Image Super-Resolution (single-image) L1-383

Signal ProcessingSpatial upsampling inverse problemδ=3 · standardL_DAG = 2.7📋 Stub — not mineable

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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.

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Forward model E

y = D_{s} \cdot (k_{a} a \cdot x) + n; D_{s} = s - f o l d s p a t ia l d ec ima t i o n, k_{a} a = an t i - a l ia s l o w - p a ss k er n e l

A high-resolution (HR) image x is anti-alias filtered, downsampled by an integer factor s, and corrupted by noise and (optionally) compression artifacts. Recovery is the inverse of this non-invertible degradation.

L-DAG

K.blur.shiftinvariant -> D.decimate.spatial -> int.spatial

K.blur.shiftinvariantD.decimate.spatialint.spatial

Well-posedness W

Existence:: true
Uniqueness:: false
Stability:: conditional
κ:: 5000

Inherently underdetermined (s^2:1 information loss); uniqueness restored only under image prior (sparse/natural-image manifold). Stability controlled by anti-alias kernel accuracy and noise level.

Solvability C

Solver class:: bicubic upsample (L+O), sparse-coding (Yang ScSR, L+O), learned (SRCNN, EDSR, RCAN, SwinIR, Real-ESRGAN)
Convergence rate q:: 2
Complexity:: O(sH * sW * C * log) for FFT-based reconstruction; learned single forward pass O(sH * sW * C * F) with F filters

Specs (0)

No L2 specs registered yet for this principle.