Redundancity of Frames and Its Effects on the Wavelet Reconstruction
Wei-Ping Zhi, Cao Huaixin · Journal of Baoji University of Arts and Sciences · 2007
Aim A characterization for the redundancity of a frame is established. Methods A new definition on redundancity of a frame is presented. A frame of Hubert space is known as redundant if there exists a proper subset of the index set such that is also a frame. Otherwise, the frame is known as nonredundant. Results Necessary and sufficient conditions for a frame to be redundant are given. Especially, it is proved that a frame is nonredundant if and only if it is a Riesz basis, Conclusion The results show that the error in wavelet reconstruction with redundant frames is less than that with or thonormal basis.