Minimal Object Characterizations Using Harmonic Generalized Polarizability Tensors and Symmetry Groups

We introduce a new type of object characterization, which is capable accurately describing small isolated inclusions for potential field inverse problems such as in electrostatics, magnetostatics, and related low frequency Maxwell problems. Relevant applications include characterizing ferrous unexploded ordnance from magnetostatic measurements magnetometry, conducting medical imaging using electrical impedance tomography, performing geological ground surveys resistivity imaging, objects by electrosensing fish to navigate identify food, the effective properties dilute composites. Our characterization builds on generalized polarizability tensor (GPT) concept provides an alternative contracted GPT. call characterizations harmonic GPTs (HGPTs) their coefficients correspond products polynomials. Then, we show that number independent HGPTs needed characterize can be significantly reduced considering symmetry group propose systematic approach determining subspace symmetric polynomials fixed its dimension. This enables us determine HGPT different groups.