Publication

Construction of Biorthogonal Wavelets Starting from Any Two Multiresolutions

Michaël Unser
1998
Journal Articles

Abstract

Starting from any two given multiresolution analyses of $L _{ 2 }$ , $\{V ^{ 1 } _{ j } \} _{ j \in Z }$ , and $\{V ^{ 2 } _{ j } \} _{ j \in Z }$ , we construct biorthogonal wavelet bases that are associated with this chosen pair of multiresolutions. Thus, our construction method takes a point of view opposite to the one of Cohen-Daubechies-Feauveau (CDF), which starts from a well-chosen pair of biorthogonal discrete filters. In our construction, the necessary and sufficient condition is the nonperpendicularity of the multiresolutions.

Official source

https://infoscience.epfl.ch/entities/publication/51f4a9c8-8b27-4501-a4e2-6335ffee4022

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Michaël Unser
1998
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/51f4a9c8-8b27-4501-a4e2-6335ffee4022

About this result

Related concepts (10)

Wavelet

A wavelet is a wave-like oscillation with an amplitude that begins at zero, increases or decreases, and then returns to zero one or more times. Wavelets are termed a "brief oscillation". A taxonomy of wavelets has been established, based on the number and direction of its pulses. Wavelets are imbued with specific properties that make them useful for signal processing. For example, a wavelet could be created to have a frequency of Middle C and a short duration of roughly one tenth of a second.

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Construction is a general term meaning the art and science to form objects, systems, or organizations, and comes from Latin constructio (from com- "together" and struere "to pile up") and Old French construction. To construct is the verb: the act of building, and the noun is construction: how something is built, the nature of its structure. In its most widely used context, construction covers the processes involved in delivering buildings, infrastructure, industrial facilities, and associated activities through to the end of their life.

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Construction management (CM) is a professional service that uses specialized, project management techniques and software to oversee the planning, design, construction and closeout of a project. The purpose of construction management is to control the quality of a project's scope, time / delivery and cost—sometimes referred to as a project management triangle or "triple constraints." CM is compatible with all project delivery systems, including design-bid-build, design-build, CM At-Risk and Public Private Partnerships.

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