Coherent Diffraction Imaging (CDI) — lensless phase retrieval L1-072

Coherent ImagingSingle-shot lensless diffractionδ=5 · challengingL_DAG = 3.5📋 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

I (k) = ∣ F O (r) ∣^{2} + n (k), O (r) s u pp or t e d o n S s u b se tO m e g a

A coherent beam illuminates an isolated object in free space; the far-field detector records the squared magnitude of its Fourier transform. Image recovery is the phase-retrieval problem: given only |F{O}|, recover O using a finite-support constraint (oversampling sigma >= 2 per dim) and non-negativity / atomicity priors.

L-DAG

B.support -> F.fourier -> L.modulus_squared -> int.spatial

B.supportF.fourierL.modulus_squaredint.spatial

Well-posedness W

Existence:: true
Uniqueness:: true
Stability:: conditional
κ:: 10000

Strongly non-convex phaseless recovery. Hayes ambiguity (global phase, conjugate flip, sub-pixel translation) resolved by support compactness. Oversampling sigma >= 2 in each dimension is necessary; beam-stop inpainting and partial coherence further degrade conditioning.

Solvability C

Solver class:: projection iterations (HIO, ER, RAAR, CF), Shrinkwrap, ADMM-CDI, Wirtinger-flow, learned (PRCGAN, CDI-Net)
Convergence rate q:: 1.2
Complexity:: O(H * W * log(H*W)) per iteration

Specs (0)

No L2 specs registered yet for this principle.