4 papers
Regularization of the inverse Laplace transform by Mollification
Pierre Maréchal, Faouzi Triki, Walter C. Simo Tao Lee
In this paper we study the inverse Laplace transform. We first derive a new global logarithmic stability estimate that shows that the inversion is severely ill-posed. Then we propo…
Lagrange duality for the Morozov principle
Xavier Bonnefond, Pierre Maréchal
Considering a general linear ill-posed equation, we explore the duality arising from the requirement that the discrepancy should take a given value based on the estimation of the n…
Tomography by Fourier synthesis
Pierre Maréchal, Abdelhadi Elasmai
We consider a particular approach to the regularization of the inverse problem of computerized tomography. This approach is based on notions pertaining to Fourier synthesis. It ref…
A proximal approach to the inversion of ill-conditioned matrices
Pierre Maréchal, Aude Rondepierre
We propose a general proximal algorithm for the inversion of ill-conditioned matrices. This algorithm is based on a variational characterization of pseudo-inverses. We show that a…