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 time-series 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 AmericaFull Article | PDF Article
S. D. Silverstein and J. M. Pimbley
J. Opt. Soc. Am. A 7(3) 356-372 (1990)
Barry J. Rye and R. Michael Hardesty
Appl. Opt. 28(5) 879-891 (1989)
Luc Gilles, Brent L. Ellerbroek, and Curtis R. Vogel
Appl. Opt. 42(26) 5233-5250 (2003)