The Extended Adjoint State and Nonlinearity in Correlation-Based Passive Imaging
Abstract
Abstract. This articles investigates the physics-based passive imaging problem, wherein one infers an unknown medium using ambient noise and correlation of the noise signal. We develop a general backpropagation framework via the so-called extended adjoint state, suitable for any elliptic PDE; crucially, this approach reduces by half the number of required PDE solves. Applications to several different PDE models demonstrate the universality of our method. In addition, we analyze the nonlinearity of the correlated model, revealing a surprising tangential cone condition-like structure, thereby advancing the state of the art towards a convergence guarantee for regularized reconstruction in passive imaging.
Fields of Study & Subjects
Quantum optics and atomic interactions
Random lasers and scattering media
Atomic and Subatomic Physics Research
Publication details
- Journal / source
- SIAM Journal on Applied Mathematics
- Volume
- 86
- Issue
- 3
- Pages
- 1076–1102
- Publication date
- 5 June 2026
- Language
- EN