Globally strictly convex cost functional for a 1-D inverse medium scattering problem with experimental data

Abstract

A new numerical method is proposed for a 1-D inverse medium scattering problem with multi-frequency data. This method is based on the construction of a weighted cost functional. The weight is a Carleman Weight Function (CWF). In other words, this is the function, which is present in the Carleman estimate for the undelying differential operator. The presence of the CWF makes this functional strictly convex on any a priori chosen ball with the center at $\left\{0\right\}$ in an appropriate Hilbert space. Convergence of the gradient minimization method to the exact solution starting from any point of that ball is proven. Computational results for both computationally simulated and experimental data show a good accuracy of this method.

References in corpus (3)

• Numerical Solution of a Coefficient Inverse Problem with Multi-Frequency Experimental Raw Data by a Globally Convergent Algorithm
• A globally convergent numerical method for a 1-d inverse medium problem with experimental data
• Convergent algorithm based on Carleman estimates for the recovery of a potential in the wave equation