In this paper, we explore a robust method for calibration of the local volatility surface for European options. Assuming the the volatility surface is smooth, we apply a second order Tikhonov regularization to the calibration problem. Additionally we propose a new approach for choosing the Tikhonov regularization parameter. Using the TAPENADE automatic differentiation tool in order to obtain ad...

In this paper we investigate the stability and convergence rates of the widely used output least-squares method with Tikhonov regularization for the identification of the conductivity distribution in a heat conduction system. Due to the rather restrictive source conditions and regularity assumptions on the nonlinear parameter-to-solution operator concerned, the existing Tikhonov regularization ...

In this paper we investigate stability and convergence rates of the Tikhonov regularization method for the identiication of the diiusion parameter in a multi{dimensional parabolic equation. By choosing a problem{adapted approach, we obtain much better results than by applying the general theory of Tikhonov regularization of nonlinear inverse problems.

Two numerical methods for the restoration of noisy images from the Hubble Space Telescope are presented. The first one stems from a B-spline expansion followed by the Tikhonov regularization method. The second one is based on a coarse smoothing coupled with the Tikhonov regularization. The effectiveness of these methods is illustrated by the restoration of some images already proposed in the li...

Compton scatter tomography is an emerging technique with attractive applications in several fields imaging such as non-destructive testing and medical scanning. In this paper, we introduce a novel modality three dimensions fixed source single detector that moves on spherical surface. We also study the Radon transform modeling data consists integrals toric surfaces. Using harmonics arrive to gen...

In this paper we consider the a posteriori parameter choice strategy proposed by Scherzer et al in 1993 for the Tikhonov regularization of nonlinear ill-posed problems and obtain some results on the convergence and convergence rate of Tikhonov regularized solutions under suitable assumptions. Finally we present some illustrative examples.

The present paper is concerned with developing tensor iterative Krylov subspace methods to solve large multi-linear equations. We use the T-product for two tensors define tubal global Arnoldi and Golub-Kahan bidiagonalization algorithms. Furthermore, we illustrate how tensor-based approaches can be exploited ill-posed problems arising from recovering blurry multichannel (color) images videos, u...

This article presents a direct application of a Tikhonov inversion with a quadratic constraint applied in the case of a corrosion diagnosis. The main originality of this method is to inject physical information during the inversion to automatically restrict the Tikhonov parameter space. This application is then tested on a real case of corrosion diagnosis from electrical measurements in the water.