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Proceedings Paper

Decomposition and inversion of von Neumann-like convolution operators
Author(s): Zohra Z. Manseur; David C. Wilson
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Paper Abstract

Methods are presented for the decomposition of two-dimensional von Neumann-like convolution operators into sums and products of smaller von Neumann-like operators. Consequences of the techniques include the face that ever second-order operator is the sum and product of five or fewer first-order operators. A totally symmetric second-order operator can be written as the sum and product of three or fewer first-order operators. In general, an nth-order von Neumann-like operator can always be written as the sum and product of three lower order operators. The following inversion result is also discussed. If the (circulant) von Neumann mean filter operator is defined on a square coordinate set with n rows and n columns, then it fails to be invertible only if either the integer 5 divides n or the integer 6 divides n. This result provides a partial solution to a question posed by P. Gader.

Paper Details

Date Published: 1 July 1991
PDF: 10 pages
Proc. SPIE 1568, Image Algebra and Morphological Image Processing II, (1 July 1991); doi: 10.1117/12.46113
Show Author Affiliations
Zohra Z. Manseur, Univ. of Florida (United States)
David C. Wilson, Univ. of Florida (United States)

Published in SPIE Proceedings Vol. 1568:
Image Algebra and Morphological Image Processing II
Paul D. Gader; Edward R. Dougherty, Editor(s)

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