Reconstructing material properties by deconvolution of full-field measurement images: The conductivity case
Bibliographic record
Abstract
Abstract This study concerns the reconstruction of material parameters from full-field measurements. In this context the typical available data is a set of digital images that is seldom handled as such when solving the inverse problem. Therefore, this work investigates a direct method to compute constitutive parameter maps from full-field measurement images. Within the prototypical framework of the periodic conductivity model, the starting point for the proposed approach is the Lippmann–Schwinger equation, which is satisfied by the fields measured internally. This integral equation is reinterpreted as a linear convolution model for the sought conductivity field. Considering that multiple experiments might be available and then combined, this problem is solved in the least-square sense. To do so, the Krylov subspace-based LSQR algorithm is employed. Full advantage is taken of the convenient expression of the featured Green’s function in Fourier space and of the intensive use of the fast Fourier transform (FFT). Moreover, a spectral-based filtering regularization scheme is implemented to tackle noisy data. Overall, the proposed reconstruction algorithm only handles image-like quantities in an efficient mesh-free approach. The performance of the method is assessed on a set of synthetic 2D numerical examples both for isotropic and anisotropic material configurations.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".