In many applications, the discretization of continuous ill-posed inverse problems results in discrete ill-posed problems whose solution requires the use of regularization strategies. The L-curve criterium is a popular tool for choosing good regularized solutions, when the data noise norm is not a priori known. In this work, we propose replacing the original ill-posed inverse problem with a nois...

Akaike's Bayesian information criterion (ABIC) has been widely used in geophysical inversion and beyond. However, little done to investigate its statistical aspects. We present an alternative derivation of the marginal distribution measurements, whose maximization directly leads invention ABIC by Akaike. show that is statistically estimate variance measurements prior maximizing measurements. Th...

Many inverse problems are concerned with the estimation of non-negative parameter functions. In this paper, in order to obtain stable approximate solutions ill-posed linear operator equations a Hilbert space setting, we develop two novel non-negativity preserving iterative regularization methods. They based on fixed point iterations combination preconditioning ideas. contrast projected Landwebe...

Based on minimizing a piecewise diierentiable lp function subject to a single inequality constraint, this paper discusses algorithms for a discretized regularization problem for ill-posed inverse problems. We examine computational challenges of solving this regularization problem. Possible minimization algorithms such as the steepest descent method, iteratively weighted least squares (IRLS) met...