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

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 and [image omitted] 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.