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. 2024 Jul 11;24(14):4496.
doi: 10.3390/s24144496.

A Learned-SVD Approach to the Electromagnetic Inverse Source Problem

Amedeo Capozzoli  1 , Ilaria Catapano  2 , Eliana Cinotti  1   2 , Claudio Curcio  1 , Giuseppe Esposito  2 , Gianluca Gennarelli  2 , Angelo Liseno  1 , Giovanni Ludeno  2 , Francesco Soldovieri  2
Affiliations

A Learned-SVD Approach to the Electromagnetic Inverse Source Problem

Amedeo Capozzoli et al. Sensors (Basel). .

Abstract

We propose an artificial intelligence approach based on deep neural networks to tackle a canonical 2D scalar inverse source problem. The learned singular value decomposition (L-SVD) based on hybrid autoencoding is considered. We compare the reconstruction performance of L-SVD to the Truncated SVD (TSVD) regularized inversion, which is a canonical regularization scheme, to solve an ill-posed linear inverse problem. Numerical tests referring to far-field acquisitions show that L-SVD provides, with proper training on a well-organized dataset, superior performance in terms of reconstruction errors as compared to TSVD, allowing for the retrieval of faster spatial variations of the source. Indeed, L-SVD accommodates a priori information on the set of relevant unknown current distributions. Different from TSVD, which performs linear processing on a linear problem, L-SVD operates non-linearly on the data. A numerical analysis also underlines how the performance of the L-SVD degrades when the unknown source does not match the training dataset.

Keywords: autoencoder; deep neural networks; inverse source; learned singular value decomposition; singular value decomposition.

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Conflict of interest statement

The authors declare no conflicts of interest.

Figures

Figure 1
Figure 1
Geometry of the inverse source problem.
Figure 2
Figure 2
The L-SVD reconstruction approach and its parallelism with SVD.
Figure 3
Figure 3
Representation of the L-SVD reconstruction strategy. The upper horizontal path refers to dAE, which takes noisy data in the input and provides denoised data as the output. The lower horizontal path represents the sAE, which reconstructs the ground truth from the originating source. The green path refers to the reconstruction path via the Σ network connecting the data and source latent spaces.
Figure 4
Figure 4
Normalized singular values (dB) of the operator matrix A__.
Figure 5
Figure 5
MLP architecture of the dAE.
Figure 6
Figure 6
MLP architecture of the sAE.
Figure 7
Figure 7
MLP architecture of the Σ network.
Figure 8
Figure 8
Two representative examples randomly selected in the test dataset, with SNR = 30 dB, showing the magnitude of inputs, outputs, and ground truth data for dAE.
Figure 9
Figure 9
Two representative examples randomly selected in the test dataset, with SNR = 30 dB, showing the magnitude of the true source (input) and the one reconstructed via sAE (output). The current sources shown in the graphs are the ones generating the radiated fields in Figure 8.
Figure 10
Figure 10
Two representative examples randomly selected in the test dataset, with SNR = 30 dB, showing the amplitude of the true source and those retrieved via TSVD and L-SVD. The true sources in the graphs are those previously shown in the examples of Figure 9.
Figure 11
Figure 11
Illustrating the missing additivity property of linearity for L-SVD.
Figure 12
Figure 12
Illustrating the missing homogeneity property of linearity for L-SVD.
See this image and copyright information in PMC

References

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