Recovering source location, polarization, and shape of obstacle from elastic scattering data

Jointly determining the point sources and obstacle from Cauchy data

“…In this paper, we adopt Morozov's discrepancy principle to choose the regularization parameter α = α(δ) > 0. Once the regularized density φ α(δ),δ ℓ , ℓ = 1, 2 is determined by solving (14), the following regularized approximations on the scattered field v(x; S) and the incident field u i (x; S 2 ) can be obtained by inserting the solution φ α(δ),δ ℓ (y), ℓ = 1, 2 into the single-layer potential representation (7) and (8), respectively, i.e.…”

“…We are now concerned with a practical application where the autonomous observer sent into an unknown environment tries to efficiently determine the signal sources and the non-penetrable solid obstacles located along the observer's path. As an intrinsic couple of the inverse obstacle and inverse source problems, such co-inversion problems attract great interest and we refer to [6,7,12,18,19,21,26,27] for the relevant studies on simultaneous recovery of the multiple targets in the scattering problems. Compared with the inverse problem with a single target to be determined, the joint inversion problem inherits the ill-posedness and nonlinearity from the inverse obstacle problem.…”

Bayesian model error method for the passive inverse scattering problem

“…For example, in [5], the number and positions of incident sources as well as the approximate shape of the obstacle were first obtained by a two-step imaging method, and then, the optimization method was employed to simultaneously recover more refined details of the obstacle and its excitation sources. We refer to [6,28,29,41] for other interesting coinversion problems. Another effective way for the passive inverse scattering is to resort to the cross-correlations between two receivers [11], as only receivers can be employed directly.…”