Elastic Scatterer Reconstruction via the Regularized Sampling Method
نویسندگان
چکیده
A three-dimensional inverse problem dealing with the reconstruction of cavities in a uniform semi-infinite solid from surface elastodynamic waveforms is investigated via the linear sampling method. To cater for active imaging applications that are often characterized by a limited density of illuminating sources, the existing near-field formulation of the linear sampling method is advanced in terms of its adjoint statement that features integration over the receiver surface rather than its source counterpart. To deal with an ill-posedness of the integral equation that is used to reconstruct the obstacle, the problem is solved by alternative means of Tikhonov regularization and a preconditioned conjugate gradient method. Computational details of the imaging procedure, including evaluation of the featured integrals as well as the implementation of the regularization approach, are highlighted. An example dealing with the reconstruction of an ellipsoidal void from noise-polluted synthetic measurements is included to illustrate the effectiveness of the proposed methodology.
منابع مشابه
On an inverse elastic wave imaging scheme for nearly incompressible materials
This paper is devoted to the algorithmic development of inverse elastic scattering problems. We focus on reconstructing the locations and shapes of elastic scatterers with known dictionary data for the nearly incompressible materials. The scatterers include non-penetrable rigid obstacles and penetrable mediums, and we use time-harmonic elastic point signals as the incident input waves. The scat...
متن کاملGeneralized optical theorems for the reconstruction of Green's function of an inhomogeneous elastic medium.
This paper investigates the reconstruction of elastic Green's function from the cross-correlation of waves excited by random noise in the context of scattering theory. Using a general operator equation-the resolvent formula-Green's function reconstruction is established when the noise sources satisfy an equipartition condition. In an inhomogeneous medium, the operator formalism leads to general...
متن کاملInequalities in Inverse Scattering Theory ∗
Until recently, reconstruction algorithms for solving inverse electromagnetic scattering problems have been based on either nonlinear optimization techniques or on linearized models based on weak scattering approximations [6]. In the past ten years a third approach to reconstruction has been developed which comes under the rubric of qualitative methods in inverse scattering theory, the most pop...
متن کاملAn Optimal Convergence Rate for the Gaussian Regularized Shannon Sampling Series
In this article, we consider the reconstruction of a bandlimited function from its finite localized sample data. Truncating the classical Shannon sampling series results in an unsatisfactory convergence rate due to the slow decay of the sinc function. To overcome this drawback, a simple and highly effective method, called the Gaussian regularization of the Shannon series, was proposed in the en...
متن کاملOptimized Sampling Patterns for Random 3D Subsampling and Parallel Imaging Reconstruction by Regularized Nonlinear Inversion
A method is presented for scan time reduction in magnetic resonance imaging by combining an optimized random sampling pattern with a nonlinear reconstruction by iterative regularized Gauß-Newton. The sampling pattern is generated using a probability density function derived from the power spectrum of a reference image, which can be either taken from a pre-scan or a template. The proposed method...
متن کامل