The inverse source problem of electromagnetics: Linear inversion formulation and minimum energy solution

We address the inverse source problem of finding the time-harmonic current distribution (source) with minimum L-2 norm (minimum energy) that generates a prescribed electromagnetic field outside the source's region of support. Using the well-known multipole expansion of the electromagnetic field we compute (via a Linear operator formalism) the sought-after minimum L2 norm-current distribution consistent with the data.