The regularity analysis of multivariate refinable functions from generalized Bernstein bases and application in remote sensing image compression

Abstract

In this paper, we investigate the smoothness properties of multivariate refinable functions based on generalized Bernstein bases in terms of the spectral radius of the corresponding transition operator restricted to a suitable finite-dimensional invariant subspace, and present a general algorithm to construct biorthogonal scaling functions φ and with the largest possible regularity. Moreover, a new family of the parameterization of filters with symmetry are constructed. We explore the applicability of the transforms presented in this paper to remote sensing image compression at high compression rates, and the results of the experiments show that the performance is outstanding.

Keywords:

• generalized Bernstein bases
• biorthogonal wavelets
• parameterization of filters
• symmetry

2000 AMS Subject Classification :

• 42C40
• 65T60
• 68U10
• 62H35
• 94A08

Acknowledgements

The authors would like to thank the referees who have reviewed it four times. Supported by the NSFC (60505007) and NSFC (60775018), the Equipment Advanced Research Project and the program for New Century Excellent Talents in University. The research was carried out in the State Key Laboratory of Virtual Reality Technologies.

Notes

References 1 2,6–10,12 14 15 17, although not cited in the text, are beneficial to this paper.