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Optical Engineering

Parallel discrete and continuous wavelet transforms
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Paper Abstract

We consider theoretically the optical implementations of both discrete and continuous wavelet transforms. Discrete wavelet transforms (DWTs) require sums (or integrals) of the product of the input function with multiple stored functions (wavelets with various shifts and scales). The inverse DWT requires the same, exceptthe given function is replaced by the wavelet coefficients determined by the DWT. We show that we can store and utilize in parallel large banks of wavelets. This should allow "instantaneous" DWT of functions of a single variable and (relatively) fast DWTs of two-dimensional functions. Of course, the same applies to the inverse DWTs. A true continuous wavelet transform (CWT) must be continuous in both shift and scale. By means of a continuous anamorphic transformation of a one-dimensional signal and a suitable choice of kernel or filter, we can allow a normal two-dimensional optical Fourier transform image processor to perform a CWT.

Paper Details

Date Published: 1 September 1992
PDF: 5 pages
Opt. Eng. 31(9) doi: 10.1117/12.59915
Published in: Optical Engineering Volume 31, Issue 9
Show Author Affiliations
H. John Caulfield, Alabama A&M Univ. (United States)
Harold H. Szu, Naval Surface Warfare Ctr. (United States)

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