An Inverse Source Problem in Optical Molecular Imaging Plamen Stefanov and Gunther Uhlmann

Conference on Inverse Problems in Honor of Gunther Uhlmann

An Inverse Source Problem in Optical Molecular Imaging

We study the direct and an inverse source problem for the radiative transfer equation arising in optical molecular imaging. We show that for generic absorption and scattering coefficients, the direct problem is well-posed and the inverse one is uniquely solvable, with a stability estimate.

Linearizing Non-linear Inverse Problems and an Application to Inverse Backscattering

We propose an abstract approach to prove local uniqueness and conditional Hölder stability to non-linear inverse problems by linearization. The main condition is that, in addition to the injectivity of the linearization A, we need a stability estimate for A as well. That condition is satisfied in particular, if A∗A is an elliptic pseudo-differential operator. We apply this scheme to show unique...

On the Inverse Problem of Finding Cosmic Strings and Other Topological Defects

We consider how microlocal methods developed for tomographic problems can be used to detect singularities of the Lorentzian metric of the Universe using measurements of the Cosmic Microwave Background radiation. The physical model we study is mathematically rigorous but highly idealized.

An Efficient Neumann Series-Based Algorithm for Thermoacoustic and Photoacoustic Tomography with Variable Sound Speed

We present an efficient algorithm for reconstructing an unknown source in Thermoacoustic and Photoacoustic Tomography based on the recent advances in understanding the theoretical nature of the problem. We work with variable sound speeds that might be also discontinuous across some surface. The latter problem arises in brain imaging. The algorithmic development is based on an explicit formula i...