# A novel sampling method for multiple multiscale targets from scattering amplitudes at a fixed frequency

@article{Liu2017ANS, title={A novel sampling method for multiple multiscale targets from scattering amplitudes at a fixed frequency}, author={Xiaodong Liu}, journal={Inverse Problems}, year={2017}, volume={33} }

A sampling method by using scattering amplitude is proposed for shape and location reconstruction in inverse acoustic scattering problems. Only matrix multiplication is involved in the computation, thus the novel sampling method is very easy and simple to implement. With the help of the factorization of the far field operator, we establish an inf-criterion for characterization of underlying scatterers. This result is then used to give a lower bound of the proposed indicator functional for…

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## References

SHOWING 1-10 OF 21 REFERENCES

### A Direct Sampling Method for Inverse Scattering Using Far-Field Data

- Mathematics
- 2012

This work is concerned with a direct sampling method (DSM) for inverse acoustic scattering problems using far-field data. The method characterizes some unknown obstacles, inhomogeneous media or…

### A study on orthogonality sampling

- Mathematics
- 2010

The goal of this paper is to study and further develop the orthogonality sampling or stationary waves algorithm for the detection of the location and shape of objects from the far field pattern of…

### Acoustic inverse scattering using topological derivative of far-field measurements-based L2 cost functionals

- Mathematics
- 2013

Originally formulated in the context of topology optimization, the concept of topological derivative has also proved effective as a qualitative inversion tool for a wave-based identification of…

### A direct sampling method to an inverse medium scattering problem

- Mathematics
- 2012

In this work we present a novel sampling method for time harmonic inverse medium scattering problems. It provides a simple tool to directly estimate the shape of the unknown scatterers (inhomogeneous…

### A Direct Imaging Method for Inverse Scattering Using the Generalized Foldy-Lax Formulation

- Mathematics, Physics
- 2014

Consider the scattering of a time-harmonic plane wave incident on a two-scale heterogeneous medium, which consists of scatterers that are much smaller than the wavelength and extended scatterers that…

### Stability estimates and reconstructions in inverse acoustic scattering using singular sources

- Mathematics
- 2000

### A simple method for solving inverse scattering problems in the resonance region

- Mathematics
- 1996

This paper is concerned with the development of an inversion scheme for two-dimensional inverse scattering problems in the resonance region which does not use nonlinear optimization methods and is…

### Characterization of the shape of a scattering obstacle using the spectral data of the far field operator

- Mathematics
- 1998

This paper is concerned with the inverse obstacle scattering problem for time harmonic plane waves. We derive a factorization of the far field operator F in the form and prove that the ranges of and…

### Inverse scattering by an inhomogeneous penetrable obstacle in a piecewise homogeneous medium

- Mathematics
- 2009

### Recent progress on the factorization method for inverse acoustic scattering problems

- Mathematics
- 2015

In this paper, we review recent progress on the factorization method for inverse acoustic scattering problems. Included are the classical factorization method for penetrable scatterers and…