Compactly Supported Tight and Sibling Frames Based on Generalized Bernstein Polynomials. (27th June 2016)

• Record Type: Journal Article
• Authors: Cheng, Ting; Yang, Xiaoyuan
• Other Names: Solimene Raffaele Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2016(2016)
• Publication Date: 2016-06-27
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2016/2463673
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : We obtain a family of refinable functions based on generalized Bernstein polynomials to provide derived properties. The convergence of cascade algorithms associated with the new masks is proved, which guarantees the existence of refinable functions. Then, we analyze the symmetry, regularity, and approximation order of the refinable functions, which are of importance. Tight and sibling frames are constructed and interorthogonality of sibling frames is demonstrated. Finally, we give numerical examples to explicitly illustrate the construction of the proposed approach.