Spectrum estimation from quantum-limited interferograms

• Published in: IEEE transactions on signal processing Vol. 52; no. 4; pp. 950 - 961
• Main Authors: Fuhrmann, D.R., Preza, C., O'Sullivan, J.A., Snyder, D.L., Smith, W.H.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.04.2004; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Applied sciences; Autocorrelation; Autocorrelation functions; Cramer-Rao bounds; Detection, estimation, filtering, equalization, prediction; Exact sciences and technology; Fast Fourier transforms; Fourier transforms; Geometrical optics; Hyperspectral imaging; Information, signal and communications theory; Least squares approximation; Mathematical models; Maximum likelihood estimation; Multiplexing; Noise; Optical interferometry; Optical noise; Parametrization; Signal and communications theory; Signal, noise; Solid modeling; Spectral analysis; Telecommunications and information theory; Fast Fourier transformation; interferometry; Signal estimation; Interferogram; Cramer-Rao bound; spectrum estimation; Spectrum; Hyperspectral imaging sensor; Least squares method; Signal processing; interferograms; Quantum limit; multiplex disadvantage; EM algorithm
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2004.824216

A quantitative model for interferogram data collected in a quantum-limited hyperspectral imaging system is derived. This model accounts for the geometry of the interferometer, the Poisson noise, and the parameterization of the mean of the noise in terms of the autocorrelation function of the incident optical signal. The Crame/spl acute/r-Rao bound on the variance of unbiased spectrum estimates is derived and provides an explanation for what is often called the "multiplex disadvantage" in interferometer-based methods. Three spectrum estimation algorithms are studied: maximum likelihood via the expectation-maximization (EM) algorithm, least squares (LS), and the fast Fourier transform (FFT) with data precorrection. Extensive simulation results reveal advantages and disadvantages with all three methods in different signal-to-noise ratio (SNR) regimes.