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Approximation by Woven Frames
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DOI：10.22130/scma.2025.2056750.2127.png)
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Abstract
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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.
Keywords:
Hilbert space
Approximation
Frame
Woven frame
Weaving frame
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