A two-step iterative inexact-Newton method for electromagnetic imaging of dielectric structures from real data

Non-Invasive Microwave Characterization of Dielectric Scatterers

“…Consequently, a regularized inversion algorithm must be used (Autieri, Ferraiuolo, & Pascazio, 2011;Lobel, Blanc-Féraud, Pichot, & Barlaud, 1997). The solving procedure is based on a two-step iterative strategy (Bozza et al, 2006;Estatico et al, 2005), in which an outer linearization is performed by means of an Inexact-Newton scheme and a regularized solution to the obtained linear system is calculated by means of a truncated Landweber algorithm (Landweber, 1951).…”

“…The result of the discretization is a (nonlinear) system of equations to be solved, usually very ill-conditioned. In order to solve, in a regularized sense, the inverse scattering problem in the discrete setting, an iterative algorithm based on an inexact-Newton method is applied (Bozza, Estatico, Pastorino, & Randazzo, 2006;Estatico, Bozza, Massa, Pastorino, & Randazzo, 2005).…”

Sparse Electromagnetic Imaging Using Nonlinear Landweber Iterations

“…For low values of permittivity, first-order linearization methods, such as the first-order Born and Rytov approximations, provide a convergent and satisfactorily accurate solution [15]. Even though higher-order schemes, such as the extended-Born [16] and second-order Born approximations [17] and the Born iterative method [18][19][20], are applicable for higher values of permittivity when compared to the first-order linearization methods, they still fail to produce convergent solutions for many practical engineering applications where investigation domains involve "strong" scatterers with high values of is the dielectric contrast defined as τ (r) = ε(r)/ε 0 − 1, r ∈ S 0, else .…”

Microwave Imaging Within the Interval Analysis Framework

“…In order to avoid nonuniqueness and instability as well as to prevent the retrieval of false solutions [28], several inversion strategies have been proposed based on (a) a suitable definition of the integral equations either in exact [29,30] or approximated [31][32][33][34][35] forms to model the scattering phenomena, (b) the exploitation of the available a-priori information on some features of the scenario/scatterers under test [15,[36][37][38][39] or/and the knowledge of input-output samples of data and reference solutions [40][41][42] and/or the information acquired during the inversion process [43][44][45][46][47], and (c) the use of suitable global optimization strategies [48][49][50][51][52][53][54][55]. Whatever the approach, inversion methods generally consider an optimization step aimed at minimizing/maximizing a suitably defined data-mismatch cost function through gradient or evolutionarybased algorithms with still not fully resolved drawbacks.…”