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Abstract: In this paper, we will present a generalization for a minimization problem from I. Daubechies, M. Defrise, and C. DeMol (2004) . This generalization is useful for solving many practical problems in which more than one constraint are involved. In this regard, we will conclude the findings of many papers (most of which are on image processing) from this generalization. It is hoped that the approach proposed in this paper will be a suitable reference for some applied works where multi-frames, multi-wavelets, or multi-constraints are present in linear inverse problems. [Copyright &y& Elsevier]

The impact of this paper is twofold. First, we study convergence rates of the iteratively regularized Gauss-Newton (IRGN) algorithm with a linear penalty term under a generalized source assumption and show how the regularizing properties of new iterations depend on the solution smoothness. Secondly, we introduce an adaptive IRGN procedure, which is investigated under a relaxed smoothness condition. The introduction and analysis of a more general penalty term are of great importance since, apart from bringing stability to the numerical scheme designed for solving a large class of applied inverse problems, it allows us to incorporate various types of a priori information available on the model. Both a priori and a posteriori stopping rules are investigated. For the a priori stopping rule, optimal convergence rates are derived. A numerical example illustrating convergence rates is considered [ABSTRACT FROM AUTHOR]

This paper presents a method for identifying the general-order poles of a meromorphic function algebraically from its values on the unit circle, which has various applications in inverse source problems in potential analysis. First, we derive a system of Dth-degree equations for N distinct poles zn of order Dn, where n = 1, 2, . . . ,N and D = max1≤n≤N{Dn}. Then, we transform these equations into linear equations for the coefficients of the Nth-degree equation whose roots are zn so that the poles are obtained algebraically from data. The obtained poles can be used as an initial solution for iterative algorithms. A method for estimating the order Dn of each pole is also proposed and is numerically verified. [ABSTRACT FROM AUTHOR]