Nonlinear Correction of the Direct Inverse Problem Solution in Real-Time Imaging

This paper proposes a direct method for quantitative real-time imaging based on a nonlinear correction of the approximate linearized imaging kernel. The correction process relies on a pseudo-Rytov approximation employing the ratio between the total and incident fields in the scattering model, which can be estimated analytically. Unlike traditional iterative algorithms, there is no need for multiple computations of the direct scattering model, gaining computational speed and robustness to numerical inaccuracies. The procedure consists of two steps. First, a fast direct inversion algorithm based on the Born approximation provides the initial guess for the permittivity distribution; this study employs the Truncated Singular Value Decomposition (TSVD) and an in-house finite element-based solver to compute the imaging operator. Second, the field correction factor is transferred onto the object's permittivity to enhance its quantitative accuracy. The proposal viability is verified in 2D synthetic experiments at microwave frequencies, verifying improvements in the reconstructed unknown permittivity.