Abstract
In this paper, we present a quotient space approximation model of multiresolution signal analysis and discuss the properties and characteristics of the model. Then the comparison between wavelet transform and the quotient space approximation is made. First, when wavelet transform is viewed from the new quotient space approximation perspective, it may help us to gain an insight into the essence of multiresolution signal analysis. Second, from the similarity between wavelet and quotient space approximations, it is possible to transfer the rich wavelet techniques into the latter so that a new way for multiresolution analysis may be found.
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The work was supported by the National Natural Science Foundation of China (Grant Nos.60135010 and 60321002) and the National Basic Research 973 Program of China (Grant No.2004CB318108).
Ling Zhang graduated from Nanjing University in 1961. He is now a professor of Computer Science Department, and the director of Artificial Intelligence Institute, Anhui University, Hefei, China. His main research interests include applied mathematics, artificial intelligence, and machine learning. He has published more than 100 papers and 4 books in these fields.
Bo Zhang graduated from Tsinghua University in 1958. He is now a professor of Computer Science and Technology Department, Tsinghua University. His main research interests include artificial intelligence, robotics, intelligent control and pattern recognition. He has published about 130 papers and 3 books in these fields.
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Zhang, L., Zhang, B. A Quotient Space Approximation Model of Multiresolution Signal Analysis. J Comput Sci Technol 20, 90–94 (2005). https://doi.org/10.1007/s11390-005-0010-8
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DOI: https://doi.org/10.1007/s11390-005-0010-8