Abstract
This chapter is designed to provide the reader with an overview of two-dimensional transforms and their uses in digital picture processing by general purpose computers. The notation is selected such that casual familiarity with matrix algebra should be sufficient to grasp the basic principles of image coding and restoration in conjunction with the use of two-dimensional image transforms. The chapter is presented in a sequence of mathematical development followed by image coding examples from both the spatial and transform domain viewpoints. Object restoration is discussed in some detail in which numerical techniques in matrix algebra are utilized to avoid singular restorations. The observant reader will note that the assumption of separability becomes a key factor in many of the formulations set forth in the chapter. The chapter contains both tutorial material as well as quite recent object restoration procedures, and it is the author’s hope that the common framework of two-dimensional transforms and matrix quadratic forms successfully provide the reader with a smooth continuum in transition between the more tutorial material and newer processing results.
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Andrews, H.C. (1975). Two-Dimensional Transforms. In: Huang, T.S. (eds) Picture Processing and Digital Filtering. Topics in Applied Physics, vol 6. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-41612-9_2
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DOI: https://doi.org/10.1007/978-3-662-41612-9_2
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