<title>Library of biorthogonal wavelet transforms originated from polynomial splines</title>

We present a library of biorthogonal wavelet transforms and the related library of biorthogonal symmetric wave- forms. For the construction we use interpolatory, quasiinterpolatory and smoothing splines with finite masks (local splines). On this base we designed a set of perfect reconstruction infinite and finite impulse response filter banks with the 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 number of vanishing moments, shape of wavelets, 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 manner. The transforms based on interpolatory splines are implemented through recursive filtering.We present encouraging results of applicarion of devised wavelet transforms to image compression.