Art Laboratory: Two Inverse Problems in Conservation Science

We apply a single inverse-problem framework to two problems in conservation science: the reconstruction of a Stradivari violin's thickness profile from its acoustic spectrum, and the detection of a hidden varnish layer in a painting from its XRF spectrum. The two cases yield opposite results. In the Stradivari case, no regularization scheme recovers the true profile from 20 modes: the inverse problem is structurally underdetermined, and the reconstruction is a homometric twin image. In the painting case, a model that ignores the varnish leaves a systematically structured residual, while a model that includes it does not; cross-validation of the two models detects the hidden layer even though the XRF measurement is depth-integrated. We conclude that the operator's failure is itself a diagnostic: it tells us whether the limit lies in the data (Stradivari) or in the model (painting). The Murphy Principle—cleanliness is not truth—holds in both cases.