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Discrete complex image method with spatial error criterion and automatic order selection

Two shortcomings of the otherwise very efficient and hence very popular DCIM approach are remedied in this study. First shortcoming is the lack of an error metric that transforms the spatial-domain error to the spectral domain. In standard DCIM procedures, OLS error minimization in the spectral domain does not correspond to the error minimization in the spatial domain. We propose an error criterion by defining an error metric in the spatial domain and mapping it to the spectral domain. Second, by using the proposed spatial error criterion we propose an automatic order selection procedure to find the number of exponentials that describes the Green's function optimally by employing MDL principle to DCIM. The resulting DCIM algorithm is implemented on three-level DCIM and tested on a typical geometry for validation.