A 70-year-old mystery about how to 'see' inside objects with a single wave source has finally been solved.
March 31, 2026
Original Paper
Global Convergence and Uniqueness for an Inverse Problem Posed by Gelfand
arXiv · 2603.27729
The Takeaway
In 1954, legendary mathematician I.M. Gelfand asked if it was possible to perfectly reconstruct an object's hidden interior using just one point of origin for waves. A new computational method finally provides a guaranteed solution, which could lead to far more accurate medical scans and geological surveys than current technology allows.
From the abstract
The first globally convergent numerical method is developed for a coefficient inverse problem (CIP) for the $n-$d, $n\geq 2$ wave equation with the unknown potential in the most challenging case when the $\delta -$ function is present in the initial condition with a single location of the point source. In fact, an approximate mathematical model for that CIP is derived. That globally convergent numerical method is developed for this model. This is a new version of the so-called convexification nu