Expectation–maximization algorithm for regression, deconvolution and smoothing of shot‐noise limited data

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Abstract
A simple algorithm for deconvolution and regression of shot‐noise‐limited data is illustrated in this paper. The algorithm is easily adapted to almost any model and converges to the global optimum. Multiple‐component spectrum regression, spectrum deconvolution and smoothing examples are used to illustrate the algorithm. The algorithm and a method for determining uncertainties in the parameters based on the Fisher information matrix are given and illustrated with three examples. An experimental example of spectrograph grating order compensation of a diode array solar spectroradiometer is given to illustrate the use of this technique in environmental analysis. The major advantages of the EM algorithm are found to be its stability, simplicity, conservation of data magnitude and guaranteed convergence.