Approximation by Woven Frames

This paper focuses on the approximation by woven frames in separable Hilbert spaces. We present an iterative method to approximate a signal $f$ based on a given weaving frame, by defining a recursive sequence that converges to the signal $f$. We show that this method converges to a signal that minimizes a specific functional involving the frame coefficients of the given weaving frame. The importance of this method is better understood when the weaving frame used has a large condition number, and the classical frame algorithm is unusable. It is necessary to point out that all numerical experiments in this paper were performed on a 64-bit 2.4 GHz Core i5 processor and 4.00 GB RAM using MATLAB version R2010a.