Approximation of the Frame Coefficients Using Finite Dimensional Methods

Abstract

A frame is a family { f,} ~ 1 of elements in a Hilbert space . Y with the property that eve,y element in. Y can be written as a (infinite) linear combination of the frame elements. Frame theo,y describes how one can choose the corresponding coefficients, which are called frame coefficients. 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. Y. The projection method is introduced to avoid this problem.