Representing spectral functions using symmetric extension

Fijoy Vadakkumpadan; Yinlong Sun

doi:10.1117/12.587791

17 January 2005 Representing spectral functions using symmetric extension

Fijoy Vadakkumpadan, Yinlong Sun

Proceedings Volume 5667, Color Imaging X: Processing, Hardcopy, and Applications; (2005) https://doi.org/10.1117/12.587791
Event: Electronic Imaging 2005, 2005, San Jose, California, United States

Abstract

This paper proposes an accurate, compact, and generic method for representing spectral functions. The focus is on smooth functions, the case of most natural spectra. While pursuing the idea of using Fourier series expansion for its advantage in representation generality, we attempt to remove the problem of Gibbs phenomenon. The solution that we propose is a new method called symmetric extension. Given a smooth spectral function S1, we first generate a new function S2 which is a mirror reflection of S1 about the upper bound of the wavelength domain. Then we create another function U that merges S1 and S2, and apply Fourier expansion to U. Because the values of U at its boundaries are equal, Gibbs oscillation is largely reduced. Besides, since U is self symmetric, all sine terms in Fourier expansion vanish and therefore we only need to keep the cosine coefficients. These make our method not only accurate, but also compact. We have tested the method with a large number of real spectra of various types, and compared with the existing methods such as direct Fourier expansion and linear model. The numerical results have confirmed the advantages of the proposed method.

Citation Download Citation

Fijoy Vadakkumpadan and Yinlong Sun "Representing spectral functions using symmetric extension", Proc. SPIE 5667, Color Imaging X: Processing, Hardcopy, and Applications, (17 January 2005); https://doi.org/10.1117/12.587791

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