Abstract

We present new high-resolution methods for the problem of retrieving sinusoidal processes from noisy measurements. The approach taken is by use of the so-called principal-components method, which is a singular-value-decomposition- based approximate modeling method. The low-rank property and the algebraic structure of both the data matrix and the covariance matrix (under noise-free conditions) form the basis of exact modeling methods. In a noisy environment, however, the rank property is often perturbed, and singular-value decomposition is used to obtain a low-rank approximant in factored form. The underlying algebraic structure of these factors leads naturally to least-squares estimates of the state-space parameters of the sinusoidal process. This forms the basis of the Toeplitz approximation method, which offers a robust Pisarenko-like spectral estimate from the covariance sequence. Furthermore, the principle of Pisarenko's method is extended to harmonic retrieval directly from timeseries data, which leads to a direct-data approximation method. Our simulation results indicate that favorable resolution capability (compared with existing methods) can be achieved by the above methods. The application of these principles to two-dimensional signals is also discussed.

© 1983 Optical Society of America

» View Full Text: Acrobat PDF (1593 KB)

References

Please [login to View References]

Author Affiliations

S. Y. Kung, K. S. Arun, D. V. Bhaskar Rao

Department of Electrical Engineering—Systems, University of Southern California, University Park, Los Angeles, California 90089-0272

Cited By

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Advanced Search

Recent ToC Categories (Beta)

• Oct 08 2009 : See the latest ISP articles in the Applied Optics feature on Digital Holography in 3-D Imaging.
• Sep 25 2009 : Energy Express: Optics Express announces a special bi-monthly supplement dedicated to rapid developments in optics for sustainable energy.
• Sep 21 2009 : The 2009 Education and Training in Optics and Photonics papers are now available.

More News

• Invisibility Visualized
  Nov 12, 2009 - Scientists and curiosity seekers who want to know what a partially or... more
• Diamonds are a Laser's Best Friend
  Sep 18, 2009 - Tomorrow’s lasers may come with a bit of bling, thanks to a new... more
• Open Wide and Say ‘Zap’
  Aug 19, 2009 - A group of researchers in Australia and Taiwan has developed a new... more