Spectral estimation is at the core to all spectrally based detection systems rather they be infrared (IR) or Raman based technologies, the standard method of spectral inference assumes a Gaussian model for the data. A less well known but alternative spectral representation can be based on a nonhomogeneous Poisson process in the frequency domain which leads to a new likelihood function that can be used for spectral inference. In particular, the very important problems of spectral estimation and spectral classiﬁcation can be approached with this new likelihood function. If an exponential model is assumed, then the parameter estimation reduces to a simple convex optimization for the spectral estimation problem. For the classiﬁcation problem with known spectra the classiﬁcation performance based on the Poisson likelihood function is shown by simulation to outperform the Gaussian classiﬁer in terms of robustness. Finally, a perfect analogy between the Poisson likelihood measure and the Kullback-Leibler measure for probability density functions is established and discussed.
Darren K. Emge, "Poisson maximum likelihood spectral inference (Conference Presentation)," Proc. SPIE 10646, Signal Processing, Sensor/Information Fusion, and Target Recognition XXVII, 106461G (Presented at SPIE Defense + Security: April 19, 2018; Published: 5 October 2018); https://doi.org/10.1117/12.2305198.5783301349001.
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