Theoretical analysis of the projection error onto discrete wavelet subspaces | Zendy

Thierry Blu | Zendy; Michaël Unser | Zendy

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<title>Theoretical analysis of the projection error onto discrete wavelet subspaces</title>

Author(s) -

Thierry Blu,

Michaël Unser

Publication year - 1999

Publication title -

proceedings of spie, the international society for optical engineering/proceedings of spie

Language(s) - English

Resource type - Conference proceedings

SCImago Journal Rank - 0.192

H-Index - 176

eISSN - 1996-756X

pISSN - 0277-786X

DOI - 10.1117/12.366787

Subject(s) - biorthogonal system , mathematics , orthonormal basis , linear subspace , filter bank , wavelet , projection (relational algebra) , algorithm , finite impulse response , discrete wavelet transform , norm (philosophy) , filter (signal processing) , wavelet transform , discrete mathematics , computer science , pure mathematics , physics , quantum mechanics , artificial intelligence , political science , law , computer vision

A filterbank decomposition can be seen as a series of projections onto several discrete wavelet subspaces. In thispresentation, we analyze the projection onto one of them---the low-pass one, since many signals tend to be low-pass.We prove a general but simple formula that allows the computation of the `2-error made by approximating the signalby its projection. This result provides a norm for evaluating the accuracy of a complete decimation/interpolationbranch for arbitrary analysis and...

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