Nuclear disarmament verification faces a paradox: inspectors must confirm that an object is a warhead without learning anything about its design. The warhead's internal structure is classified, but its identity as a weapon must be authenticated. The measurement must reveal enough to verify and nothing more.
The single pixel X-ray transform addresses this by measuring only the total intensity of X-rays transmitted through an object, integrated over the entire detector — one number per projection angle, rather than a spatially resolved image. From these aggregate measurements, the goal is to reconstruct enough of the object's structure to authenticate it while provably preventing detailed design recovery.
The transform is nonlinear, continuous, Fréchet-differentiable, and convex. These mathematical properties are not curiosities — they determine what reconstruction is possible. Convexity ensures that optimization algorithms find the global minimum rather than getting trapped. Fréchet differentiability enables gradient-based methods. Continuity ensures stability: small measurement errors produce small reconstruction errors rather than catastrophic artifacts.
The reconstruction pipeline uses Douglas-Rachford splitting with total variation denoising, operating on rotationally symmetric objects to reduce the problem to one dimension. The total variation prior preserves edges — the sharp boundaries between different materials in a warhead — without requiring knowledge of what those materials are.
The approach embodies a designed information asymmetry. The measurement apparatus is deliberately coarse (one pixel instead of thousands), and the mathematical framework is chosen to ensure that coarseness is not a deficiency but a feature. Less data is not less useful when the goal is authentication rather than imaging.