Coherent Optical Wavelet Transforms

Yao Li

After a successful application to the analysis of seismic data in 1984, geophysicist J. Morlet1 formalized the concept of wavelets by generalizing similar mathematical and physical decomposition concepts from the previous works of Harr (1910), Gabor (1946), Calderon (1964), etc.. Closely related to the concept of pyramids, the key component of the wavelet theory is a set of look-alike functions called wavelets that can form an efficient and powerful decomposition basis. Any square-integrable signal can be selected as the so-called mother wavelet that, in turn, generates a family of daughter wavelets by dilations.

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