Scattering matrix decomposition in microwave imaging of realistic numerical breast phantoms

A scattering matrix is formed using a discrete approximation of the exact scattering relation between observed fields and the contrast profile of a three-dimensional numerical breast phantom. The numerical regime allows observation of the exact fields over the imaging volume and the subsequent analysis of the information content of the scattering data. A technique using the singular value decomposition is employed to evaluate the effective rank of the scattering system and an upper bound on image fidelity in the least-squares class of solutions. The analyses illustrate the information content of various sets of scattering data and emphasize the increase in both resolution and signal-to-noise requirement as operating frequency increases.