A Learned-SVD Approach to the Electromagnetic Inverse Source Problem.

Area of Science:

• Computational physics
• Applied mathematics
• Artificial intelligence

Background:

• Ill-posed inverse problems are challenging in various scientific fields.
• Traditional regularization methods like Truncated SVD (TSVD) have limitations in reconstructing complex sources.
• Deep neural networks offer a novel approach to address these challenges.

Purpose of the Study:

• To propose and evaluate a novel artificial intelligence approach, learned singular value decomposition (L-SVD), for solving 2D scalar inverse source problems.
• To compare the reconstruction performance of L-SVD against the canonical Truncated SVD (TSVD) regularization scheme.
• To investigate the ability of L-SVD to retrieve faster spatial variations of the source and incorporate a priori information.

Main Methods:

• Developed a hybrid autoencoding deep neural network architecture for L-SVD.
• Implemented and compared L-SVD with TSVD for a canonical 2D scalar inverse source problem.
• Utilized numerical tests based on far-field acquisitions for performance evaluation.
• Analyzed the impact of training data on L-SVD performance.

Main Results:

• L-SVD demonstrated superior reconstruction performance compared to TSVD, indicated by lower reconstruction errors.
• L-SVD successfully retrieved faster spatial variations of the source, a limitation for TSVD.
• The L-SVD method effectively incorporates a priori information about unknown current distributions.
• Performance degradation of L-SVD was observed when the unknown source deviated from the training dataset.

Conclusions:

• Learned singular value decomposition (L-SVD) offers a powerful, non-linear alternative to linear methods like TSVD for inverse source problems.
• L-SVD's ability to leverage training data and a priori information enhances source reconstruction accuracy and detail.
• Careful dataset curation is crucial for optimal L-SVD performance, highlighting the importance of domain knowledge in AI model training.