框架的冗余性及其对小波重构的影响(英文)

Redundancity of frames and its effects on the wavelet reconstruction

目的给出框架冗余性的一个刻画。方法定义了冗余框架。如果一个框架的指标集存在一个真子集使得也是一个框架,那么就说这个框架是冗余的,否则它就是非冗余的。结果经过研究得出了框架冗余的充分必要条件。特别地,一个框架是非冗余的当且仅当它是一个Riesz基。结论这些结果表明用冗余框架进行小波重构要比用正规正交基进行小波重构的误差小。

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 Hilbert 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 orthonormal basis.