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A wreath product group approach to signal and image processing .II. Convolution, correlation, and applications

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5 Author(s)
G. Mirchandani ; Dept. of Electr. & Comput. Eng., Vermont Univ., Burlington, VT, USA ; R. Foote ; D. N. Rockmore ; D. Healy
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For pt.I see ibid., vol.48, no.1, p.102-32 (2000). This paper continues the investigation of the use of spectral analysis on certain noncommutative finite groups-wreath product groups-in digital signal processing. We describe the generalization of discrete cyclic convolution in convolution over these groups and show how it reduces to multiplication in the spectral domain. Finite group-based convolution is defined in both the spatial and spectral domains and its properties established. We pay particular attention to wreath product cyclic groups and further describe convolution properties from a geometric view point in terms of operations with specific signals and filters. Group-based correlation is defined in a natural way, and its properties follow from those of convolution (the detection of similarity of perceptually similar signals) and an application of correlation (the detection of similarity of group-transformed signals). Several examples using images are included to demonstrate the ideas pictorially

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IEEE Transactions on Signal Processing  (Volume:48 ,  Issue: 3 )