A library of biorthogonal wavelet transforms originated from polynomial splines

Amir Z. Averbuch*, Valery A. Zheludev

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review


We present a library of biorthogonal wavelet transforms and the related library of biorthogonal symmetric waveforms. For the construction we use interpolatory, quasiinterpolatory and smoothing splines with finite masks (local splines). With this base we designed a set of perfect reconstruction infinite and finite impulse response filter banks with linear phase property. The construction is performed in a "lifting" manner. The developed technique allows to construct wavelet transforms with arbitrary prescribed properties such as the number of vanishing moments, shape of wavelets, and frequency resolution. Moreover, the transforms contain some scalar control parameters which enable their flexible tuning in either time or frequency domains. The transforms are implemented in a fast way. The transforms, which are based on interpolatory splines, are implemented through recursive filtering. We present encouraging results towards image compression.

Original languageEnglish
Pages (from-to)323-334
Number of pages12
JournalProceedings of SPIE - The International Society for Optical Engineering
StatePublished - 2001
EventWavelets: Applications in Signal and Image Processing IX - San Diego, CA, United States
Duration: 30 Jul 20011 Aug 2001


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