Wavelets for image processing, in Handbook of Applied Mathematics (J. Satsuma, S. Oishi, and M. Sugihara, eds.), Asakura Publishing Co., pp.512-515, 2013 (in Japanese).

Abstract

This section discusses how wavelets and related techniques are used in image processing, and particularly focuses on image approximation, compression, denoising, and feature extraction. One of the main reasons why wavelets are used for so many image processing applications is their capability to efficiently capture and compactly represent singular image features such as edges and corners compared to the Fourier or cosine transforms. Wavelets in image processing has a long history. Marr's research on visual information processing in late 1970s and the Laplacian pyramid of Burt and Adelson in early 1980s significantly influenced the development of the Multiresolution Analysis by Mallat and the compactly supported wavelet orthonormal basis by Daubechies.

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