Inverse problem for a random potential

On recent progress of single-realization recoveries of random Schrödinger systems

“…This type of inverse problems also arises in the deterministic magnetic anomaly detections using geomagnetic monitoring [11,12] with passive measurements. While [11,12,17,26] focus on deterministic setting with passive measurements, the works [2,6,7,[18][19][20]27,33] pay attention to random settings. We are particularly interested in the case with a single realization of the random sample.…”

“…The single-realization recovery has been studied in the literature. In this paper we mainly focus on [8,[18][19][20][21][22][23][24][25].…”

“…In our study, both the source f and the potential q are assumed to be compactly supported. We shall treat [8,[18][19][20][21][22][23][24][25] in more details. In [8,18,19], q is assumed to be a migr field while f is either zero or point a point source, i.e.…”

“…In [18,19] the authors considered the inverse scattering problem for the twodimensional random Schrödinger system (−…”

“…We note that the near-field data are used in [18,19], while in [8], the authors used the far-field data.…”