Image Denoising (Gaussian, Poisson, mixed) L1-385
Unclaimed Principle — open for contribution
This Principle is declared in the catalog but has no reference solver, no pinned dataset, and is not registered on-chain. There is no reward pool. Submitting a cert against this Principle today will record the cert for reproducibility but pay zero PWM.
To claim it as a Bounty #7 contribution: open a PR adding (1) a reference solver, (2) ≥1 dataset pinned to IPFS, (3) updates to the L3 manifest with dataset CIDs. After verifier-agent triple-review, the founders' 3-of-5 multisig signs PWMRegistry.register() and the Principle becomes mineable.
Forward model E
A clean image x is corrupted by pixelwise noise n(r) whose distribution depends on the capture mode (Gaussian for low-light DSLR, Poisson for photon-shot-noise limited, Rician for MRI, Speckle for SAR/ultrasound).
L-DAG
Well-posedness W
- Existence:
- true
- Uniqueness:
- false
- Stability:
- stable
- κ:
- 1
Identity operator with additive noise — trivially well-posed in forward sense; inverse relies on prior (TV, non-local, learned). Mismatch primarily in noise-model specification.
Solvability C
- Solver class:
- TV (ROF), BM3D, NLM, Wiener, DnCNN, N2N, Noise2Void, Restormer, SwinIR
- Convergence rate q:
- 2
- Complexity:
- O(H*W*C) per iteration for local filters; O(H*W*C*P^2) for NLM patch-match; learned single forward