Recoverability-guided reduced-target inversion for microwave imaging: a synthetic breast-imaging study

Microwave breast-imaging inversions are often formulated in latent or constitutive parameter spaces that include variables that may not be independently recoverable for a given measurement configuration. This paper presents a recoverability-guided reduced-target inversion framework in which the inverse target is constructed from measurement-supported directions of a noise-weighted local Jacobian. Candidate latent variables are classified as observable, weakly inferable, or strongly confounded. Separable variables are retained, whereas strongly confounded variables are represented by dominant composite descriptors. The weighting matrix is defined using the assumed measurement-noise covariance, such that observability is evaluated relative to measurement uncertainty. The method is demonstrated in a controlled synthetic microwave breast-imaging study using multifrequency transmission data acquired in craniocaudal and mediolateral oblique views. At the selected operating point, the reduced target retained a compact subset of the six-variable latent state, substantially improved the conditioning of the local Jacobian, and preserved the projected inversion error relative to unreduced latent-state inversion. The reduced target also outperformed a dimension-matched principal component analysis baseline under the tested noise conditions. These results support recoverability-guided target construction as a proof-of-concept strategy for acquisition-aware microwave inverse problems, rather than as clinical validation of microwave breast imaging.