On the local minima in a tomographic imaging technique

The Contrast Source-Extended Born Model for 2d Subsurface Scattering Problems

“…(13), wherein E s represents the measured and thus noise affected scattered field data and the modified contrast ξ embeds the electromagnetic characteristic of the unknown scatterers. Then, from the formal analogy with the traditional model, it follows that it is possible to directly exploit all usual solution schemes, such as for instance the modified gradient approach [16,20], the distorted [5] or the quadratic [13] ones.…”

“…As matter of fact, the optimization task cannot be tackled through global approaches, whose computational cost is not affordable due to the large number of unknown parameters, and local optimization methods are usually exploited. However, due to the nonlinear relationship amongst the data and the unknowns, these latter may lead to "false" solutions deeply different from the ground truth [16], so that it is necessary to understand how to reduce the occurrence of these false solutions (for instance by means of suitable a priori information or proper regularization).…”

RF breast cancer detection employing a noncharacterized vivaldi antenna and a MUSIC-inspired algorithm

“…Those imaging solutions also suffer from reliability problems due to the occurrence of false solutions. This is a common consequence of deterministic minimization algorithms [5].…”

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.…”