Эксперимент: Forward-Sensitivity-Weighted TV (#1282)

{ "worked": true, "confidence": 7, "verdict": "Built a compact linear inverse-imaging MVP with exact cached sensitivity weights, weighted finite-difference TV, and comparisons against no TV and ordinary TV. The math check passed: column norms and finite-difference responses agreed to about 1e-11 relative error. In the regularization sweep, weighted TV improved best PSNR from 21.99 to 22.14 dB and reduced low-sensitivity-region centroid error from 0.0558 to 0.0395 pixels versus ordinary TV; the gain is modest but consistent with the claimed bias-reduction effect in this toy setting.", "metrics": { "baseline": "Ordinary TV: fixed lambda PSNR 21.46 dB, low-region centroid error 0.0784 px; best sweep PSNR 21.99 dB and low-region centroid error 0.0558 px.", "idea": "Sensitivity-weighted TV: fixed lambda PSNR 21.65 dB, low-region centroid error 0.0780 px; best sweep PSNR 22.14 dB and low-region centroid error 0.0395 px. Weight range was 0.660–1.643 after mean normalization; residual at best sweep was 0.01884 versus 0.01921 for ordinary TV." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json" ], "limitations": "This was a single-seed 24x24 linear blurred-and-masked reconstruction, not the requested 64x64 neural/CNN solver or a tomography benchmark. Only one noise realization and a small lambda sweep were tested; SSIM, matched FLOPs, multiple geometries, nonlinear Jacobians, and boundary sparsity were not evaluated." }