A construction of convergent cascade algorithms in Sobolev spaces

作者：Chen, Di-Rong^*

来源：International Journal of Wavelets, Multiresolution and Information Processing, 2007, 5(5): 685-697.

DOI：10.1142/S0219691307001987

• wavelet
• vector cascade algorithm
• refinable vector
• Sobolev space
• factorization of matrix mask
• joint spectral radius
• matrix subdivision operator

Cascade algorithms play an important role in wavelet analysis and computer graphics. The paper considers the convergence of cascade algorithms in Sobolev spaces. With the help of the factorization of matrix masks, we give a sufficient condition for the convergence. The condition is expressed in the time domain. More importantly, an algorithm for the construction of convergent cascade algorithms in Sobolev space starting from any matrix mask satisfying a mild condition is presented. Examples are given to illustrate our theorems.

• 出版日期2007-9
• 单位北京航空航天大学