Image Processing and the Arithmetic Fourier Trans-form

D W Tufts; Z Fan; Z Cao

doi:10.1117/12.951665

17 May 1989 Image Processing and the Arithmetic Fourier Trans-form

D W Tufts, Z Fan, Z Cao

Proceedings Volume 1058, High Speed Computing II; (1989) https://doi.org/10.1117/12.951665
Event: OE/LASE '89, 1989, Los Angeles, CA, United States

Abstract

A new Fourier technique, the Arithmetic Fourier Transform (AFT) was recently developed for signal processing. This approach is based on the number-theoretic method of Mobius inversion. The AFT needs only additions except for a small amount of multiplications by prescribed scale factors. This new algorithm is also well suited to parallel processing. And there is no accumulation of rounding errors in the AFT algorithm. In this paper, the AFT is used to compute the discrete cosine transform and is also extended to 2-D cases for image processing. A 2-D Mobius inversion formula is proved. It is then applied to the computation of Fourier coefficients of a periodic 2-D function. It is shown that the output of an array of delay-line (or transversal) filters is the Mobius transform of the input harmonic terms. The 2-D Fourier coefficients can therefore be obtained through Mobius inversion of the output the filter array.

Citation Download Citation

D W Tufts, Z Fan, and Z Cao "Image Processing and the Arithmetic Fourier Trans-form", Proc. SPIE 1058, High Speed Computing II, (17 May 1989); https://doi.org/10.1117/12.951665

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