Riesz frames and approximation of the frame coefficients

摘要

A frame is a fmaily {f_i}~∞_i=1 of elements in a Hilbert space H with the property that every element in H can be written as a (in finite) linear combination of the frame elements. Frame theory describes how one can choose the corresponding coefficients, which are called frame coef- ficients. From the mathematical point of view this is gratifying, but for applications it is a problem that the calculation requires inversion of an operator on H. The projection method is introduced in order to avoid this problem. The basic idea is to con- sider finite subfamilies {f_i}~n_i=1 of the frame and the orthogonal projection P_n onto its span.