It is 2004, and the Nyquist–Shannon doctrine has hardened into common sense: to recover a signal you must sample at twice its bandwidth, full stop. But the signals that matter — medical images, spectra, photographs — are sparse in the right basis, and sparsity is information the classical count ignores. Recover a sparse signal from far fewer linear measurements than dimensions, with a proof, not a prayer: conditions on the measurement matrix under which convex relaxation provably finds the exact sparse solution, with high probability, from random measurements. The application waiting on the theorem is not abstract: MRI scan time scales with measurement count, and a child who must hold still — or be anesthetized — is the unit in which this theorem's success is measured.
Chose Adaptive querying — wrong. Sparse recovery was the one that fit.
Nowak's research directly sits at the intersection this problem describes — 'signals meet machine learning' — with substantial published work on sparse recovery, active sensing, and the statistical theory of reconstructing structured signals from limited measurements, placing him in close proximity to the compressed-sensing research program this problem is built around. His active-learning and sparse-recovery toolkit engages the same underdetermined-measurement regime and structural assumptions (sparsity) that make provable exact recovery possible, even though he is not the originator of the restricted-isometry-property proof itself. He is one of the stronger non-founder carriers in this pool given his direct research proximity.
Erdos's probabilistic method — proving existence by showing random constructions succeed with positive probability — is structurally close kin to how the restricted isometry property is proven for random measurement matrices in compressed sensing, giving him genuine, if indirect, methodological relevance. But he had no engagement with harmonic analysis, sparse-signal recovery, or convex optimization specifically, and died in 1996 before this problem's 2004 setting and the compressed-sensing breakthrough it describes. His contribution would be foundational-methodological — the probabilistic-existence-proof technique later researchers used — rather than the applied signal-processing theorem itself.
Battle #31 · 8/9/2026, 6:21:24 PM · this result is deterministic: the same two personas on this problem always resolve the same way.