Fig. 2: Representative results with semantic regularization for prototypical EM inverse scattering problems.

a Considered configuration of an ill-posed 2D EM inverse scattering problem. b Illustration of two-step solution to the inverse scattering problem in the framework of the proposed method showing the measurements, the two embeddings obtained with the encoder (of which \({{{{{{\boldsymbol{\alpha }}}}}}}_{0}\) is the semantic embedding), and the reconstructed permittivity distributions obtained from the embeddings with the decoder. c T-SNE visualization of different \(\Delta {{{{{\boldsymbol{\alpha }}}}}}\) for a fixed semantic prior. The red star indicates \(\Delta {{{{{\boldsymbol{\alpha }}}}}}=0\). The insets show example reconstructions with different \(\Delta {{{{{\boldsymbol{\alpha }}}}}}\) for a few selected semantic priors. d Illustration of the ability to manipulate the reconstruction with the semantic embedding in order to conceal or change a vulnerable object. The ground-truth semantic priors for the ground truth DoIs shown in the first row are: “high-contrast digit-3 and middle-contrast cycle”, “low-contrast digit-0 and low-contrast triangle”, “low-contrast digit-9 and high-contrast triangle”, “high-contrast digit-3 and middle-contrast square”. The second row shows the reconstructions obtained with these semantic priors, i.e., without any protection. To partially conceal the DoI in the reconstruction, the following phrases are integrated into the modified semantic priors in the third row: “conceal digit”, “conceal digit”, “conceal digit”, “conceal shape”. To alter the appearance of an object, the following phrases are integrated into the modified semantic priors in the fourth row: “change the digit as middle-contrast digit-3”, “change the digit as low-contrast digit-8”, “change the digit as low-contrast digit-3 and change the shape as middle-contrast triangle”, “change the digit as middle-contrast digit-2 and change the shape as low-contrast square”. Details about the MSE evaluation can be found in Supplementary Note 13.