Wavelet and frame transforms originated from continuous and discrete splines

Amir Z. Averbuch, Valery A. Zheludev

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


New classes of diadic and triadic biorthogonal wavelets and wavelet-type frames in signal space are presented. The construction employs interpolatory filters with rational transfer functions that originate from continuous and discrete splines. These filters have linear phase. They are amenable either to fast cascading or parallel recursive implementation. The wavelets are applied to compression of still images, where they demonstrate a superb efficiency. Robust error recovery algorithms presented utilize the redundancy inherent in frame expansions. Experimental results recover images when (as much as) 60% of the expansion coefficients are either lost or corrupted. The proposed approach inflates the size of the image through framelet expansion and multilevel decomposition, thus providing redundant representation of the image.

Original languageEnglish
Title of host publicationAdvances in Nonlinear Signal and Image Processing
PublisherHindawi Publishing Corporation
Number of pages56
ISBN (Print)9775945550, 9789775945556
StatePublished - 2007

Publication series

NameEurasip Book Series on Signal Processing and Communications
ISSN (Print)1687-2789
ISSN (Electronic)1687-2797


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