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.
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