Radka Turcajova Flinders Univ. and Cooperative Research Ctr. for Sensor Signal and Information Processing (United States) Jaroslav Kautsky Flinders Univ. and Cooperative Research Ctr. for Sensor Signal and Information Processing (Australia)
Because multiresolution analyses and wavelet bases are generated by translating and dilating scaling and wavelet functions, these functions must satisfy some special equations involving Toeplitz and Toeplitz-like operations. These relations can be exploited when such functions are to be constructed or their properties are studied. In the case of multiwavelets, where more than one scaling functions generate the multiresolution analysis, the corresponding operators are block Toeplitz-like. We discuss here some basic properties of these operators and compare them to the classical case of one scaling function. Using these observations we study the convergence of the cascade algorithm and derive sufficient conditions for existence of solution to a two-scale dilation equation.
"Block Toeplitz-like operators and multiwavelets", Proc. SPIE 2491, Wavelet Applications II, (6 April 1995); doi: 10.1117/12.205454; https://doi.org/10.1117/12.205454