Frame Construction Method Bsaed On Quantum Measurement

Frame theory plays an important role in the theory of signal processing besides the wavelet theory.Quantum signal processing provides new ideas for the method of processing signal.Our objective of this paper is new model for signal processing,especially frame expansion analysis,based on the study of basic theory of the quantum imformation.Cognitive Maps is an important graphic means of representing causal relationship between concepts and analyzing inference patterns.We for first time propose a Quantum Cognitive Map Model which introduce quantum information theory into Cognitive Maps.The advantage of the model is more information preserving and better approaching the real world.We also apply the quantum information theory into the frame theory.Our goal is to propose the frame reconstruction method without phase information.First,theory of quantum measurement and quantum tomogram is related to the frame theory.Then,we pose the concept of signal matrix,and presents two typical frames needed including SICPOVM and Maximal Mutually Unbiased bases. Finally,the robustness of this frames is discussed.