Matrix methods of constructing wavelet filters and discrete hyper-wavelet transforms

Optimal model for biorthogonal wavelet filters

“…6 The first author of this work put forward a new concept for discrete hyper-wavelet transforms. 3 It is substantially independent of the continuous wavelet theory, but it is a useful tool for solving some problems of wavelet theory. With this concept, the scope of wavelets is enlarged, making it possible to find better wavelets in a wider scope.…”

An Excellent Wavelet for Image and Video Compression

“…Matrix M loses its orthogonality which is 2-circular matrix [3] of a biorthogonal wavelet, so T MM is no longer unitary. Paper [5] has proved that if λ is an eigenvalue of matrix…”

“…In the same wavelet family, we can use the degree of eigenvalues being close to 1 to measure ' M s orthogonal degree. The eigenvalues of T MM for CDF97 in the case of minimal matrix [3] Fig.2 and Fig.3 are the spectral radius of W97 and CDF97 transform matrix, respectively. Horizontal coordinate denotes the order of matrix, Vertical coordinate denotes the spectral radius of matrix.…”

“…Guoqiu Wang ever put forward a set of methods to construct the wavelet filters based on algebra structure [3] . In paper [4] , a family of generic 9-7-tap wavelets was constructed which containing a parameter.…”

Spectral Radius of Biorthogonal Wavelets With Its Application

“…(1.5) and (1.6) can be rewritten as the form of 2-circular matrix [10], which can be defined by the 2-circular operator.…”