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Matrix Factorization for Image Processing

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Applied Matrix and Tensor Variate Data Analysis

Part of the book series: SpringerBriefs in Statistics ((JSSRES))

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Abstract

Some of important methods for signal processing, such as principal component analysis (PCA), independent component analysis (ICA), non-negative matrix factorization (NMF), and sparse representation (SR), can be discussed in a unified framework where a data matrix is decomposed into a product of two specific matrices. Differences of those methods are understood as different constraints on decomposed matrices. Characteristics of those methods are discussed and compared by giving examples of image processing.

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Acknowledgments

The author greatly appreciates Dr. Hideitsu Hino of University of Tsukuba and Mr. Toshiyuki Kato of Waseda University for their helpful comments and figures in Sects. 4.2 and 4.5.

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Authors and Affiliations

  1. Faculty of Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo, 169-8555, Japan

    Noboru Murata

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  1. Noboru Murata
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Correspondence to Noboru Murata .

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  1. Faculty of Design, Kyushu University, Fukuoka, Fukuoka, Japan

    Toshio Sakata

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Murata, N. (2016). Matrix Factorization for Image Processing. In: Sakata, T. (eds) Applied Matrix and Tensor Variate Data Analysis. SpringerBriefs in Statistics(). Springer, Tokyo. https://doi.org/10.1007/978-4-431-55387-8_4

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