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Least-squares spectral analysis (LSSA) is a method of estimating a frequency spectrum, based on a least squares fit of sinusoids to data samples, similar to Fourier analysis.〔 Fourier analysis, the most used spectral method in science, generally boosts long-periodic noise in long gapped records; LSSA mitigates such problems. LSSA is also known as the Vaníček method after Petr Vaníček, and as the Lomb method〔 (or the Lomb periodogram) and the Lomb–Scargle method (or Lomb–Scargle periodogram), based on the contributions of Nicholas R. Lomb〔 and, independently, Jeffrey D. Scargle.〔 Closely related methods have been developed by Michael Korenberg and by Scott Chen and David Donoho. ==Historical background== The close connections between Fourier analysis, the periodogram, and least-squares fitting of sinusoids have long been known. Most developments, however, are restricted to complete data sets of equally spaced samples. In 1963, J. F. M. Barning of Mathematisch Centrum, Amsterdam, handled unequally spaced data by similar techniques, including both a periodogram analysis equivalent to what is now referred to the Lomb method, and least-squares fitting of selected frequencies of sinusoids determined from such periodograms, connected by a procedure that is now known as matching pursuit with post-backfitting or orthogonal matching pursuit.〔Y. C. Pati, R. Rezaiifar, and P. S. Krishnaprasad, "Orthogonal matching pursuit: Recursive function approximation with applications to wavelet decomposition," in ''Proc. 27th Asilomar Conference on Signals, Systems and Computers,'' A. Singh, ed., Los Alamitos, CA, USA, IEEE Computer Society Press, 1993.〕 Petr Vaníček, a Canadian geodesist of the University of New Brunswick, also proposed the matching-pursuit approach, which he called "successive spectral analysis" and the result a "least-squares periodogram", with equally and unequally spaced data, in 1969. He generalized this method to account for systematic components beyond a simple mean, such as a "predicted linear (quadratic, exponential, ...) secular trend of unknown magnitude", and applied it to a variety of samples, in 1971. The Vaníček method was then simplified in 1976 by Nicholas R. Lomb of the University of Sydney, who pointed out its close connection to periodogram analysis. The definition of a periodogram of unequally spaced data was subsequently further modified and analyzed by Jeffrey D. Scargle of NASA Ames Research Center, who showed that with minor changes it could be made identical to Lomb's least-squares formula for fitting individual sinusoid frequencies. Scargle states that his paper "does not introduce a new detection technique, but instead studies the reliability and efficiency of detection with the most commonly used technique, the periodogram, in the case where the observation times are unevenly spaced," and further points out in reference to least-squares fitting of sinusoids compared to periodogram analysis, that his paper "establishes, apparently for the first time, that (with the proposed modifications) these two methods are exactly equivalent."〔 Press〔 summarizes the development this way: Michael Korenberg of Queen's University in 1989 developed the "fast orthogonal search" method of more quickly finding a near-optimal decomposition of spectra or other problems,〔 similar to the technique that later became known as orthogonal matching pursuit. In 1994, Scott Chen and David Donoho of Stanford University have developed the "basis pursuit" method using minimization of the L1 norm of coefficients to cast the problem as a linear programming problem, for which efficient solutions are available.〔 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Least-squares spectral analysis」の詳細全文を読む スポンサード リンク
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