis/synthesis systems based on filter banks. Although this work was done in the context of speech coding systems, the results apply to a far broader class of problems. This new formalism has three specific advantages. First, it allows for the description of many different techniques and approaches with one unifying theory. Second, it enables the decoupling of the effects of the various distorting elements in the system design process, allowing each to be addressed separately. Finally, it allows for the relatively simple invention of entirely new techniques in such a way that the relationship of the new approaches to previously developed techniques is always clear.

A new filter bank theory for time-frequency representation

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A procedure for designing exact reconstruction filter banks for tree-structured subband coders

Time-domain filter bank analysis: a new design theory

A 2.4 kbit/s MELP coder candidate for the new U.S. Federal Standard

A procedure for designing exact reconstruction filter banks for tree-structured subband coders

A new filter bank theory for time-frequency representation