Representation and compression of operators in bases of second-generation wavelets using the lifting scheme

Focuses on the representation of differential operator in second-generation wavelet (SGW) domain. One kind of polynomial biorthogonal interpolating wavelet (PBIW) using the lifting scheme is constructed. The non-standard form representation of operators in bases of general lifting biorthogonal interpolating wavelets (BIW) and surface wavelets is obtained. Furthermore, an optimal design criterion of adaptive filters for operator compression is proposed.