## State-space and singular-value decomposition-based approximation methods for the harmonic retrieval problem

JOSA, Vol. 73, Issue 12, pp. 1799-1811 (1983)

http://dx.doi.org/10.1364/JOSA.73.001799

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### 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

**Citation**

S. Y. Kung, K. S. Arun, and D. V. Bhaskar Rao, "State-space and singular-value decomposition-based approximation methods for the harmonic retrieval problem," J. Opt. Soc. Am. **73**, 1799-1811 (1983)

http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-73-12-1799

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