Discrete Complex Image Method With Automatic Order Selection

The discrete complex image method (DCIM) has been well-established and widely employed as a tool to compute spatial-domain Green's functions in planar multilayered media. Although the use of the DCIM in conjunction with the method of moments has been quite satisfactory for the efficient analysis of printed structures in layered media, it has not been considered much as a legitimate tool for commercial applications. Up until recently, there has been mainly two reasons for the reluctance of its acceptance in commercial products: the lack of a proper error criterion in the spatial domain and the manual selection of the order of images. As the former shortcoming has recently been eliminated by establishing a proper error criterion in the spatial domain, this paper intends to propose a viable solution for the latter problem, i.e., for the choice of the number of images. Note that, thus far, this choice has been based on the number of significant singular values obtained as a by-product of the method, which is neither rigorous, nor optimum in any sense, and renders it nonrobust and unreliable. As a remedy for this remaining shortcoming, a model selection approach known as minimum description length (MDL) has been introduced into the algorithm of the DCIM with success. The MDL approach, exploiting the regularities in the data, selects the order of the model based on the tradeoff between the quality of fitting and complexity of the model.