Exact ML estimation of spectroscopic parameters

In a paper on spectroscopic imaging Spielman et al. (1988) made the important point that apriori information about the compounds present can and should be incorporated into the estimation of spectroscopic signal parameters. They proposed using the maximum likelihood (ML) approach for parameter estimation, but failed to incorporate properly the full apriori information that was assumed to be available. Consequently they ended-up with a spectroscopic imaging method that is only a suboptimal approximation of the ML method. In this paper we derive the exact ML method, present a computationally efficient implementation of it and illustrate numerically the performance gain that can be achieved over the method of Spielman et al.