MUSIC Algorithm for Two-Dimensional Inverse Problems With Special Characteristics of Cylinders

A multiple signal classification (MUSIC) algorithm is proposed to determine the positions of small cylinders, which have some special characteristics that may lend traditional MUSIC unsuccessful. The TM case is discussed in detail. Up to three independent currents are induced on each cylinder in the TM case. However, for a cylinder, if the material property is the same as the background medium in one or two of the principal axes, or if the geometry makes one or two of the induced currents very small with respect to the others (so as to be negligible in noisy scenario), the number of significant sources may be less than three and the traditional MUSIC may fail in locating the cylinder. In such event, knowledge of the direction of the induced source becomes mandatory to locate the cylinder. The proposed method determines the direction of the induced source and uses the background Green's function corresponding to it as MUSIC's test function. The method uses minimization of the analytical expressions and gives good results in noise-free as well as noisy scenarios.