A regularized iterative algorithm for limited-angle inverse Radon transform

The tomography problem is investigated when the available projections are restricted to a limited angular domain. It is shown that a previous algorithm proposed for extrapolating the data to the missing cone in Fourier space is unstable in the presence of noise because of the ill-posedness of the problem. A regularized algorithm is proposed, which converges to stable solutions. The efficiency of both algorithms is tested by means of numerical simulations. © 1983 Taylor and Francis Group, LLC.

A new proposition on the martingale representation theorem and on the approximate hedging of contingent claim in mean-variance criterion

In this work we revisit the problem of the hedging of contingent claim using mean-square criterion. We prove that in incomplete market, some probability measure can be identified so that becomes -martingale under .This is in fact a new proposition on the martingale representation theorem. The new results also identify a weight function that serves to be an approximation to the Radon-Nikodým derivative of the unique neutral martingale measure.