Single-Pixel Imaging (random basis compressive sensing) L1-026
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 single photodetector integrates scene radiance weighted by a sequence of m modulating patterns (Bernoulli, Gaussian, or structured bases); each pattern yields one scalar measurement. The m scalars form the compressed measurement vector.
L-DAG
Well-posedness W
- Existence:
- true
- Uniqueness:
- true
- Stability:
- conditional
- κ:
- 4000
Underdetermined (m << n) compressive recovery; random sensing matrices with i.i.d. Bernoulli/Gaussian entries satisfy RIP w.h.p. when m >= C * s * log(n/s) for s-sparse signals in a known basis.
Solvability C
- Solver class:
- L1-proximal (FISTA, ISTA, SPGL1), TV (GAP-TV), learned (LISTA, ISTA-Net)
- Convergence rate q:
- 2
- Complexity:
- O(m * n) per iteration (dense Phi); O(n * log n) for structured Phi (Hadamard, noiselet)