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

Area of Science:

• Medical Imaging
• Electromagnetics
• Computational Science

Background:

• Microwave breast imaging inversions often use complex parameter spaces with non-recoverable variables.
• Existing methods struggle with ill-posed inverse problems due to measurement limitations.

Purpose of the Study:

• To develop a recoverability-guided inversion framework for microwave breast imaging.
• To construct an inverse target based on measurement-supported directions and noise-weighted Jacobians.

Main Methods:

• Classified candidate latent variables into observable, weakly inferable, or strongly confounded categories.
• Constructed a reduced target by retaining separable variables and using composite descriptors for confounded ones.
• Defined a weighting matrix based on measurement-noise covariance to evaluate observability.

Main Results:

• The reduced target significantly improved the conditioning of the local Jacobian.
• Preserved projected inversion error compared to unreduced latent-state inversion.
• Outperformed principal component analysis baseline under tested noise conditions.

Conclusions:

• Recoverability-guided target construction is a viable proof-of-concept for acquisition-aware microwave inverse problems.
• This approach enhances the stability and accuracy of microwave breast imaging inversions.
• Further research is needed for clinical validation of microwave breast imaging.