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Blur identification and image restoration with the expectation-maximization algorithm

The iterative expectation-maximization (EM) algorithm for identifying unknown blur, noise, and image parameters under Gaussian modeling assumptions is described. A new form of the equations updating parameter estimates is given, from which convergence conditions and symmetry properties of the parameter estimates are derived. The frequency domain resolution defined by the digital image is not appropriate for accurate parameter estimation. Instead, a version of the EM algorithm with frequency resolution appropriate for the blur point spread function (PSF) is proposed. Results are presented from a test of the reduced resolution algorithm, in which the importance of the initial PSF is studied.