A pinboard by Souvik Roy

Postdoctoral fello, University of Wurzburg, Germany

Pinboard Summary

Theoretical and numerical aspects of inverse problems related to medical imaging and optimal control

My primary research area is on theoretical and numerical methods inversion of the circular, elliptic, broken-ray, spherical and conical Radon transform with centers on a circle or sphere (the data acquisition set). Such inversions are essential in various image reconstruction problems arising in medical imaging like ultrasound, single-scattering optical tomography, photoacoustic tomography and intravascular imaging. My aim is to derive analytical inversion formulae for reconstruction of a function from its Radon transform with partial radial data. Moreover, I also devise efficient computational algorithms to simulate the reconstruction procedure such that they are fast and robust even in presence of noisy data.

Another field of my research is the study of optimal control problems related to stochastic models in the frameworks of partial differential equations (Fokker-Planck, Liouville, piecewise deterministic processes). Such models arise in controlling crowd motion, transportation problems and differential games. My research is to build effective models, providing theoretical results of existence and uniqueness of optimal controls and devising higher order numerical algorithms to solve the optimality systems using non-smooth methods. In addition, I provide a comprehensive numerical analysis (higher order error estimates in L^2 and L^1 norms) for the underlying state equations which are either parabolic or hyperbolic scalar and systems.

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