Some topics on optimal dual frames in Hilbert spaces

Document Type : Expository article (original)

Authors

• Fahimeh Arabyani-Neyshaburi
• Ali Akbar Arefijamaal

Faculty of Mathematics and Computer Sciences, Hakim Sabzevari University, Sabzevar, IRAN

10.22067/tmsj.2021.41429

Abstract

In data transmissions usually a part of the data vectors are reshaped or erased, and we need to perform the reconstruction by using the partial information at hand. Hence, one of the deepestand most precious problems in frame theory is optimal dual problem, which asks for finding the best dual frames that minimize the reconstruction errors when erasures occur. In this paper, we will review on application of dual frames in signal processing, then we mention optimal reconstruction problem and some achievements and finally we state some open problems in this respect for readers.



 

Keywords

• Frames
• dual frames
• optimal duals
• reconstruction formulas

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