ABSTRACT
This chapter shows that the type of approach can be generalized to inverse problems with piecewise constant solutions. It summarizes some results about stochastic calculus and the level-set regularization of inverse problems. The stochastic level-set approach is applied to the binary tomography and to the phase contrast tomography inverse problem. The chapter presents the level-set regularization approach of inverse problems and some aspects of stochastic calculus and the level-set regularization approach of inverse problems. It explains the difference between the Ito and Stratonovich stochastic integrals and the deterministic level-set algorithm with the modified algorithms with the stochastic evolution. The tomographic reconstruction from few projections is a very ill-posed problem with many applications in medical imaging or material science. X-ray in-line phase contrast tomography is a very sensitive technique for soft tissues within dense materials. Stochastic level-set evolution the deterministic optimization of the level-set function is often stopped in local minima.
