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.

Abstract. A new parameter choice method for Tikhonov regularization of discrete ill-posed problems is presented. Some of the regularized solutions of a discrete ill-posed problem are less sensitive than others to the perturbations in the right-hand side vector. This method chooses one of the insensitive regularized solutions using a certain criterion. Numerical experiments show that the new met...

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 ...

We consider an operator equation) (, A R f f Au ∈ = , (1) where is the linear continuous operator between real Hilbert spaces H and F. In general our problem is ill-posed: the range R(A) may be non-closed, the kernel N(A) may be non-trivial. We suppose that instead of exact right-hand side f we have only an approximation) , (F H L A ∈ F f ∈ δ , δ δ ≤ − f f. To get regularized solution of the eq...

We are concerned with the numerical solution of linear parameter identification problems for parabolic PDE, written as an operator equation Ku = f . The target object u is assumed to have a sparse expansion with respect to a wavelet system Ψ = {ψλ} in space-time. For the recovery of the unknown coefficient array, we use Tikhonov regularization with `p coefficient penalties and the associated it...

We propose in this paper an effective meshless and integration-free method for the numerical solution of multidimensional inverse heat conduction problems. Due to the use of fundamental solutions as basis functions, the method leads to a global approximation scheme in both the spatial and time domains. To tackle the ill-conditioning problem of the resultant linear system of equations, we apply ...

In magnetic resonance electrical impedance tomography (MREIT), currents are applied to an object, the resulting magnetic flux density measured using MRI and the conductivity distribution reconstructed using these MRI data. In this study, we assess the ability of MREIT to monitor changes in the conductivity distribution of an agarose gel phantom, using injected current pulses of 900 μA. The phan...

This paper is concerned with acoustical engineering and mathematical physics problem for the near-field acoustical holography based on equivalent source method (ESM-based NAH). An important mathematical physics problem in ESM-based NAH is to solve the equivalent source strength, which has multiple solving algorithms, such as Tikhonov regularization ESM (TRESM), iterative weighted ESM (IWESM) an...