Local Fourier dictionary: a natural tool for data analysis

Naoki Saito

doi:10.1117/12.366817

26 October 1999 Local Fourier dictionary: a natural tool for data analysis

Naoki Saito

Proceedings Volume 3813, Wavelet Applications in Signal and Image Processing VII; (1999) https://doi.org/10.1117/12.366817
Event: SPIE's International Symposium on Optical Science, Engineering, and Instrumentation, 1999, Denver, CO, United States

Abstract

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 such images.

Citation Download Citation

Naoki Saito "Local Fourier dictionary: a natural tool for data analysis", Proc. SPIE 3813, Wavelet Applications in Signal and Image Processing VII, (26 October 1999); https://doi.org/10.1117/12.366817

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