The local Fourier dictionary: A natural tool for data analysis, in Wavelet Applications in Signal and Image Processing VII (M. A. Unser, A. Aldroubi, and A. F. Laine, eds.), Proc. SPIE 3813, pp.610-624, 1999. Invited paper.
The local Fourier dictionary contains a large number of
localized complex exponential functions.
Representations of a function using the dictionary elements locally
inherit many nice properties of the conventional Fourier representation, such
as translation invariance and orientation selectivity.
In this paper, after giving an intuitive review of its construction,
we describe an algorithm to recover location-dependent shifts of local
features in signals for matching and registration, and propose a
best local translation basis selected from the local Fourier basis.
Then we will report our preliminary results on the statistical analysis of
natural scene images using the local Fourier dictionary, whose purpose is
to examine the importance of sparsity, statistical independence,
and orientation selectivities in representation and modeling of
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Get the official version via doi:10.1117/12.366817.
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