Image Deblurring (non-blind and blind deconvolution) L1-382
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 latent sharp image x is degraded by a shift-invariant 2D convolution kernel k (motion blur, out-of-focus blur, atmospheric turbulence) and additive sensor noise. Recovery is either non-blind (kernel known) or blind (kernel jointly estimated with image).
L-DAG
Well-posedness W
- Existence:
- true
- Uniqueness:
- within OTF support
- Stability:
- conditional
- κ:
- 1000
Non-blind: deconvolution is ill-conditioned with kappa proportional to |OTF|^-1 at high frequencies; Tikhonov regularization bounds kappa_eff. Blind: bilinear in (k, x) and non-convex; only locally well-posed under sparse-gradient prior.
Solvability C
- Solver class:
- Wiener filter, Richardson-Lucy, TV-ADMM, plug-and-play (PnP-BM3D), learned (SRN-DeblurNet, MPRNet, NAFNet)
- Convergence rate q:
- 2
- Complexity:
- O(H*W*log(H*W)) per FFT iteration; blind MAP typically 10-100 iterations; learned methods single forward pass O(H*W*C)