Parallel discrete and continuous wavelet transforms

H. John Caulfield; Harold H. Szu

doi:10.1117/12.59915

1 September 1992 Parallel discrete and continuous wavelet transforms

H. John Caulfield, Harold H. Szu

Author Affiliations +

Optical Engineering, Vol. 31, Issue 9, (September 1992). https://doi.org/10.1117/12.59915

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.

Citation Download Citation

H. John Caulfield and Harold H. Szu "Parallel discrete and continuous wavelet transforms," Optical Engineering 31(9), (1 September 1992). https://doi.org/10.1117/12.59915

Published: 1 September 1992

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available