Magnetic tomography is an ill-posed and ill-conditioned inverse problem since, in general, the solution is non-unique and the measured magnetic field is affected by high noise. We use a joint sparsity constraint to regularize the magnetic inverse problem. This leads to a minimization problem whose solution can be approximated by an iterative thresholded Landweber algorithm. The algorithm is pro...

We consider a new idea for solving Tikhonov regularized discretized ill-posed problems. The optimization problem is formulated as a nonlinear least squares problems containing the Tikhonov regularization parameter λ. In order to find the size of the regularization parameter and attain good convergence in the optimization method we use the nonlinear Land a-curve. The nonlinear L-curve is a direc...

This paper introduces new methods of identification and estimation the first-price sealed bid auction model compares them with previous existing ones. The first method allows us to estimate directly (through an iterative algorithm) cumulative distribution function private values without estimating beforehand. In second method, we use a quantile approach. Although is complex nonlinear inverse pr...

Parameter identification problems for partial differential equations usually lead to nonlinear inverse problems. A typical property of such problems is their instability, which requires regularization techniques, like, e.g., Tikhonov regularization. The main focus of this paper will be on efficient methods for determining a suitable regularization parameter by using adaptive finite element disc...

Usually when determining parameters with an inverse method, it is assumed that parameters or properties, other than those being sought, are known exactly. When such known parameters are uncertain, the inverse solution can be very sensitive to the degree of uncertainty. The stochastic regularization method can be modi ed to reduce this sensitivity. This paper presents such a modi cation. In addi...

In this paper, we consider large-scale linear discrete ill-posed problems where the right-hand side contains noise. Regularization techniques such as Tikhonov regularization are needed to control the effect of the noise on the solution. In many applications such as in image restoration the coefficient matrix is given as a Kronecker product of two matrices and then Tikhonov regularization proble...

In this article, a matching pursuit algorithm is developed to improve the performance of a passive multiplexing technique based on compressed sensing. This deconvolution technique is applied to RADAR imaging in the microwave range, starting from previous studies based on a compact coding device and L1-norm regularizations. This study demonstrates that in this context, the quality of the reconst...

In this paper we consider the regularization of the inverse problem of diffuse optical tomography by standard regularization methods with quadratic penalty terms. We therefore investigate in detail the properties of the associated forward operators, and derive continuity and differentiability results, which are based on derivation of W 1,p regularity results for the governing elliptic boundary ...

the determination of an unknown boundary condition, in a nonlinaer inverse diffusion problem is considered. for solving these ill-posed inverse problems, galerkin method based on sinc basis functions for space and time will be used. to solve the system of linear equation, a noise is imposed and tikhonove regularization is applied. by using a sensor located at a point in the domain of $x$, say $...